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2016 | Buch

Special Topics in Structural Dynamics, Volume 6

Proceedings of the 34th IMAC, A Conference and Exposition on Structural Dynamics 2016

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Über dieses Buch

Special Topics in Structural Dynamics, Volume 6. Proceedings of the 34th IMAC, A Conference and Exposition on Dynamics of Multiphysical Systems: From Active Materials to Vibroacoustics, 2016, the sixth volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on:

• Analytical Methods

• Biological Systems

• Dynamic Systems

• Dynamics of Multi-Physical Systems

• Structural Control

• Simulation

Inhaltsverzeichnis

Frontmatter
Chapter 1. Online Input and State Estimation in Structural Dynamics
Abstract
This paper presents two applications of joint input-state estimation in structural dynamics. The considered joint input-state estimation algorithm relies upon a limited set of response measurements and a system model, and can be applied for online input and state estimation on structures. In the first case, the algorithm is applied for force identification on a footbridge. The second case shows an application where strains in the tower of an offshore monopile wind turbine are estimated. In both cases, real measured data obtained from in situ measurements are used for the estimation. The dynamic system model, used in the estimation, is for both case studies obtained from a finite element model of the structure. The quality of the force and response estimates is assessed by comparison with the corresponding measured quantities.
K. Maes, G. De Roeck, A. Iliopoulos, W. Weijtjens, C. Devriendt, G. Lombaert
Chapter 2. Modeling and Testing of the Anti-Vibration Base for Michelangelo’s Pietà Rondanini
Abstract
The famous statue Pietà Rondanini by Michelangelo Buonarroti (sculpted in the second half of 1500) was recently moved to a new position in a museum in Castello Sforzesco, Milan. In this new location, the vibration levels, due to the close presence of underground tracks, has been considered worthy of specific attention; therefore both the Municipality of Milan and the Cultural Heritage ministry asked for the design of a new base capable of mitigating the vibration input to the statue. In addition, since Milan is a seismic area (although with moderate risk), it was also required to include in the base design an anti-seismic device. The protection from the underground action (which is in the range between 16 and 80 Hz) requires the development of a system with low natural frequency and rather limited damping, to have a steep filtering after resonance. However in case of an earthquake, the low frequency range would be strongly excited, with the eventual risk of an extreme event like rocking. A second device is thus introduced to protect the statue from earthquakes, consisting in a low friction slide of the same type as those used to protect buildings from the same kind of events. The coupling between the two types of protection imposed a careful design and testing of the complete system made up of the base and the statue. The design of the base was developed by means of an experimental-numerical approach. A measuring campaign using a large 6 degrees of freedom shaking table was used to test a full scale prototype of the base supporting a marble 1:1 copy of the statue. A multibody model of the full installation (complete base and statue) was developed, qualified by means of experimental data, and used to optimize the parameters, such as the mass distribution, positions of the elastomeric supports and the damping of the devices. The final system is now installed in the museum, protecting the Pietà.
Alfredo Cigada, Edoardo Sabbioni, Ali Siami, Emanuele Zappa
Chapter 3. Estimation of Frequency and Damping of a Rotating System Using MEOT and Virtual Sensor Concept
Abstract
Currently, to obtain an understanding of the frequency and damping of the modes of a rotating system, an impact test or a shaker test is done to find the frequency at which the modes of the system exist. Then, an operating test is done to obtain an understanding of the orders of the system. A Mode Enhanced Order Track (MEOT) can be used to obtain the frequency and damping of various modes directly from the operating data of a rotating system but it cannot find modes which are very close together in frequency or those that are repeated. The MEOT is a method described in Dr J.R. Blough’s PhD dissertation, which has not been tested on data obtained from an actual rotating system. This data was taken from a Toro Leaf Blower, using a laser tachometer and 7 triaxial sensors. Using Mode enhanced Order Tracking, the frequency and damping of different modes was found. These were then compared to the results obtained from an Impact Test performed on the Toro Leaf Blower. This method was also tested after using the virtual sensor concept on the data. A virtual sensor was created for each triaxial sensor. The results obtained from the impact test, MEOT and the MEOT performed on the virtual sensor data were then compared and analysed.
Sharang Inamdar, Randall J. Allemang, Allyn W. Phillips
Chapter 4. Multibody/FEM Numerical Tool for HIL Scaled Offshore Wind Turbine
Abstract
Nowadays the study of the renewable sources of energy is one of the most important lines of research. For this reason the wind tunnel researchers of Politecnico di Milano want to apply new hardware in the loop approach to study floating offshore wind turbines scale models by reproducing at the same time both the aerodynamic and hydrodynamic phenomena involved. These experiments allow to have a better understanding of the operating conditions of these structures and to properly set the control algorithm for the blades pitch in order to have a better exploitation of the wind stream. In addition the results of the experimental phase could be used to validate the numerical codes. While it is possible to physically reproduce the wind profile with a good approximation, the sea waves effect has to be simulated by means of a 6-DoF parallel kinematic machine. The result is a coupled system in which two flexible structures, the turbine and the robot, cannot be regarded as two separate entities. The aim of this paper is to provide a multibody model to perform dynamic analysis of this coupled system and to study how the pose of the manipulator and the wind profile affect the results.
H. Giberti, M. Belloli, I. Bayati, E. Fiore
Chapter 5. Detection and Identification of Firearms Upon Discharge Using Floor-Based Accelerometers
Abstract
Vibration monitoring and analysis techniques have significant potential to improve security and threat detection in the built environment. The cornerstone of the Virginia Tech Smart Infrastructure Laboratory (VTSIL) is the highly instrumented Goodwin Hall on the VT campus. This 5-story classroom and laboratory building is instrumented with over 200 accelerometers hard-wired throughout its 160,000 square feet, providing a platform for research and education in structural health monitoring, dynamic model validation, and occupancy studies, among other smart building applications. One of the major research goals for VTSIL is to utilize vibration data to develop advanced security strategies, including threat detection, identification, and localization. Toward realizing this goal, a mobile cement and I-beam platform was built and instrumented with accelerometers. This test-bed recorded vibration signatures during the event of a person discharging a firearm while standing atop the platform. This paper includes initial results that demonstrate there are detectable differences in sensor measurements between a handgun, rifle, and shotgun. Initial analysis of this vibration data using the singular value decomposition demonstrates that one can deduce the type of firearm discharged regardless of differences in the shooter (male, female, weight, etc.), thus justifying the pursuit of advanced vibration-based threat detection and identification systems.
M. Kasarda, P. Tarazaga, M. Embree, S. Gugercin, A. Woolard, B. Joyce, J. Hamilton
Chapter 6. An Adaptive Markov Chain Monte Carlo Method for Bayesian Finite Element Model Updating
Abstract
In this paper, an adaptive Markov Chain Monte Carlo (MCMC) approach for Bayesian finite element model updating is presented. This approach is known as the Adaptive Hamiltonian Monte Carlo (AHMC) approach. The convergence rate of the Hamiltonian/Hybrid Monte Carlo (HMC) algorithm is high due to its trajectory which is guided by the derivative of the posterior probability distribution function. This can lead towards high probability areas in a reasonable period of time. However, the HMC performance decreases when sampling from posterior functions of high dimension and when there are strong correlations between the uncertain parameters. The AHMC approach, a locally adaptive version of the HMC approach, allows efficient sampling from complex posterior distribution functions and in high dimensions. The efficiency and accuracy of the AHMC method are investigated by updating a real structure.
I. Boulkaibet, T. Marwala, M. I. Friswell, S. Adhikari
Chapter 7. Modal Parameters of Multiple-Disk Shaft System from Multiple Reference Impact Test
Abstract
The proposed work is intended for Experimental Modal Analysis (EMA) of a multi-disk shaft system to estimate its modal parameters, i.e., natural frequencies, damping ratios, and mode shapes. The considered system is excited by a roving impact hammer at a set of excitation points, and the vibration response is measured at a number of response points (taken as reference points) using piezoelectric accelerometers. The Frequency Response Function (FRF) matrix and the corresponding Impulse Response Function (IRF) matrix are estimated, which allows the detection and estimation of repeated or closely coupled modes, known to exist in the considered structure. The estimated FRF and IRF matrices are employed with both time and frequency domain algorithms to estimate the desired modal parameters. Modal frequencies are estimated from Finite Element analysis using ANSYS and compared with the experimentally obtained frequencies.
Naim Khader, Mohammad Ramadan
Chapter 8. Identification of Aerodynamic Properties of Bridge Decks in Arbitrary Motion
Abstract
Flutter, buffeting response and vortex shedding are crucial factors when designing long-span bridges. An analysis of these phenomena requires experimental data, which can be provided by wind tunnel tests. The forced vibration method is chosen in this study because it is considered to be more reliable and better suited to provide data at high velocities, large amplitudes and more intense turbulence. The models currently used to describe self-excited forces in bridge engineering are linear. However, it is a well-known fact that the principle of superposition does not hold in fluid dynamics. Several case studies have shown that it is a fair approximation when predicting wind-induced dynamic response of bridges if the response is dominated by one vibration mode in each direction. Yet, it is uncertain how well the current models will be able to predict the self-excited forces for a more complicated motion. Currently developing experimental setup will enable the performance of forced vibration tests by applying an arbitrary motion. This paper focuses on extending three identification methods developed for single harmonic motion such that they can be applied in more complex motion patterns. Numerical simulations of forced vibration tests were performed to test the performance of those extended methods.
Bartosz Siedziako, Ole Øiseth, Nils Erik Anders Rønnquist
Chapter 9. A Multiphysical Modelling Approach for Virtual Shaker Testing Correlated with Experimental Test Results
Abstract
A virtual shaker testing simulation environment aims to predict the outcome of a spacecraft vibration test numerically, prior to its physical execution at the environmental test facility. Therefore, it needs to comprise the complex dynamical characteristic of the test setup and facility in order to calculate and predict the interaction between the electrodynamic shaker system, test specimen, and vibration controller as it occurs during tests of large spacecraft. A currently derived one-dimensional multiphysical shaker model with three degrees-of-freedom, e.g. the 160 kN electrodynamic shaker of the European Space Agency (ESA), is based on a tailored experimental system identification methodology to estimate the system’s parameter. The model is validated by subsequent simulations to recalculate and predict the test results. The main focus of the paper is the enhancement of the shaker model to encompass additionally, lateral and rotational dynamics of the shaker table as well as the coupling with test specimen dynamics and control system performance. The improvements are based on analytical modelling steps in conjunction with the exploitation of experimental test results of hammer impact excitations, and closed-loop random and sine control testing performed on the shaker, loaded with a dummy specimen and excited with different excitation levels.
S. Waimer, S. Manzato, B. Peeters, M. Wagner, P. Guillaume
Chapter 10. Characterizing the Dynamics of Systems Incorporating Surrogate Energetic Materials
Abstract
It is hypothesized that by understanding the mechanical behavior of explosive materials it may be possible to use an object’s mechanical response to distinguish between objects that contain explosive materials and those that do not. While the materials will typically be embedded in a system and the system behavior will play a role in the response, the focus here is on the identification of mechanical material properties and behavior of surrogate explosive materials. Base excitation swept sine tests were conducted to characterize the uniaxial dynamic response of a mass-surrogate material system. The tests were conducted to gain an understanding of the dynamic behavior near resonance, repeatability of measured responses, and how these change over long periods of time. Linear and nonlinear viscoelastic models were fitted to the data and changes to material parameter estimates were examined as excitation levels changed and also as the composition of the surrogate materials changed. Recommendations for future development of the model structure are given.
Jelena Paripovic, Patricia Davies
Chapter 11. Multimodal Damping of a Plate with a Passive Piezoelectric Network
Abstract
Multimodal vibration reduction can be obtained by coupling a mechanical structure to an electrical network approximating its modal properties. This strategy is applied to the control of a clamped plate with a 2D network of passive electrical components. The plate and the network are coupled through a periodic array of piezoelectric patches that enables the energy conversion. The network is experimentally implemented with inductors and transformers in order to create electrical resonances that present a spatial distribution approaching the first mode shapes of the plate. By tuning electrical resonances to mechanical ones, it becomes possible to introduce the equivalent of a tuned mass effect. This effect only occurs if the electrical and mechanical mode shapes are sufficiently close, which requires specific network topology and boundary conditions. Once the network is tuned, adding resistors introduces damping that can lead to a broadband vibration reduction of the plate. It is thus shown that a 2D control can be implemented with a purely passive solution, which could be of great interest for many embedded applications.
B. Lossouarn, M. Aucejo, J.-F. Deü, K. A. Cunefare
Chapter 12. State Estimation: A Model-Based Approach to Extend Test Data Exploitation
Abstract
Design models can drastically improve the applicability of testing and allow measuring previously unmeasurable quantities and designing reduced test configurations. A common workflow is followed: a multiphysics system model provides a prediction of the system states which is corrected by the estimation algorithms using the measurement data. The model can then generate data of the non-measurable quantities (e.g. virtual sensors). A wide range of models can be used, including analytical, 1D lumped parameter and 3D distributed parameter models. Key is that they are easy to evaluate and have a small number of states, while capturing the dominant physics. Novel model order reduction techniques enable the use of more complex models. A wide range of state estimation approaches has been developed such as the (linear, extended, unscented, …) Kalman Filter and the Moving Horizon Estimator. All approaches require a trade-off between accuracy and computational load so that conventional estimators must be tailored to deal with high-fidelity nonlinear models of industrial complexity. The approach is illustrated with two cases: the estimation of hard-to-measure vehicle body forces using the extended Kalman filter and the application to an electro-mechanical drivetrain subject to unknown input forces. Methodological aspects are evaluated and different estimators are compared.
Herman Van der Auweraer, Steven Gillijns, Stijn Donders, Jan Croes, Frank Naets, Wim Desmet
Chapter 13. Generation of Traveling Waves in a 2D Plate for Future Drag Reduction Manipulation
Abstract
In most systems, friction drag is an obstacle to be hurdled and is a large source of energy inefficiency in airplanes, ships, pipes, etc. By reducing the amount of friction drag between a fluid and a surface, large energy savings are possible. This study investigates the generation of traveling surface waves propagating in the spanwise direction (perpendicular to flow) that can later be applied to decrease the friction drag in turbulent flow. A thin plate with C-F-C-F boundary conditions is excited by two piezoelectric actuators at the same frequency but with a phase difference between them. The operational deflection shapes are captured at five different frequencies where one to four regions of traveling waves exist in the plate at each frequency, with some moving in opposing directions. The traveling waves have standing waves superimposed, where the form of the standing waves are determined by the participation of nearby modes. This work provides initial assessment on the generation of traveling waves in 2D structures that can potentially be used for drag reduction in the future.
Patrick F. Musgrave, V. V. N. Sriram Malladi, Pablo A. Tarazaga
Chapter 14. Surrogate Granular Materials for Modal Test of Fluid Filled Tanks
Abstract
Experimental vibration certification of launcher cryogenic tanks is an important issue in the aerospace industry. Liquid hydrogen is indeed too dangerous to be used in tank vibration tests. Unlike most fluids used in aerospace industry such as liquid oxygen, surrogate fluids cannot be used to approach the modal behavior of a tank filled with liquid hydrogen because of its particularly low mass density. However granular materials could safely replace liquid hydrogen for vibration testing of tanks.This work aims at proposing an innovative methodology to determine the geometry and the material properties of substitution grains in order to keep the same mode shape and eigen frequencies of a vertical cylindrical tank studied considering 2D horizontal slices. Assuming that the tank slices are sufficiency far enough from the free-surface not to be affected by sloshing effects, the fluid-structure interaction is purely inertial. This methodology is based on the homogenization of a granular material composed of spheres with an elastic behavior. Thus the tank filled with grains can be modeled by a membrane surrounded by a circular beam. An experimental test bench developed to validate the methodology, as well as analytical and numerical simulation results of fluid-beam and membrane-beam interactions, are presented on the first modes.
Pierre-Louis Chiambaretto, Miguel Charlotte, Joseph Morlier, Philippe Villedieu, Yves Gourinat
Chapter 15. Dynamics of a Hydroelastic Oscillating Cylinder with Added Viscoelastic Damping for Passive Control of Vibrations
Abstract
In the scope of flow around cylindrical structures, the vortex shedding phenomena are those that have attracted considerable attention from many mechanical and civil engineering domains. Since, these phenomena—dependent on a number of factors—may have disastrous effects in engineering practice, such as economic loss, damage of installations, loss of power-generating time, etc. This is a reason for which in the last decades, a great deal of effort has been devoted to the development of numerical and computational procedures for dealing with the problem of vortex shedding phenomena. Among the various new developments for dealing with the problem of vortex-induced vibration, the use of viscoelastic materials is considered as an interesting strategy, since they present great efficiency in mitigating vibrations levels at moderate application and maintenance costs. In this paper, the Immersed Boundary Method combined with the Virtual Physical Model is used to investigate the forces and response associated with the vortex-induced vibration of a rigid oscillating cylinder incorporating viscoelastic damping. In the context of fluid-structure interactions, an important issue addressed herein is the modeling procedure of the viscoelastic behavior in the time domain, which is performed by using a fractional-order constitutive model. After the presentation of the underlying theoretical foundations related to the various aspects of the numerical modeling procedure, numerical simulations with a viscoelastically damped oscillating cylinder performed in a wide range of oscillating amplitude and forcing frequency are presented and discussed aiming at demonstrating the influence of viscoelastic damping on the flow structure and fluid forces.
Bruno Sousa Carneiro Da Cunha, Antônio Marcos Gonçalves de Lima, Alice Rosa da Silva
Chapter 16. Dynamic Analysis of Fluid-Filled Piping System on Flexible Foundation
Abstract
In this paper, dynamic modeling of fluid-filled piping system coupled with general flexible foundation by discrete springs has been investigated. A method combined the transfer matrix method (TMM) and frequency response function (FRF)-based substructure method has been proposed to enhance the computation efficiency. Fluid-structure interaction of the fluid-filled piping system has been taken into consideration in the TMM by variable separation. By using this method, the natural frequencies and FRFs of the coupled system can be obtained. The engineering applications with plate-like foundation have been simulated. Very good agreement has been obtained compared with the results by finite element method (FEM). Parametric studies are carried out to illustrate the influences of stiffness of spring and plate on the dynamic behaviors of the coupled system. This study will shed some light on designing fluid-filled piping system on flexible foundation in engineering practice.
Longlong Ren, Xiuchang Huang, Zhengguo Zhang, Hongxing Hua
Chapter 17. Incremental Dynamic Analyses of Steel Moment Resisting Frames with Superelastic Viscous Dampers
Abstract
This study aims to evaluate the seismic performance of steel moment resisting frames upgraded with shape memory alloy (SMA)-based self-centering viscous dampers. The superelastic viscous damper (SVD) relies on SMA cables for re-centering capability and employs viscoelastic (VE) damper that consists of two layers of a high damped (HD) blended butyl elastomer compound to augment its energy dissipation capacity. First, the design and mechanical behavior of SVDs are described. A nine-story steel frame building is selected for the numerical analyses. The building is analyzed as (1) a conventional special moment resisting frame (SMRF), (2) a dual SMRF-buckling restrained brace (BRB) system, and (3) a SMRF with SVDs. A model of the steel building for each configuration is developed to determine the dynamic response of the structure. The incremental dynamic analysis is used to evaluate the behavior of each building under seven ground-motion records. The analytical results indicate that the SVDs improve the response of steel frame buildings under different level of seismic hazards.
Baikuntha Silwal, Osman E. Ozbulut, Robert J. Michael
Chapter 18. Structural Control Using a Semiactive Friction Damper
Abstract
All civil structures are prone to vibrations caused by external sources such as earthquakes, wind, mechanical loads and anthropogenic loads. However, structural control systems have proven to be effective in reducing excessive vibrations. This article describes a Semiactive-Variable-Friction-Damper that was designed for reducing the dynamic response of structures subject to seismic excitation. The structural control device, which consists of a hydraulic brake activated with a servomotor, was identified and characterized in order to design a decentralized control strategy. A small-scale benchmark structure was built and the structure with control system was tested on a shaking-table. Results of the structural response with and without the control system are compared, with the friction device reducing story drift by up to 90 %.
Juan S. Mantilla, Daniel Gómez, Peter Thomson
Chapter 19. Seismic Response of SMA Reinforced Shear Walls
Abstract
This paper presents the performance of concrete shear walls reinforced with Shape Memory Alloys (SMAs) using nonlinear numerical modelling. A hysteretic constitutive model for Superelastic (SE) SMA reinforcing bars that was recently implemented into a nonlinear finite element analysis package applicable to reinforced concrete membrane structures and compatible with a compression field approach is presented. The objective of the model is to provide simple formulations that satisfactorily capture the forward and reverse transformations phases that superelastic SMAs experience when subjected to mechanical loading. The finite element model was corroborated with experimental results of a slender SMA reinforced concrete shear wall subjected to reverse cyclic loading. The model captures salient features of behaviour, including strength, ductility, energy dissipation, load-displacement response, cracking patterns, and failure modes. Nonlinear static analyses are conducted on the SMA reinforced shear wall and assessed against a companion traditional reinforced concrete shear wall. The comparison includes strength, ductility, and displacement recovery capacities. In addition, the effect of increasing axial load on the performance of the SMA and traditional reinforced walls is presented.
Marina Maciel, Dan Palermo, Alaa Abdulridha
Chapter 20. Stability of MIMO Controllers for Floor Vibration Control
Abstract
There are many research studies in the literature that have been devoted to active control of human-induced vibrations in civil engineering structures. This technology has been implemented in floors and footbridges in order to improve their vibration serviceability performance. Most of these works have focused on single-input single-output (SISO) controller schemes, i.e. comprising of a single sensor and actuator pair. Their closed-loop stability properties expressed in terms of the gain margin (GM) and phase margin (PM) can easily be evaluated from techniques such as root locus studies of the closed-loop systems and Nyquist contour plots.
For multiple-input multiple-output (MIMO) controller schemes, i.e. systems with multiple sets of actuators and sensors, evaluation of their stability properties is not so obvious and most past researches hardly show this although it is taken into account in one way or another. This is the focus of this work. It presents a study of MIMO stability of a control set-up comprising of two sensors and actuators and further reviews what might be regarded as the appropriate controller gains for velocity based controllers. The approaches used to evaluate the stability properties of this control scheme comprise of comparative studies covering the generalized Nyquist criterion, plots of eigenvalues of the closed-loop system and relative gain arrays (RGA). A limiter on the actuator displacement to disturbance loop both for SISO and MIMO studies is introduced to reduce potential stroke saturation.
Donald Nyawako, Paul Reynolds, Emma Hudson
Chapter 21. Extraction of Wave Dispersion Characteristics in a Discrete Chain Using Complex Modal Decomposition
Abstract
The dispersion relationship of a discrete chain of masses is extracted from numerically simulated data by applying complex modal decomposition. When an impulse excitation is applied to one end of a semi-infinite mass-spring chain, a wave is generated and propagates down the chain. This wave consists of various modes. The time record for the generated data is limited such that the wave reflection does not return to the “sensed” masses. For example, a 250-mass chain is simulated, and we consider (or sensed) the time record of the first 100 masses. The data collected from the numerical simulation consists of the displacements of each mass at each time step. This data is then used to extract complex modes using the complex orthogonal decomposition (COD) and smooth complex orthogonal decomposition. The extracted complex modes accommodate modal traveling waves. We then compute the frequencies and wave numbers from modal coordinates and mode shapes, respectively. The amplitudes and frequencies of the modes are also estimated using Rayleigh’s quotients. The COD extracted dispersion relationship matched the analytical prediction of the dispersion curve for the linear mass chain.
Rickey A. Caldwell Jr., Smruti Panigrahi, Brian F. Feeny
Chapter 22. Approximate General Responses of Multi-Degree-of-Freedom Systems with Parametric Stiffness
Abstract
In the work presented, the solutions and stability of multi-degree-of-freedom Mathieu-type systems are investigated. An approach combining Floquet theory with harmonic balance is used to find the system response. The assumed Floquet-type solution consists of a product between an exponential part and a periodic part. The periodic part is approximated with a finite number of harmonics, and without making further assumptions, this solution is directly applied the original differential equations of motion. A harmonic balance analysis results in an eigenvalue problem. The characteristic exponents are the eigenvalues and the corresponding eigenvectors provide the Fourier coefficients of the harmonic part of the solution. By examining the solutions of the eigenvalue problem, the initial conditions response, frequency content, and stability characteristics can be determined. The approach is applied to two and three DOF examples. For a few parameter sets, the results obtained from this method are compared to the numerical solutions.
Gizem Acar, Brian F. Feeny
Chapter 23. Harmonic Forcing of a Two-Segment Elastic Rod
Abstract
This work is on the motions of non-homogeneous elastic rods. In a previous work the natural frequencies and associated mode shapes were determined for a two-segment rod, in which the geometric and material properties were constant in each segment. Here the steady state response due to harmonic forcing is investigated using two strategies. The first employs the exact displacement equations. For harmonic forcing in time, the response is periodic and general solutions to the resulting differential equations can, in principle, be found for each segment. The constants involved are found from boundary and interface conditions and then response, as a function of forcing frequency, can be obtained. The procedure is cumbersome and problematic if the forces vary spatially, due to difficulties in finding “particular integrals”. An alternative method is developed in which geometric and material discontinuities are modeled by continuously varying functions (here logistic functions). This leads to a single differential equation with variable coefficients, which is solved numerically using MAPLE®’s PDE solver. For free-fixed boundary conditions and spatially constant force good agreement is found between the two methods, lending confidence to the continuous varying approach, which is then used to obtain response for spatially varying forces.
Arnaldo J. Mazzei Jr., Richard A. Scott
Chapter 24. An Unified Framework for Studying Gear Dynamics Through Model Reduction Techniques
Abstract
Contribution of gear, shaft and bearing stiffnesses to the gear dynamics is an important aspect that can affect the gearbox behavior. Nowadays, it is possible to simulate the gear mating with a very accurate numerical approach, but with the drawback of very huge computational effort. Gear designers in first design steps need instruments able to give good description of gear dynamics without spending much time in high performance numerical simulations. They need an easy instrument for making decisions in a short time. In this paper, an unified framework for studying gear dynamics is proposed. The gears and mechanical elements are modeled in a very simple way, reducing as much as possible the number of dofs, but maintaining the highest fidelity and with different complexity levels. This is reached using MoGeSeC master dofs selection and building a reduced parametric LTI model of each element. The gear mating model is the interface and it is handled with different nonlinear Maxwell models. By using block-oriented approach, it is possible to have a library of increasing complexity elements that depict the gear dynamics and share the same platform, so it is possible to increase the model complexity simply changing a block in the simulation framework and to compare the different approaches.
Carlo Rosso, Elvio Bonisoli
Chapter 25. Application of the Harmonic Balance Method to Centrifugal Pendulum Vibration Absorbers
Abstract
The harmonic balance method (HBM) is a powerful analysis tool for nonlinear vibrating systems, provided that the forms of the nonlinearities of the system result in a manageable algebraic system of equations. The authors of Cochelin and Vergez (J Sound Vib 324(1):243–262, 2009) created a framework that modifies the structure of the equations of motion involving a wide variety of nonlinearities into a quadratic form, which then can be approximated with HBM with as many assumed harmonics the problem needs for a satisfactory accuracy. In this work, we employ this framework for the analysis of centrifugal pendulum vibration absorbers (CPVA). The crucial step of this framework is the recasting of the variables into the required form. It has been shown that the dimensionless equations of motion for point mass CPVAs with general paths fitted to a rigid rotor can be put into the quadratic polynomial form. Two benchmark problems with known dynamical characteristics are investigated and the results show that this approach provides a powerful tool for investigating steady-state responses of these absorber systems. This will be very beneficial for design evaluations of CPVA systems where parameter values do not allow for the application of perturbation methods and/or make direct simulations very time consuming.
Mustafa A. Acar, Steven W. Shaw
Chapter 26. Development of Multi-Physics Dynamics Models for High-Frequency Large-Amplitude Structural Response Simulation
Abstract
An analytic approach is demonstrated to reveal potential pyroshock-driven dynamic effects causing temporary power losses in the Thermo-Electric (TE) module bars of the Mars Science Laboratory (MSL) Multi-Mission Radioisotope Thermoelectric Generator (MMRTG). This study utilizes high-fidelity finite element analysis with SIERRA/PRESTO codes to estimate wave propagation effects due to large-amplitude suddenly-applied pyroshock loads in the MMRTG. A high fidelity model of the TE module bar was created with ∼30 million degrees-of-freedom (DOF). First, a quasi-static preload was applied on top of the TE module bar, then transient tri-axial displacement inputs were simultaneously applied on the preloaded module. The applied displacement inputs were derived from measured acceleration signals during MMRTG shock qualification tests performed at the Jet Propulsion Laboratory. An explicit finite element solver in the SIERRA/PRESTO computational environment, along with a 3000 processor parallel super-computing framework at NASA-AMES, was used for the simulation. The simulation results were investigated both qualitatively and quantitatively. The predicted shock wave propagation results provide detailed structural responses throughout the TE module bar, and key insights into the dynamic response (i.e., loads, displacements, accelerations) of critical internal spring/piston compression systems, TE materials, and internal component interfaces in the MMRTG TE module bar. They also provide confidence on the viability of this high-fidelity modeling scheme to accurately predict shock wave propagation patterns within complex structures. This analytic approach is envisioned for modeling shock sensitive hardware susceptible to intense shock environments positioned near shock separation devices in modern space vehicles and systems.
Armen Derkevorkian, Lee Peterson, Ali R. Kolaini, Terry J. Hendricks, Bill J. Nesmith
Chapter 27. An Efficient Simulation Method for Large-Scale Systems with Local Nonlinearities
Abstract
In practice, most mechanical systems show nonlinear characteristics within the operational envelope. However, the nonlinearities are often caused by local phenomena and many mechanical systems can be well represented by a linear model enriched with local nonlinearities. Conventional nonlinear response simulations are often computationally intensive; the problem which becomes more severe when large-scale nonlinear systems are concerned. Thus, there is a need to further develop efficient simulation techniques. In this work, an efficient simulation method for large-scale systems with local nonlinearities is proposed. The method is formulated in a state-space form and the simulations are done in the Matlab environment. The nonlinear system is divided into a linearized system and a nonlinear part represented as external nonlinear forces acting on the linear system; thus taking advantage in the computationally superiority in the locally nonlinear system description compared to a generally nonlinear counterpart. The triangular-order hold exponential integrator is used to obtain a discrete state-space form. To shorten the simulation time additionally, auxiliary matrices, similarity transformation and compiled C-codes (mex) to be used for the time integration are studied. Comparisons of the efficiency and accuracy of the proposed method in relation to simulations using the ODE45 solver in Matlab and MSC Nastran are demonstrated on numerical examples of different model sizes.
Yousheng Chen, Andreas Linderholt, Thomas Abrahamsson
Chapter 28. A Modal Superposition Method for the Analysis of Nonlinear Systems
Abstract
In the determination of response of nonlinear structures, computational burden is always a major problem even if frequency domain methods are used. One of the methods used to decrease the computational effort is the modal superposition method for nonlinear systems where the modes of the linear system are used in the calculation. However, depending on the type of the nonlinearity, in order to obtain an accurate response, the number of modes retained in the response calculations needs to be increased, which increases the number of nonlinear equations to be solved. In this study, a method is proposed to decrease the number of modes used for systems having nonlinearities where the equivalent stiffness varies between two limiting values. For such systems, one can define different linear systems for each value of the limiting equivalent stiffness. In this study, it is proposed to use a combination of these linear mode shapes in the modal superposition method. It is shown that proper combination of mode shapes of different linear systems provides satisfactory results by keeping the number of modes used at a minimum. The method is demonstrated on case studies where describing function method is used in the analysis of the nonlinear system.
Erhan Ferhatoğlu, Ender Ciğeroğlu, H. Nevzat Özgüven
Chapter 29. Adaptive Harmonic Balance Methods, A Comparison
Abstract
Harmonic balance method (HBM) is one of the most popular and powerful methods, which is used to obtain response of nonlinear vibratory systems in frequency domain. The main idea of the method is to express the response of the system in Fourier series and converting the nonlinear differential equations of motion into a set of nonlinear algebraic equations. System response can be obtained by solving this nonlinear equation set in terms of the unknown Fourier coefficients. The accuracy of the solution is greatly affected by the number of harmonics included in the solution; hence, increasing the number of harmonics increases the accuracy of the solution at the expense of computational effort. Therefore, it is desirable to use an adaptive algorithm where the number of harmonics can be optimized in terms of both accuracy and computational effort. Until now, various adaptive harmonic balance methods have been formulated to perform this task. This paper presents an overview and a comparison of these adaptive harmonic balance methods in terms of their effectiveness.
Onur Sert, Ender Ciğeroğlu
Metadaten
Titel
Special Topics in Structural Dynamics, Volume 6
herausgegeben von
Dario Di Miao
Pablo Tarazaga
Paolo Castellini
Copyright-Jahr
2016
Electronic ISBN
978-3-319-29910-5
Print ISBN
978-3-319-29909-9
DOI
https://doi.org/10.1007/978-3-319-29910-5

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