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## Über dieses Buch

This book consists of selected and peer-reviewed papers presented at the 13th International Conference on Vibration Problems (ICOVP 2017). The topics covered in this book are broadly related to the fields of structural health monitoring, vibration control and rotor dynamics. In the structural health monitoring section studies on nonlinear dynamic analysis, damage identification, viscoelastic model of concrete, and seismic damage assessment are thoroughly discussed with analytical and numerical techniques. The vibration control part includes topics such as multi-storeyed stacked tuned mass dampers, vibration isolation with elastomeric mounts, and nonlinear active vibration absorber. This book will be useful for beginners, researchers and professionals interested in the field of vibration control, structural health monitoring and rotor dynamics.

## Inhaltsverzeichnis

### Estimation of Inertial Parameters of a Rigid Rotor Having Dynamic Unbalance on Active Magnetic Bearing

Non-uniform distribution of mass in a rigid rotor causes dynamic unbalance, as none of its principal axes of inertia is oriented along or parallel to the axis of rotation and the centre of mass is offset from the spin axis. A set of linear differential equations having time-varying coefficients express the dynamic behaviour. This paper assumes the rotor suspended on at least two Active Magnetic Bearings (AMBs) with known properties. Offset of centre-of-mass from the bearing centreline and skewness of inertial principal axes with respect to it, are estimated by minimizing the least square value of difference in response (at two planes close to the AMBs), predicted by the model with dynamic unbalance and the one with no unbalance at each time step. The estimated inertial parameters are found to be very close to the values used to simulate the actual model. Since the rigid rotor model is generic in nature, the procedure may be used to identify the inertial properties in actual situation without stopping the rotor. Thus, AMBs may be utilized to identify inertial properties and for smart balancing.

B. Nayek, A. S. Das, J. K. Dutt

### Sub-synchronous Vibration of Rotors Supported on Gas Foil Bearing

The applications of Gas Foil Bearings have been narrowed due to low damping and nonlinear characteristics. Moreover the presence of sub-synchronous and super synchronous frequencies introduces undesirable nonlinear effects to the system. Therefore, it is necessary to investigate and identify the parameters that cause this nonlinearity and hence ensure stable operation. In this work an attempt has been made to investigate the impact of various design parameters on sub-synchronous vibration of rotors supported on GFB. A nonlinear transient analysis has been carried out to obtain the transient trajectories of the journal centre.

Kamal Kumar Basumatary, Karuna Kalita, Sashindra K. Kakoty

### Some Numerical Studies on Coupled Turbine–Generator Rotor System Models

Coupled turbine–generator rotor systems are unique in their vibration behavior compared to individual rotor systems. Changes in geometric and dynamic parameters of individual rotor systems and coupling affect the overall response. Since there is also bound to be inherent misalignment at the coupling location, along with residual unbalance in the system, the rotor response contains harmonics corresponding to both unbalance and misalignment. A coupled Jeffcott rotor system with central discs integrated with active magnetic bearing (AMB) is considered in this work. The mathematical model is formulated from four degrees of freedom coupled Jeffcott rotor systems using Lagrange’s equations. A SIMULINKTM model is created to generate vibration and current responses in the time domain. Secondly, a full-spectrum FFT analysis of the time-domain signal is performed to examine the harmonics of the rotor’s vibration response and AMB’s current response. The change in the nature of rotors’ response for various permutations of unbalance and angular misalignment is studied. The advantage of full spectrum over time-domain signals and orbit plots in diagnosing misalignment has been demonstrated.

R. Siva Srinivas, Rajiv Tiwari, Ch. Kanna Babu

### Sommerfeld Effect Characterization in Anisotropic Non-ideal Rotor System

Ideal drive is usually considered for analysis of rotor dynamic systems. In reality, all the drives are non-ideal and they provide a limited amount of power. Moreover, the drive dynamics is also influenced by the dynamics of the driven systems. Dynamic analysis of rotor and drive coupling is a very complex task. Increase in input power of drive at resonance region may lead to increase in the transverse vibrations without increasing the rotor spin. At that moment, for a critical power input, the rotor spin speed escapes from resonance region and jumps to a very high rotor speed. This jump phenomenon is known as Sommerfeld effect. This effect is usually seen during coast up and coast down operations. The severity of Sommerfeld effect may lead to persistent large synchronous whirl amplitudes and capture of rotor speed at the resonance frequency, which may damage the rotor, bearings, and other equipment. Thus, smooth passage through resonance during coast up and coast down in rotor dynamic systems requires prior knowledge of its Sommerfeld effect and drive-rotor interaction, based on which, appropriate speed regulation controllers can be developed. In this paper, the characterization of Sommerfeld effect in an unbalanced rotor system is addressed. This unbalanced system is placed on an anisotropic two-degrees-of-freedom foundation and is driven by DC motor. The jump phenomenon of the rotor system, considering an ideal drive, is characterized by the steady-state power balance method. The transient simulation of the said system is carried out with the aid of a bond graph model, and jump voltage required to escape different resonance zone is obtained. Transient solutions may show premature jumps; however, the quasi-static simulation results exactly match with those obtained from steady-state analysis.

A. Bisoi, S. K. Bharti, A. K. Samantaray, R. Bhattacharyya

### Investigation of Vibration Characteristics of Ball Bearing Defects Using Dimensional Analysis

A systematic approach is proposed to investigate dynamic characteristics of a rotor-bearing system subjected to bearing looseness. The vibrations in rotating machines due to the unbalance in the rotating parts are studied. In this context, the mathematical model of rotor-bearing system for unbalance condition is developed using dimensional analysis. In order to diagnose the vibration characteristics of unbalanced rotor-bearing system, the experimental setup is designed and developed which is used to simulate the combined mechanical faults for different working conditions. The vibrations in rotating machines due to unbalance and clearance/looseness in the bearings for different loads and speeds are studied. The good correlation between the mathematical model and experimental results are presented. The results from the mathematical model can be effectively used to determine the influence of unbalance and clearance/looseness in the rotor-bearing system.

Abhishek P. Mohite, A. M. Badadhe, R. G. Desavale

### A Study on Multicomponent Failure Interactions Within a Planetary Gearbox of a Wind Turbine

Condition-based maintenance methods are being used in expensive and crucial equipment thereby provides the maintenance team with the information required without actually dismantling or shutting down the machine. For example, wind turbines and large stationary gearboxes use this method to predict the health of the system, thereby avoiding the possibility of a catastrophic failure. Studies related to fixed axis gearbox are more when compared to studies related to planetary gearbox. Multiple studies related to single component fault diagnosis have been carried out over the past years. However, studies on multicomponent fault detection are comparatively less. Nevertheless, the practical application requires multicomponent fault diagnosis technics to reliably predict failures as the machinery used would have more than one point of failure. This paper reports a study on multi-fault diagnosis conducted in a scaled-down model of a wind turbine planetary gearbox subjected to stationary loading. A uniaxial piezoelectric accelerometer was used to acquire vibration data which was then processed with an algorithm after the features were extracted using statistical feature extraction. The power spectral density was analysed to interpret the results obtained.

Hemanth Mithun Praveen, G. R. Sabareesh, Onkar Phatak

### Thrust Bearing Influence on the Stability Analysis of Turbocharger Rotor-Bearing System

The paper focuses on modeling and dynamic analysis of an on-board rotor over the floating-ring bearings by considering the additional effects due to a thrust bearing and axial preload. Initially, finite element analysis is used to get the unbalance response of the rotor system. The unsteady Reynolds equations are solved using finite difference approach with appropriate boundary conditions for finite length case. The time-varying bearing forces along with the rotor system of equations are solved by time-integration schemes. Further, the thrust bearing at the compressor end is modeled by its equivalent springs to study its influence on the stability of the overall system. The dynamic response of the system is investigated for various stiffness and axial preload condition at different rotor speeds. In addition, the influence of the thrust bearing forces on the overall dynamic stability of the rotor is studied. It is identified that the influence of thrust bearing forces is relatively small on the unbalance response at higher speeds of operation.

Rajasekhara Reddy Mutra, J. Srinivas, Devender Singh

### Impact of Unsteady Aerodynamic Loads on a Large-Scale Horizontal Axis Wind Turbine Rotor in Axial Motion

This paper investigates the unsteady aerodynamic performance due to oscillatory motion. The wind flows velocity is constant across the wind turbine rotor is applied, therefore, the attached flow on a 2-D airfoil and the aerodynamic critical damping of the large-scale horizontal axis wind turbine (LS-HAWT) blade structure are considered. The blade element momentum (BEM) theory is developed to estimate the aerodynamic forces acting on the blade. From this study, it has been observed that the flow conditions on airfoil profile oscillation in plunge motion at some frequency, which is similar to the eigen-frequency for the LS-HAWT blade. Here, the aerodynamic damping for its eigen-modes is estimated. Finally, it found that the wind turbine blade has an oscillatory frequency is close to the blade frequency. However, the computational fluid dynamics (CFD) has relatively too extensive computational time compared to the BEM code and it may computationally speed up the computational process.

Umesh Chaudhary, Praveen Tripathy, Sisir Kumar Nayak

### A Full Spectrum Analysis of a Jeffcott Rotor with Switching Crack in the Presence of Internal and External Damping

This paper presents the full spectrum analysis of a cracked Jeffcott rotor with the internal and external damping. In this study, a mathematical model is developed for a Jeffcott rotor considering both external and internal damping, crack force, and unbalance force. The crack in the rotor model is considered as switching crack function in the form of a rectangular shape, which provide forces that generate the forward and backward whirls at varied harmonics. The assumption of weight dominance simplifies the switching crack model to a linear one; however, it gives rise to the internal damping due to rubbing on crack faces. The rotor model is numerically simulated to provide responses from two orthogonal directions to obtain the full spectrum analysis to show both forward and backward whirls.

D. K. Roy, Rajiv Tiwari

### Active Control of Internal Damping Instabilities in a Cracked Rotor with Magnetic Bearing

In high-speed rotating machinery, the internal damping becomes predominant that further aggravates the appearance of cracks in the rotor due to severe unstable vibrations. The internal damping comes into existence in thick shafts when the fibers of the material are alternately compressed and stretched due to the asynchronous whirling motion. The presence of internal damping in rotors is also influenced by the appearance of the crack due to rubbing of fatigue crack fronts during its opening and closing, which has an additional effect of reducing the stiffness of the shaft. The aim of the present paper is to actively control through magnetic bearings (MB), the unstable vibrations induced by the internal damping in the presence of switching crack and unbalances in a rotor system. Equations of motion of a simple Jeffcott rotor are derived considering both external and internal damping, switching crack model, unbalance force, and active MB force. The chosen crack model gives multiple harmonics not only in the forward whirl but also in the backward whirl. The active MB system, which is used here as a controller and not for supporting the rotor static load, utilizes PID control law, which requires tuning of control law parameters for stable control of the rotor system. Rotor responses are obtained through a numerical simulation to study interplay between instability of rotor due to internal damping and its active control through the MB. Full (or directional) spectrum plots are utilized to demonstrate both the forward and backward harmonics of the rotor whirling at different rotor speeds due to the presence of switching crack with and without active MB. Nyquist plots are provided to check the stability of the rotor system at different operating speeds.

Nilakshi Sarmah, Rajiv Tiwari

### Simultaneous Estimation of Speed-Dependent Parameters in a Coupled Turbo Generator System

In the modern industrial world, turbo generator system consists of driver and driven shaft performs significant role in power transmissions. A small amount of abnormality/fault leads to catastrophic failure of critical components (e.g., bearing, coupling, rotor, gearbox, etc.) in turbo generator systems. The catastrophic failure of these critical component results huge economic loss sometimes even worse loss of human life to the firm. Two flexible shafts with a rigid disc at mid, connected together with a flexible coupling and mounted over flexible bearings at ends is considered as an abstract representation of turbo generator system. Shafts are modeled with Timoshenko beam theory and finite element approach is used to get EOM. Based on the least squares approach, an algorithm is established to quantify speed-dependent multi-fault parameters in a coupled rotor-bearing system. For brevity, one-plane analysis is carried out in this analysis, whereas the developed algorithm could be easily extended for two-plane analysis.

Monalisha Satapathy, Mohit Lal

### Crack Detection in an Overhung Rotor System Using External Harmonic Excitation

This paper presents an experimental approach for crack identification in an overhung rotor system supported on rigid bearings. The existence of coupling phenomena between bending and lateral vibration due to the presence of crack is used for the identification of crack in an overhung rotor system. The natural frequency of the rotor system has been obtained using impact hammer analysis and compared with the finite element analysis. The crack identification procedure involves the application of external axial excitation through a thrust shaker. The overhung rotor system is excited axially through a shaker with frequency equal to its first natural frequency and subharmonic of first natural frequency obtained through impact modal analysis. The response measured in the lateral and radial direction shows that there is a difference in the amplitude of the external excitation frequency and its harmonics measured for crack and healthy rotor system. The lateral response has more amplitude peaks at excitation frequency and its harmonic for cracked rotor when excited with frequency equal to the first natural frequency and its subharmonic. The peaks are more prominent for subharmonic of first natural frequency as external excitation. A considerable difference in the amplitude of X and 2X components can be seen in radial response for cracked rotor and healthy rotor when excited with frequency equal to the first natural frequency and its subharmonic. The application of external harmonic excitation with frequency equal to first natural frequency and its subharmonic can be very well used for crack detection in overhung rotor system without stopping it.

R. Tamrakar, N. D. Mittal

### Determination of Local Flexibility Coefficients of a Functionally Graded Shaft with Breathing Crack

Stress intensity factors (SIFs) play a fundamental role in the calculation of local flexibility coefficients (LFCs) in a cracked structure. Many researchers have calculated SIFs in a cracked beam or rotor made of homogeneous materials, but for functionally graded (FG) materials is scarce. The radially graded FG shaft consists of aluminum oxide (Al2O3) as ceramic constituent and stainless steel (SS) is as metal constituent and properties of material are computed following power law gradation under thermal gradient. LFCs of a spinning FG shaft with breathing crack behavior are determined analytically with the help of Castigliano’s theorem and energy principal of Paris. A MATLAB code is developed and validated with the literatures results. The effects of crack size and orientation, gradient index, and thermal gradient are examined on the direct and cross-couple LFCs. Numerical results show that magnitudes of LFCs increase with an increase in orientations of crack, maximum, while crack is completely open and then decrease with an increase in the orientations of crack. In addition, the magnitudes of LFCs increase while crack size, gradient indices, and thermal gradients also increase.

Debabrata Gayen, Debabrata Chakraborty, Rajiv Tiwari

### Physical Condition Monitoring of an Angle Section Thin-Walled Curved Beam Based on Non-destructive Assessment

This paper presents an integrated approach to monitor the physical condition of an angle section curved beam based on the estimation of the crack parameters, namely amount of the damage intensity and location. This approach of identification is established by integrating the response surface methodology (RSM) and genetic algorithm (GA). Numerical finite element (FE) model of the cracked beam has been connected to the present approach to carry out trial experiments to generate response surface functions (RSFs) for free, forced, and heterogeneous dynamic response data. Thereafter, the errors between the computed response surface functions and measured dynamic response data have been minimized using GA to obtain the crack parameters. The varying location and damage intensity of a single crack has been considered in the present study. The present approach has been found to reveal excellent accuracy in guessing of crack parameters and shows great potential in the crack identification, as it requires only the current response data of the cracked beam.

Palash Dey, Sudip Talukdar

### Prediction of Fatigue-Ratcheting Failure of a Piping System Using Iterative Response Spectrum Method

The present work describes the application of a numerical technique to predict fatigue-ratcheting failure level for a typical six-inch carbon steel piping system. The failure prediction is done by choosing limits on ratcheting and fatigue usage factor. Strain accumulation in the system is predicted using the numerical method. In this method, ratcheting in the piping loop is evaluated by carrying out response spectrum analysis at system level using the envelope characteristics at component level. Fatigue usage factors are evaluated using alternating stress along with Miner’s rule. These estimated levels are compared with excitation levels for static collapse evaluated from closed-form equations from literature.

A. Ravi Kiran, G. R. Reddy, M. K. Agrawal

### Structural Health Monitoring Using Improved Subspace Identification Method by Including Rotational Degrees of Freedom

In the present study, system identification and subsequent damage detection of support-excited multi-story linear time-invariant structural systems are carried out using a data-driven subspace identification method. Traditionally, buildings are idealized as shear buildings and hence only translational degrees of freedom are considered. The effect of including rotational degrees of freedom in the identification technique is studied for improvement in accuracy of the identified stiffness matrix. The study is conducted on the Phase-I IASC-ASCE structural health monitoring benchmark problem using earthquake-simulated data. Since it is not possible to measure the rotational dynamic response of structural systems, these are considered as unmeasured degrees of freedom and the identification has been performed as a special case of the limited sensors problem. The HRZ lumping method is used to assign masses at the rotational degrees of freedom. An iterative technique has been proposed to obtain the full mode shape matrix, including rotational components, from the available response data at the translational degrees of freedom. Different damage scenarios have been considered and the extent of improvement in the accuracy of the stiffness matrices with better damage localization after considering rotational degrees of freedom has been demonstrated. To verify the results, different recorded earthquake data are used for the analysis of the simulated benchmark building. The robustness of the technique in the presence of noise has also been studied.

Diptojit Datta, Anjan Dutta

### Investigation on the Vibration Response to High-Intensity Pressure Waves During a Solid Rocket Motor Operation

Launch vehicles experience peak vibro-acoustics stress during its captive firing or liftoff. The starting pressure rise transient in solid rocket motor chamber and subsequent flow of supersonic jet exhaust from the rocket nozzle generate high-intensity pressure waves. These pressure waves with different wavelengths are capable of exciting various structural elements of the launch vehicle. Especially the panel type of structural components located in very close vicinity to the supersonic jet and coming directly in the path of high-intensity pressure waves experience significant vibration. Hence, it is imperative to assess the vibration response of typical panel structures to high sound-level environment near the supersonic jet. Particularly, in the near field, these pressure waves behave in a nonlinear manner. Hence, developing a transfer function between vibrations to acoustics is essential for the proper design of structures for dynamic environment. In the present investigation, a typical panel structure instrumented with microphones and accelerometers are mounted near to a scaled down solid rocket motor supersonic jet exhaust. The plate is analyzed for its modes and frequency response function (FRF) by both experimental modal analysis (EMA) and finite element analysis (FEA). Also, the critical frequency of the plate is found out theoretically. The inclination of the plate with respect to the jet axis is varied for investigating the interaction of impinging and grazing waves. Further, the microphone and accelerometer measurements for different inclinations of the panel are analyzed by deriving power spectra and correlation functions. The ignition overpressure (IOP) wave interaction with the panel during the startup of the solid rocket motor is corroborated with the accelerometer response in the time domain. The high-intensity nonlinear Mach wave’s interaction with plate is analyzed from microphone and accelerometer time series data. The skewness of microphone and accelerometer data are compared. Finally, the frequency-dependent transfer function of vibration response to acoustic power input and vibrational efficiency factor is derived.

Jopaul K. Ignatius, Ramakrishna V. Venkata, Sankaran Sathiyavageeswaran

### Damage Identification of Structures Using Limited Power Mode Shapes and Power Modal Curvature

Damages of different forms occur frequently within the life of structures due to its aging, action of the environment, improper design, inferior construction and accidental loading, etc. Several damage identification methods are available using different techniques like modal flexibility, curvature mode shapes, and modal strain energy to detect the location and magnitude of damage of an existing structure [5,6]. In this paper, power mode shape and limited power modal curvature index are used to identify damage in different structure. The parameters (flexural rigidity, axial rigidity, etc.) are updated using the inverse approach in MATLAB interface. The use of noise in the simulation further enhances the accuracy of the algorithm.

S. Saha, T. Sohail, A. Bose, J. S. Ali

### Optimal Noise Filtering Method for Lamb Waves in Identification of Crack in Cylindrical Structures

The presence of narrowband coherent noise and random noise, which are induced by extraneous modes and reflections, etc., poses the challenge in wave-based online crack detection testing. The goal of this investigation is to set up the powerful multi-feature methods of signal examination for issues of guided wave-based nondestructive technique (NDT) in barrel-shaped shell structures. Filtration of time-frequency signal of elastic waves through the noisy signal is explored in the present examination utilizing matched filtering technique (MFT) and wavelet denoising strategies. We likewise propose wavelet matched filter method (WMFM), a blend of the wavelet denoising and matched filtering technique, which can altogether enhance the exactness of signal peaks and distinguish relatively small damage, particularly in enormously noisy data. Also, the capabilities of wavelet and matched filtering methods are compared. To provide better insight for performance evaluation of denoising methods, processing of received Lamb wave signals with a low signal-to-noise ratio (SNR) is addressed. The interaction of guided waves with circumferential damage is analyzed by utilizing this method. Guided wave excitation and the communication law with the round indent in the hollow cylinder are considered through associating Lamb wave theory with finite element method.

Ambuj Sharma, Sandeep Kumar, Amit Tyagi

### PCA Based Condition Assessment of RC Framed Building

Output-only algorithms are most useful for modal identification when input excitations are not easily available. In the present study, a principal component analysis (PCA) based method is utilized to extract the modal characteristics of the Millikan library building, where only structural responses are available (output-only). This study also considers the changes in the modal behavior of the building, before and after the major earthquake events. Detection of these changes can help in better decision-making, for monitoring the health of the structure and to devise a suitable plan for retrofitting.

Swarup Mahato, Diptojit Datta, Arunasis Chakraborty, Anjan Dutta

### Modeling and Experimental Studies on the Dynamics of Bolted Joint Structure: Comparison of Three Vibration-Based Techniques for Structural Health Monitoring

Detection of inadequate tightening in bolted joints is quintessential to ensure structural rigidity and to prevent catastrophic failure. Studies show that 30% of assembly failures occur due to inadequate tightening. In the present study, three vibration-based techniques are presented and compared to detect inadequate tightening of bolted joints. Variation in the damped natural frequency, variation in the damping ratio, and variation in the dynamic joint stiffness are studied with varying tightening torques in the bolted joint. The results show that all the three dynamic parameters vary with the tightness of the bolted joint. Dynamic joint stiffness varies significantly as opposed to the damping ratio and damped natural frequency as tightening torque reduces. In order to verify the results of dynamic stiffness method, ANSYS is used to model and analyze the joint. The experimental setup used to calculate the parameters consists of two Euler–Bernoulli beams connected with single lap bolted joint.

A. Deka, A. Rao, S. Kamath, A. Gaurav, K. V. Gangadharan

### Nonlinear Dynamic Analysis of a Simply Supported Beam with Breathing Crack Using Proper Orthogonal Decomposition Based Reduced-Order Modeling

The nonlinearity associated with a bridge is considered and the bridge is modeled as a simply supported beam (SSB) with breathing crack in Abaqus CAE Environment. The breathing mechanism (opening and closing) of the crack is achieved by the application of periodic loading in the transverse direction, in out of plane orientation to the crack and in parallel to the crack orientation of the beam. In this study, damage initiation (crack propagation) is neglected and the research is carried out only for the static crack. Using FEA, the higher order PDEs are converted into a set of coupled ODEs using Galerkin’s weak formulation. The refined mesh is adopted near the crack tip zone and intentionally increases the computational time. In order to reduce the simulation time without losing its accuracy, reduced-order modeling (ROM) approach is implemented in the cracked model to obtain the computationally efficient and equivalent model for the dynamic analysis. With this, we capture more than 99% of the system energy using subspace projection on to the full domain with two proper orthogonal decomposition (POD) modes. Additionally, the effective properties (mass, linear, and nonlinear stiffness, damping, and forcing amplitude) of the nonlinear dynamical system are obtained and incorporated into the Duffing oscillator’s equation of motion, with a cubical stiffness, which is identified from the static deflection of the beam and is solved using state-space approach using Matlab ode45 Algorithm. However, the parametric study is also conducted for different types of forcing amplitudes and frequencies to check the consistency of the ROM with the FEA Abaqus simulation and is in good agreement with its responses. The aperiodic behavior is identified in the linear range and the periodic doubling route to chaos is identified in the nonlinear range qualitatively in this model.

Vigneshwaran Krishnaswamy, Manoj Pandey

### Efficient Measurement of the Vibrational Rogue Waves by Compressive Sampling Based Wavelet Analysis

Nonlinear rogue waves appear as a result of spectral stochastic supercontinuum generation in nonlinear dynamical models, such as the nonlinear Schrödinger equation (NLSE). They are observed in the fields including but are not limited to fluid mechanics and optics. Rogue wave phenomena can also be observed in solid mechanics, where the envelope of a surface vibrational wave packet of an Euler–Bernoulli beam or Kirchhoff–Love plate can be modeled in the frame of the NLSE. Their efficient measurement and early detection is important to analyze critical displacements, stresses, and resonance. One of the possible techniques for their measurement and detection is to measure the triangular wavenumber (Fourier) spectra that become evident at the early stages of their development. One can treat such a spectra as a sparse signal due to energy located at the few central modes. Therefore compressive sensing can be used as an efficient tool for the measurement and prediction of vibrational rogue waves. However, Fourier analysis can only detect whether a vibrational rogue wave will develop or not in the vibrating medium. In order to locate its occurrence location, wavelet analysis deems necessary if a spectral analysis approach is utilized. In this paper, we discuss the possible usage of the compressive sampling based wavelet analysis for the efficient measurement and for the early detection of one-dimensional (1D) vibrational rogue waves. We study the construction of the triangular (V-shaped) wavelet spectra using compressive samples of rogue waves that can be modeled as Peregrine and Akhmediev–Peregrine solitons. We show that triangular wavelet spectra can be acquired by compressive sampling at the early stages of the emerging vibrational rogue waves. Our results may lead to development of the efficient vibrational rogue wave measurement and early sensing systems with reduced memory requirements which use the compressive sampling algorithms. In typical solid mechanics applications, compressed measurements can be acquired by randomly positioning single sensor and multi-sensors.

Cihan Bayındır

### Online Condition Monitoring of a Flexible Rotor System with the Help of Active Magnetic Bearings

Health monitoring of rotating machines is highly important for continuously running plants such as power generation industries, cryogenic engines of space vehicles, and multi shaft aero engines. In past, vibration based condition monitoring techniques attained a prime position among the researchers but the vibration based condition monitoring technique has less adaptability in a higher frequency range; to overcome this limitation, online condition monitoring, i.e., active controlling with the help of controlling parameters of Active Magnetic Bearings (AMBs) is presented in this article. An identification methodology is developed to estimate the characteristic parameters of AMBs, coupling misalignment in addition with inherent unbalance of the system. Shafts are considered as flexible and modeled with the Euler–Bernoulli beam theory. Proportional–Integral–Derivative (PID) controller is used for controlling the current in AMB. Finite Element Method (FEM) is used to obtain Equations of Motion (EOMs) of the coupled rotor system. The developed EOMs are modeled in the SIMULINKTM and solved by fourth-order Runga–Kutta method to obtain the displacement and the current response. Fast Fourier Transform (FFT) is used to convert the time domain responses into frequency domain responses. For brevity, half spectrum analysis is carried out to obtain the multi-frequency responses at different operating conditions. The proposed methodology is tested against different levels of measurement noise to check the robustness of the system for estimating the characteristic parameters using multi-frequency responses.

Sampath Kumar Kuppa, Mohit Lal

### Experimental Identification of the Fractional Parameter for a Viscoelastic Model of Concrete at Different Ages Based on the Impulse Excitation Technique

The experimental procedure for identifying a fractional parameter for concrete has been suggested by utilizing the experimental device RFDA Basic, which allowed the authors to measure internal friction, as well as the components of the complex elastic modulus. The main principle of the instrument is based on the Impulse Excitation Technique. Slight impact applied to a specimen of a special shape with specific support conditions initiates vibrations of the sample. The signal is recorded by a microphone and is transferred to a PC. RFDA software calculates resonant frequencies and corresponding values of damping, or internal friction. Using the internal friction test data, the vector diagrams have been constructed. The fractional parameter has been found directly from the vector diagrams. According to the experimental results, within the concrete age interval between 3 and 182 days, the average value of the fractional parameter has decreased by 276.33%, i.e., by more than two times. This phenomenon could be explained by the microstructural changes of concrete during its hardening: viscosity is substantially decreasing, while the elastic properties take on the dominating position.

Ivan I. Popov, Yury A. Rossikhin, Marina V. Shitikova

### Seismic Damage Assessment of Integral Abutment Bridge

Seismic vulnerability assessment of bridge is an important subject in the domain of bridge engineering. Both for functional bridges and new bridges, possible damages during strong ground shaking need to be assessed properly for their performance evaluation and any requirement of strengthening options. For assessment of seismic damages in bridges, damage states need to be established for the components. Although, past studies have focussed on the possible damage states, detailed investigation on damage states has not been carried out for integral abutment bridges. The present study aims to obtain realistic quantitative damage state estimates for the structural components of a continuous cast-in situ concrete deck bridge with integral abutments during possible seismic action. Adaptive nonlinear static analysis is carried out on the spline model of the bridge with soil-structure interaction effects at soil-pile and abutment-backfill interfaces. It is observed that abutment piles are the most vulnerable components for the considered bridge and govern the displacement capacity of the bridge system.

B. F. Ahmed, K. Dasgupta

### Physical Parameter Estimation of Non-classically Damped Systems from Spatially Incomplete Modal Parameters

In this paper, an approach is developed to identify the physical parameters of a class of non-classically damped systems in the situation of incomplete instrumentation, i.e., when not all active degrees of freedom (DOFs) of the system are instrumented (excited/observed). The proposed method starts with the initially identified spatially incomplete complex modes, and sequentially considers each row of the complex eigenvalue problem, to estimate the complete set of physical parameters, along with the complete complex mode shapes. It is shown that only two consecutively instrumented DOFs are theoretically sufficient for identifying the complete set of physical parameters. The proposed method is validated using a numerical example, also considering the effect of noise in the initially identified modal parameters.

M. S. Chauhan, C. K. Sharma, D. Ghosh, S. Mukhopadhyay

### Ball Bearing Fault Diagnosis Based on Vibration Signals of Two Stroke IC Engine Using Continuous Wavelet Transform

Ball bearings are used in the different critical fields of engineering applications such as IC engine, centrifugal pump and fans. In IC engine, the ball bearing is one of the critical components and it takes various types of dynamic loads and stresses. Condition monitoring of such ball bearing is very significant to avoid the catastrophic failure of rotating components in IC Engine. This article describes the fault detection of roller ball bearing of an IC engine gearbox with the use of signal processing technique such as spectrum analysis and Continuous Wavelet Transform (CWT) analysis. Vibration signals of IC engine are used to identify the fault in the ball bearing and to detect the healthy and fault bearing conditions.

K. N. Ravikumar, C. K. Madhusudana, Hemantha Kumar, K. V. Gangadharan

### Identification of Loosening of Bolts in a Steel Plane Frame Structure Using Fourier Decomposition Method

In the present study, an adaptive Fourier Decomposition Method (FDM) is applied to identify damage at connections. For that purpose, an experimental single-story plane frame model is considered. The beam and columns of the frame are connected by angles and bolts, and the damage is introduced by loosening bolts at different locations. The frame is excited at the right top corner using a hammer, and strain time histories are collected from different points. The FDM and Empirical Mode Decomposition (EMD) algorithm are applied to characterize the damage sensitive features. The results obtained from the FDM are compared with the EMD algorithm, which shows that the performance of FDM is better, which motivates to extend its application further to estimate the amount of bolt loosening in terms of extracted damage sensitive features.

Joy Pal, Pushpendra Singh, Sauvik Banerjee

### An Intelligent and Robust Fault Diagnosis System for Identification of Centrifugal Pump Defects in Frequency Domain Using Corrupted Vibration and Current Signatures

Historically, fault diagnosis techniques in industries were experience based. These techniques, however, are very tedious and involve a lot of human error. Therefore, intelligent methods need to be developed for the sustained operation of vital equipment like centrifugal pumps (CPs). In the present investigation, multiple independent and coexisting hydraulic and mechanical faults in a CP are attempted to be classified. The faults include blockages (discharge and suction), dry runs, impeller cracks and CP cover plate damages. The blockage faults are considered with varying severities. The current and vibration signatures are collected in time-domain by experimentally simulating the faults on the CP. These signatures are later converted into frequency domain. Support vector machine (SVM) classifier in conjunction with the Gaussian RBF kernel is used to develop the expert system for the fault diagnosis. To inspect the algorithm’s robustness, noisy/corrupted fault data is used to test the algorithm. The prediction accuracies thus obtained are compared with the non-corrupt data’s classification performance.

J. S. Rapur, Rajiv Tiwari

### A Comparative Study on the Primary System Response and Energy Harvesting from Linear and Nonlinear Tuned Vibration Absorbers

In this work, the performance of linear and nonlinear tuned vibration absorbers are investigated with the objective of reducing the amplitude of the primary system and maximizing the energy harvested from the secondary system. The equations of motions are formulated for a general case and the periodic solutions of the system are generated with the Harmonic Balance Method (HBM), and continued using a path following algorithm. A parametric study is conducted to analyze the response characteristics of the system under various values of parameters. Optimization of the system by choosing critical parameters is done using Response Surface Methodology and Genetic Algorithm. It is found that the introduction of nonlinearity improves the performance of the system compared to its linear counterpart for the carefully chosen parameter values.

P. V. Rasil Raj, B. Santhosh

### Vibration Control of Benchmark Building with Single and Multi-storey Stacked TMDs

Tuned mass dampers (TMDs) placed in skyscrapers show huge deflections and accelerations as they absorb a lot of the energy from the main structure. The responses of these TMDs need to be controlled with some additional dampers to keep their motion in check. The current paper deals with the numerical study of a similar system (stacked TMD system) in which a TMD (secondary TMD) is used to control the main TMD (primary TMD), which, in turn, is used to control the structure. Primary TMD is also analogous to important equipment such as a server placed in a building which needs to be controlled. In this study, the response of a 76-storey Benchmark building is investigated under across-wind loads. Dynamic Time History Analysis of the building is performed in MATLAB 2010a using the wind time history data by state-space method. In addition to deflections, drift and acceleration responses are also evaluated. Two systems of primary TMD have been studied. One system consists of conventional TMD, i.e., single mass-stiffness-damping device. The second system consists of three mass-stiffness-damping systems connected in series (i.e., the mathematical model is similar to a multi-storey frame). Thus, in combination with secondary TMD, in all four systems are studied. It is found that all the four systems give fairly good and similar results for the structure (up to 57% overall response reduction). However, Single storey stacked TMD system reduces the response of Primary TMD the most. Thus, this is the most effective system. Also, it is observed that multi-storey or Multi DOF TMD can be used in place of single storey or Single DOF TMD to distribute the heavy TMD mass along the different DOFs.

S. N. Madhekar, S. M. Marathe

### On Reduction of Force Transmission Using Shape Memory Alloy as an Isolator

Force transmissibility characteristics of shape memory alloy (SMA) bar are studied under isothermal operating condition. State-space formulation of the thermomechanical model is employed for numerical analysis. Single jump, double jumps and flat zones are observed in the force transmissibility curves at different forcing amplitudes. Providing small external damping eliminates the flat zones present in the force transmissibility curves.

S. Jose, G. Chakraborty, R. Bhattacharyya

### Magneto-rheological Tuned Liquid Column Dampers to Improve Reliability of Wind Turbine Towers

The size of wind turbines has increased exponentially since their induction. Modern multi-megawatt wind turbines are highly flexible structures supported by tall slender towers. These towers cost approximately 30% of the complete wind turbine assembly. It becomes very apparent that these towers need to be protected against damage induced by dynamic inflow wind. This paper uses probabilistic tools to assess the improvement of structural reliability when these towers are equipped with Magneto-Rheological Tuned Liquid Column Dampers (MR-TLCDs). A reduced-order dynamic system of the wind turbine based on the Lagrangian formulation is coupled with two MR-TLCDs to suppress tower fore-aft and side-to-side vibrations. Multiple aeroelastic simulations are conducted for various full-field inflow wind fields generated using the TurbSim package distributed by NREL. The magneto-rheological dampers are operated in a semi-active mode under optimal control framework to take advantage of the fact that these fluids can change their property (i.e., shear stress) instantaneously when subjected to a magnetic field. This allows instantaneous modification of damping of the device. This variable damping is used here as a semi-active control input. Response reduction of approximately 30–40% is obtained for side-to-side motion while less reduction is obtained in fore-aft vibrations due to high aerodynamic damping. Multiple limit states are established in this study to assess the reliability of the tower. Numerical investigations conducted ascertain the effectiveness of the semi-active controllers to improve the structural response and reliability of the wind turbine towers.

S. Sarkar, B. Fitzgerald, B. Basu, Arunasis Chakraborty

### Tuned Combined Liquid Damper for Seismic Vibration Control of Structures

A new type passive vibration controlling device named Tuned Combined Liquid Damper (TCLD) is introduced in this paper; which is a combination of Tuned Liquid Column Damper (TLCD) and rectangular Tuned Liquid sloshing Damper (TLD), both working simultaneously as a single unit to mitigate structural vibration. The new device works on the principle of liquid sloshing combined with the nonlinear relative liquid motions in the columns; to dissipate vibrational energy. The configuration of this new device makes it very much efficient and space-saving, and thus the design and installation of the device are also less costly than other types of liquid damper. First, the equation of motion of the primary structure and the new device TCLD is developed by combining the effects of TLCD and rectangular TLD when they are coupled together in a single container. A parametric investigation is carried out to obtain the effective range of design parameters of the damper by using a numerical time-domain procedure (Newmark-Beta method), and by using those parameters, the efficiency of the proposed device in mitigating structural responses caused by different real earthquake excitations is also investigated in this paper. A practical way is recommended for the design of a TCLD to mitigate structural vibrational responses.

Arka Mitra, Rama Debbarma, Debasis Panda

### Analysis of Tristable Energy Harvesters Under Random Excitations

This manuscript analyzes the performance of a tristable vibration energy harvester under Gaussian white noise excitation. Broadband vibration energy harvesting has attracted significant research attention and is targeted toward obtaining large power output over a wide range of frequencies. Nonlinearity can be introduced into vibration energy harvesting systems through multi-stability. In cantilever-type vibration energy harvesters, multi-stability could be achieved by the introduction of magnetic interactions. When two external magnets are used, the harvester can have up to three stable static equilibrium positions. The harvester with two stable states has been explored widely, both theoretically and experimentally. Recently, the harvester with three stable states is shown to perform better than its bistable counterpart in the presence of a linearly increasing harmonic sweep excitation. Ambient vibrations are random in nature, and the performance of tristable energy harvesters under such excitations needs to be studied. To begin with, we study the performance of tristable energy harvesters under Gaussian white noise excitation through numerical simulations. The simulations show that beyond a certain critical amplitude of excitation, the harvesters undergo inter-well oscillations and harvest more power. This implies that if the variance of the random ambient excitation is known, then the harvester could be optimized so that the mean harvested power is maximized.

A. Kumar, Shaikh Faruque Ali, A. Arockiarajan

### Development of Ride Dynamics Mathematical Model for the Military Vehicle with Active Suspension System

The current paper aims to develop a ride dynamics math model of the entire military vehicle, with incorporation of the desired controller technique. The vehicle comprises 18 degree of freedom, viz., sprung mass bounce, pitch and roll about its CG, bounce for each of the 14 unsprung masses as well as for the driver’s seat. Coupled governing differential equations of motion for passive as well as active systems have been derived using state-space approach, and solved in Matlab. Various options are explored for optimising location of the controller such as PID and LQR, in order to obtain the desired vibration reduction at the driver’s location. Comparative dynamic analyses are carried out between the passive and active controlled system over standard terrain profiles, from which the optimum controller location is selected. This mathematical study would play a key role in fine-tuning the suspension properties as well as for deciding upon the optimum implementation of the controller with enhanced crew comfort at reduced cost.

Ambarish Jakati, C. Jebaraj, Saayan Banerjee

### Broadband Piezoelectric Energy Harvesting Using an Array of Mistuned Inverted Cantilever Beams

An energy harvesting device built on the lines of capitalizing the linear resonance of the system works well only when the natural frequency is close to the excitation frequency. To overcome this limitation of the linear harvester, this work investigates the prospect of using an array of mistuned cantilevers for broadband energy harvesting. The common device configuration of inverted beams with tip masses has been adopted in this study. The considered system is highly nonlinear for tip masses beyond Euler buckling load, and it has two potential wells on either side of the unstable zero position. The non-linear characteristics of the harvester are studied as a preliminary investigation to identify the values of mistuning parameters used in the current work. Numerical simulations have been carried out to understand the influence of mistuning parameters such as length of the beams and tip masses on the frequency band of the harvester power. Comparative studies on the power bandwidth of array of mistuned linear and non-linear harvesters are performed. Observations show that an array of non-linear harvesters enhanced the frequency bandwidth of the power more than that of its linear counterpart.

M Aravindan, Shaikh Faruque Ali

### Nonlinear Active Vibration Absorber Using HBM Method

This paper presents analysis of a nonlinear time-delayed active vibration absorber attached to a nonlinear single degree of freedom (DOF) spring-mass-damper primary system. In the proposed model, a piezoelectric stack actuator is attached to reduce the vibration of the primary system, which undergoes external harmonic and base excitation. The analysis is carried out by considering acceleration feedback of the primary mass. Harmonic balance method (HBM) is used to obtain the solution of the governing equation of motion of the system for the primary resonance condition. The proposed design for the absorber is fail-safe design, which requires less voltage for actuating actuator to absorb the vibration of the primary mass.

S. Mohanty, Santosha Kumar Dwivedy

### Optimal Location of Piezoelectric Patch in Passive Vibration Control

The importance of placing the piezoelectric patch at the optimal location for getting the maximum vibration control using the shunt circuit technique is discussed here. A shunt circuit damper converts the mechanical vibration to the electrical energy, which is then dissipated as heat using resistors. The energy dissipated by the device increases with respect to the energy absorbed by the piezoelectric patch in the circuit. Hence, placing the patch in a location where it can produce maximum electric potential results maximum energy dissipation. Performance of this device is investigated on an aluminium cantilever beam for three types of shunt circuit conditions by optimising the design variables using genetic algorithm and fmincon in MATLAB. Further, sensitivity analysis shows that the arbitrary placing of the patch causes detuning at some locations and induces negative damping to the system. The numerical study indicates that at the optimal location, the performance of the device improves significantly in terms of percentage reduction in tip velocity. Moreover, a considerable reduction in the resistance value is obtained by the use of genetic algorithm.

M. Mohamed Sajeer, Arunasis Chakraborty

### Vibration Control of Torsionally Coupled Building Using Tuned Liquid Column Ball Damper

In this present study, the efficiency of the combined circular tuned liquid column ball damper (CTLCBD) and tuned liquid column ball damper (TLCBD) is demonstrated in order to suppress the torsional responses of building, excited by wind. The results from the numerical simulation reveal that combined CTLCBD and TLCBD is effective in suppressing torsionally coupled response. The reduction achieved by the damper system is around 38% in peak rotational displacement and around 28% in peak rotational acceleration.

Dhirendra Kumar Pandey, Sudib Kumar Mishra

### A Nonlinear Hybrid Energy Harvester

This manuscript discusses a magnetically coupled nonlinear hybrid piezo-electromagnetic energy harvester under harmonic base motion. Linear energy harvester works optimally when the natural frequency of the harvester meets the resonating frequency, elsewhere harvested power falls drastically. Most of the ambient vibration sources are random in nature. Hence, considering the realistic application, narrowband linear vibration energy harvesters are inefficient. Alternatively, nonlinear energy harvesters are capable of producing the electrical power over a broad frequency range. Hence, to acquire the optimum power in the broader frequency range, a magnetically coupled hybrid piezo-electromagnetic energy harvester is developed. In this current work, a tip loaded unimorph piezo cantilever beam configuration is used to scavenge electrical energy from the strain developed in the piezoelectric patch and spring-magnetic mass attached to another end of the cantilever beam with solenoid arrangements are used to scavenge electrical energy from the relative motion between magnetic mass and solenoid. This hybrid harvester is coupled with magnetic oscillators to introduces nonlinearity in the developed harvester. This paper compares, the energy harvested from the hybrid harvester with that of conventional piezoelectric and electromagnetic harvesters for both linear and nonlinear systems.

M Rajarathinam, P V Malaji, Shaikh Faruque Ali

### Optimal Design of MRTLCD for Semi-active Vibration Control of Building Structures Using Genetic Algorithm

Seismic response reduction has remained an active area of research in the last few decades. In this context, the magneto rheological tuned liquid column damper (MRTLCD) is one of the common semi-active/active devices. The semi-active damping devices require less power supply to change their damping characteristics than any other active damping devices, and can be able to reduce structural responses when subjected to uncertain forces. With this in view, the aim of this study is to address the optimal design of MRTLCD considering a shear building frame for more robust performance. Linear quadratic regulator (LQR) algorithm is used to calculate the control force. In general, the weighing matrices associated with LQR are decided by the trial and error method. For this purpose, the Genetic Algorithm (GA) is used to construct suitable weighing matrices. To achieve this goal, multi-objective design optimization is solved by using GA to find the optimal design parameter of MRTLCD and the optimum value of weighing matrices of LQR. The numerical analysis presented in this paper clearly establishes the benefits of the proposed GA-based optimization over the trial and error approach by considering five-story shear building frame.

Sourav Das, Arunasis Chakraborty
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