Advances in Structural Vibration

Torsional vibrations are inherent in the operation of reciprocating machines, which is one of the leading causes of mechanical failures. This work analyzes the torsional vibration attenuation of a crankshaft of a single-cylinder reciprocating compressor when identical resonators are attached. The shaft is modeled by a continuous nonlinear system, considering the inertia variation of the crank-slider mechanism with rotation and under a concentrated harmonic excitation. Two main configurations are presented, without and with resonators. At first, the nonlinear and linearized systems are compared for two different crank length values. Results show that the systems present similar behaviors for a low value of the crank length. On the other hand, when the crank lengths are raised, the resonance frequencies are slightly shifted backward and the response exhibits nonlinear effects. The second case presents the system response when the resonators are attached. The performance of the resonators is evaluated for two crank length values as in the previous analysis. In both cases, the resonators can reduce the vibration amplitudes in the neighborhood of the target frequency, even when the nonlinearity is increased in the system response.

Challenging applications within the high-performance centrifugal compressor industry, such as CO₂ reinjection turbo compressors on offshore platforms, have become increasingly common. These machines operate under high pressure, necessitating equipment manufacturers (OEMs) and users to develop more sophisticated manufacturing technologies and complex acceptance tests. The frontier of manufacturers’ knowledge has been pushed by high-density gasses, which introduce uncertainties in machine design, particularly regarding their rotodynamic stability. The number of end users requiring stability verification has grown, highlighting the subsidiary risk of increased unbalance sensitivity in this turbomachinery. This risk is referred to as Rotodynamic Design Uncertainties. Despite a single machine performing satisfactorily on its OEM test foundation, there remains a risk that it may fail to operate in an offshore plant. Recognizing this little-acknowledged reality, we are conducting research to address this design anomaly: Rotodynamic Design Uncertainties. We propose small modifications to the ADX vibration monitoring system, developed by LEDAV/COPPE/UFRJ, to enable a dataset project to be carried out at PETROBRAS/REFAP, followed by subsequent analysis of the results in the LEDAV environment using the ARTEMIS System.

Two-phase flow in ducts, especially in intermittent patterns, presents unique challenges due to the complex interaction between the liquid and gas phases. This article investigates fluid–structure coupling in horizontal ducts transporting gas–liquid two-phase flow, focusing on the amplification of duct vibration at the cut-on frequencies of circumferential wave modes. This amplification, resulting from the interaction between fluid pressure waves and the duct’s structural modes, is particularly significant at specific frequencies where energy transfer occurs between the fluid and the structure. Using acceleration, pressure, and void fraction measurements, the study demonstrates that the interaction between fluid pressure waves and the duct’s structural modes leads to a significant increase in vibration at specific frequencies. This amplification occurs near the cut-on frequencies of circumferential modes, where energy transfer occurs between the fluid and the structure. The research explores the localized nature of this coupling, utilizing the coherence function to show that the coupling is stronger in specific regions of the duct. Additionally, the time-domain modulation of the vibrational response caused by the passage of bubbles and liquid pistons is investigated. The results demonstrate that the bubble passage frequency can be estimated from the demodulation of the acceleration signal filtered at the cut-on frequencies. This finding suggests that the duct’s vibrational response can be used as a non-intrusive indicator of the void fraction in two-phase flows.

The application of smart materials in rotating systems as vibration attenuators is well-established due to their vibration reduction capabilities. One of the most common types of smart materials used is Shape Memory Alloys (SMA), which exhibit property changes in response to temperature (shape memory effect—SME) or mechanical stress (superelasticity—SE). The objective of this research is to compare and analyze the manufacturing of superelastic NiTi blade-type springs, considering different heat treatment methods, mechanical forming processes, and fabrication techniques (shape setting), with the aim of achieving a balance in properties. By optimizing these factors, it was possible to obtain a final austenitic temperature of 14.88 °C, an increased hysteresis damping of 78.44%, and a rupture strength of 1285.23 MPa. These results demonstrate the high potential of the springs in passive vibration reduction in rotating systems.

The accurate prediction of lateral vibration in beams subjected to axial loads is of great practical interest due to its wide use in describing the dynamic behavior of structures in the field of civil, mechanical, and aerospace engineering. A distinct example of its application can be found in problems involving overhead cables of transmission lines, for which the corresponding Euler–Bernoulli beam model is widely used. Although the analytical formulation for calculating natural frequencies and mode shapes for beams under tensile axial loading is well known and developed, it is worth noting that in certain applications, such as in the case of overhead cables, the results obtained may exhibit numerical instabilities for some boundary conditions. In the vast majority of studies, the mode shapes are described in terms of trigonometric and hyperbolic functions, despite the fact that hyperbolic functions tend to grow rapidly to infinity as their argument increases, which can cause numerical errors, especially in the vicinity of the beam supports. On the other hand, numerical simulations indicate that more accurate and reliable results can be obtained when the analytical solutions are expressed by linear combinations of trigonometric and exponential terms. In this context, the present work aims to compare the two aforementioned ways of describing the analytical solutions for calculating natural frequencies and their respective mode shapes of vibration with respect to overhead cables of transmission lines. In this effort solutions are developed for two classical boundary conditions (fixed–fixed and fixed-simply supported) and one non-classical boundary condition (simply supported with torsional springs). Numerical simulations are carried out in the MATLAB® environment. A significant gain is observed in the use of the preferred formulation, especially in terms of a more accurate prediction of mode shapes for the type of structure under consideration.

Reduction of non-revenue water is one of the main goals of the water industry. It is estimated that 40% of water pumped via distribution systems in Brazil is lost, but there are states which have losses of 70%. One way of minimizing this problem is by massive investment in replacing old metallic pipes by plastic pipes made from PVC (Polyvinyl Chloride) and HDPE (High Density Polyethylene) material. Furthermore, early detection and location of leaks plays a major role in reducing losses. This can be conducted using vibro-acoustics techniques, but there are problems with plastic pipes compared to metallic pipes, especially when using leak noise correlators. This is because the leak noise that propagates through the pipe is heavily attenuated in plastic pipes reducing the amplitude and hence distance that this noise can propagate. Leak noise correlators use knowledge of the leak noise velocity and an estimate of the difference between the arrival times of the leak noise at two sensors placed on the pipe at available access points. Generally, the pipe geometry (wall thickness and pipe nominal radius) and its Young’s modulus have a profound effect on leak noise attenuation and velocity. Moreover, the surrounding medium also has an additional effect. In this paper some web-based software is described that simulates different scenarios to help users of leak noise correlators to understand the physics behind the problem and to help them select the properties of some filters that need to be set to obtain reliable results. The software is based on a wave-type model which takes into account the pipe vibration response due to excitation by a leak. Inputs to the model are the pipe geometry, material properties of the pipe and surrounding medium, distance between the sensors and sensor type (accelerometer, geophone and hydrophone). These parameters are then used to estimate the leak velocity, time delay, frequency bandwidth (CPSD-Cross-Power Spectral Density) and leak location, which are given in a user-friendly graphical interface.

The rise in pollution has prompted an increased demand for sustainable materials. In this review, we explore studies that investigate natural materials for acoustic absorption panels. This chronological literature review surveys studies that consider natural fibers for sound absorption, considering their technical feasibility by tabulating the Noise Reduction Coefficient. We collected and analyzed articles from Scopus, Engineering Village, Google Scholar, and ScienceDirect databases. For the selection of fibers, the following criteria were applied: the sound absorption coefficient must be obtained experimentally for greater accuracy, be single-layered, not present any added binder, have tables or graphs of the sound absorption coefficient by frequencies of at least 250–2000 Hz, and the difference in thickness between the thinnest and thickest layer tabulated should be a maximum of 0.05 m. NRC revealed low values for banana pseudostem (0.15), cotton (0.30), corn fiber (0.30), and cork (0.30). On the other hand, other fibers such as sheep wool (0.70), kenaf (0.70), coconut fiber (0.50), and betung bamboo (0.50) demonstrated exceptional results, confirming that natural fibers are viable options for sound absorption purposes.

Operational Modal Analysis (OMA) extracts modal parameters of systems that are excited by unknown ambiental excitation, being broadly used in the monitoring of civil structures. In the past decades, research has been made to enable the application of OMA in rotating machines, dealing with challenges such as harmonic excitation, nonlinearities, and the lack of proper excitation. With the popularization of machine learning techniques, many researchers have been using these tools to overcome some challenges in this research field. Clustering techniques, that can group information about datasets without prior knowledge of their characteristics, has been used along with statistical methods to automate OMA so that it can be used for condition monitoring. Recently, automatic OMA (AOMA) was applied to rotating machinery data. This paper evaluates one of these AOMA algorithms, successfully tested with data from a test rig with a rotor supported by hydrodynamic bearings, in a more complex dataset, with data from a rotor supported by magnetic bearings and influenced by gas seal. The results show that the proposed algorithm can extract modal parameters close to the ones extracted by EMA and by the mathematical modeling of the test rig, being robust even when a more complex system is analyzed.

This work investigates a novel metamaterial concept using the Wave-based Finite Element Method. The metamaterial comprises a periodic-like structure manufactured through fused filament deposition, featuring internal cavities filled with water. Experimental characterization of the dynamics of the periodic system without internal fluid confirms good agreement with numerical predictions obtained through frequency response function measurements. Furthermore, the dynamic behavior of the two-phase periodic metastructure is experimentally examined, where waves interact within the heterogeneous medium consisting of both fluid and solid phases. In this case, the resulting wave characteristics depend on the properties of both phases. It was shown that the fluid-filled metastructure exhibits vibration reduction through the whole frequency range compared to the case lacking internal fluid. Additionally, it was seen that the frequency range near the second attenuation band of the periodic metastructure without fluid can be enlarged after the fluid inclusion within the cavities of its unit cells, as a consequence of mass increase and damping effects. Consequently, this work presents a promising avenue for metastructure design, with potential applications in structural dynamics and acoustics.

Renewable energy sources are gaining global attention as solutions to the challenges of fossil fuels. Solar, wind, hydro, geothermal, and biomass energy harnesses continuously replenished resources, reducing environmental impacts and lessening reliance on non-renewables. An emerging concept in solar energy is the installation of floating photovoltaic plants on water bodies using platforms to mount solar panels. However, variable solar radiation intensity due to location requires efficient utilization, and intermittency can be mitigated by energy storage. Adaptable solar panel positioning through tracking systems is crucial for optimizing sunlight exposure. While these systems are common on land, their application to floating plants is complex. This study aims to evaluate the potential benefits of incorporating solar tracking systems in floating photovoltaic plants, specifically in the Amazon region of Brazil. Mathematical models and simulations will analyze panel dynamics under equatorial conditions to improve the energy production efficiency and sustainability of Amazon floating solar installations. This research contributes to the advancement of renewable technology and sustainable energy practices in the region.

In oil exploration and production, drilling is one of the most important processes. Undesirable vibrations, intrinsic to the drilling process, can lead to fatigue failure, resulting in loss of efficiency due to downtime and, consequently, loss of productivity and high costs. The present work proposes the analysis of fatigue in drill strings under torsional vibrations with the stick–slip phenomenon, considering the frequency domain (or spectral) approach as an alternative to the time domain approach. The stick–slip occurs when the torque imposed by the top drive is not enough to overcome the resistance offered by the environment and, in the process of rock-bit interaction, the bit becomes stationary for a period, causing large fluctuations in the angular speed and, in turn, in shear stress, characterizing failure by fatigue. Spectral Methods for fatigue life analysis, although recent, have shown great potential in several applications and therefore, there is much to be explored given their viability in engineering problems due to the lower computational cost and time processing, being advantageous for complex problems with large amounts of data. In this approach, concepts such as Power Spectral Density (PSD) are used to calculate the Spectral Moments, employed in the various methods of this nature for determining fatigue life. The Dirlik and Tovo-Benasciutti Methods, being widely used not only in academia, have proved to be advantageous. These methods are compared with the rainflow method, used as a reference.

The interaction between the turbulent wake of the rotor and the stator vanes has been identified as one of the broadband noise main sources in a turbofan engine, in addition to the tonal noise. Studies inspired by the owl’s silent flight have shown that the application of certain natural properties of its wings, such as the serrated pattern on the leading edge (Wavy Leading Edge), are effective for reducing aircraft noise. The objective of this work is to analyze it on the stator vanes source diagnostic test (SDT) low-noise model of the EESC/USP rig-fan bench. The geometry of the new vanes was defined and printed for the experimental tests and the analysis of noise emissions. The bench has acoustic instrumentation for data acquisition, and for its spectral analysis, the Welch method is used in signal processing. Tests were carried out with fan rotation speeds from 800 to 1800 rpm for both stators. The acoustic measurements of the WLE stator showed a reduction of 1.5–4 dB in low and medium frequencies in broadband noise, while there was an increase at high frequencies of up to 1.2 dB. From this study, it is understood that there is no ideal serration that reduces noise for all types of conditions that are imposed; nevertheless, it is more efficient at low rotation speeds, which could be used to improve the aircraft landing or takeoff conditions.

In drill strings, stick-slip vibrations are a particular case of torsional vibrations, which cause large fluctuations in the angular velocity at the bottom of the well, resulting in premature wear of the bit and other components of the drilling system. This work introduces a sliding mode controller designed to regulate the torque applied to the top of the column in order to mitigate or eliminate stick-slip vibrations in the dynamic behavior of the drillstring. The drillstring is modeled as a two-degree-of-freedom lumped parameter model, representing its torsional behavior at both the top of the column and the bottom hole. The controller stability analysis is performed from the Lyapunov stability theory, in order to guarantee the system convergence to the desired state. Initially, the behavior of the system without the action of the controller is investigated and later, its influence on the dynamic behavior of the system is analyzed. For the studied cases, the controller was able to eliminate stick-slip vibrations, keeping the column angular velocity at the desired value, presenting results in agreement with experimental and field data. The chattering behavior is also verified and its elimination through a signal saturation function, guaranteeing an adequate behavior to the developed controller.

Four-Wheeled Autonomous Vehicles have emerged as an innovative technology with significant potential to revolutionize the transportation industry. In the past decade, research efforts in this field aim to develop strategies ranging from the development of Advanced Driver Assistance Systems (ADAS) to the creation of fully autonomous navigation strategies. In this context, mathematical models of the four-wheeled robots are an essential part of developing autonomous navigation techniques. Whether using complete or simplified mathematical models of the vehicle, the control synthesis requires accurate model parameters. This work presents experimental methods to obtain some of the main physical parameters that determine the dynamic model of four-wheeled vehicles, including its mass, center of gravity, and principal moments of inertia. The uncertainties of these measurements are presented aiming to estimate the reliability and precision of the results obtained. Furthermore, a cornering stiffness estimation method based on the vehicle lateral dynamics is proposed. Experimental results obtained from a four-wheeled 1:5 scaled electrical vehicle, with real electronic differential distribution are presented.

Wind turbine gearboxes are subjected to fluctuating torque conditions, which may generate vibration problems. This paper analyzes the mesh displacement of a helical gear pair, inspired by the challenges posed in simulating the high-speed stage of the wind turbine gearbox. The detailed mesh model, considering static transmission error, time-varying mesh stiffness, and backlash, associated with a 12-degree-of-freedom gear pair model better represents this system. The model also takes into account a load torque factor to prevent over-speed conditions. Results show a comparison between the system’s response in the absence of backlash and when backlash is introduced. When there is no backlash, both the driving and driven gears exhibit quasi-periodic behavior. When there is a backlash, single-sided impacts occur along the permanent response of the gear system, a severe vibration condition that may cause damage to the system.

A sustainable development is essential for the future of the planet. Therefore, the technology must satisfy current needs without compromising the ability of future generations to meet their own needs. Hence, this work assesses the stability conditions of a free piston engine powering a linear permanent magnetic generator. This kind of machine uses renewable fuels and has greater energy efficiency. The numerical model used to do it englobe three physical domains: electromagnetism, dynamics, and thermodynamics. The proposed machine works in its resonance frequency. Therefore, a sensitivity analysis was played out, interpreting how the three variables influence the engine cycle stability: the inlet pressure, air–fuel ratio and the associated mechanical spring stiffness. It was shown that when working in resonance the machine is more robust and less influenced by the thermodynamics conditions.

This chapter investigates the use of Magnetorheological (MR) dampers in aircraft landing gear, aiming to improve safety, efficiency, and comfort during the landing. MR dampers can adjust the damping force in real time, adapting its behavior to specific needs during this critical phase of the flight. The study considers the Spencer dynamic model, which includes non-linear characteristics, such as that the hysteretic effect, and the decrease in the damping force if the velocity approaches zero. The work introduces force decomposition to the actuator into hydraulic, pneumatic, and active components. The landing gear system is modeled with two degrees of freedom, taking into account the vertical oscillations. The analysis is conducted by numerical simulations using the fourth-order Runge–Kutta integrator method. The results are evaluated in terms of shock absorption efficiency and vibration comfort. The results obtained demonstrate the potential of the technologies based on MR dampers to improve flight safety and efficiency. Furthermore, these technologies have potential industrial applications to make landings more comfortable for passengers.

In recent years, the implementation of damping systems in civil structures has gained considerable attention, with emphasis on special building projects under dynamic loadings. In this scenario, due to their mechanical simplicity and controllable properties, Magneto-Rheological Elastomer (MRE) has stood out as providing an interesting alternative for vibration isolation. In these materials, the magnetic particles present in the elastomeric matrix are easily polarized in the presence of an external magnetic source, generating non-linear and reversible changes in the material, within a few milliseconds. In this way, the present work investigated numerically the efficiency of a certain damping system with MRE in isolating vibrations at the base of a bridge superstructure. The elastomer was simulated as a visco-elastic material of Kelvin–Voigt, and its stiffness and viscosity were regulated for five different scenarios. The unidimensional equivalent mechanical model was considered a single-degree-of-freedom (SDOF) system, and the ground motion generated by seismic excitations corresponded to shear excitations at the base. The base-isolated tests provided acceleration transmissibility under the different applied magnetic fields. It was observed that the viscoelastic support (VS) was able to shift the resonance frequency and the attenuation of transmissibility peak efficiently through field control. Moreover, with an adequate approach in the frequency domain, the random signal of a real earthquake was also inserted into the system for the evaluation of the isolator material. The findings demonstrated the good performance of the proposed MRE and its possibility of seismic vibration mitigation.

In this work, the modal and the forced vibration dynamic analyses are carried out in a railway vehicle model with 25 degrees of freedom. The objective of this work is to study the dynamic characteristics (modes and frequencies of vehicle vibration), as well as the analysis of forced vibration, allowing the simulation of resonance conditions and their critical speeds, important for the study of vehicle stability, safety, and passengers’ comfort. The tridimensional model has a passenger car body, two bogies, and four wheelsets. Models of vertical, lateral, and rotational track irregularities are used. In mechanical contact between wheels and rails, the theories of Hertz and Kalker, and also Vermeulen and Johnson are used. The equations of motion of the coupled system are numerically integrated using the Newmark Method, in the MatLab software. It is possible to conclude that the railway track irregularities associated with critical traffic speeds produce vibrations in the vehicle. Due to the damping of the system, these vibrations are attenuated between the rigid bodies through the primary suspensions, between the wheels and bogies; and secondary suspensions, between the bogies and the passenger car body.

Limb tremors, prevalent in neurodegenerative diseases like Parkinson’s disease, often lead to social discomfort and restrict daily activities. In addressing this challenge, using vibration-attenuating devices emerges as a promising technique, considering drug sensitivity, treatment invasiveness, and therapeutic efficacy. This study delves into optimizing the configuration of mechanical vibration absorbers to mitigate limb tremors in Parkinson’s patients, exploring variations in absorber position and size. Controller efficacy is assessed by analyzing response magnitude and amplitude reduction across frequency and time domains. Findings underscore the significant tremor amplitude reduction achieved through vibration-absorbing devices, with parallel absorbers demonstrating the most effective configuration. Additionally, the study investigates the impact of employing more than two absorbers in parallel along the forearm and explores novel absorber designs tailored for limb tremor control. Analytical upper limb numerical models and passive controls are employed to estimate limb vibration characteristics and evaluate control efficiency across varying levels of tremor pathology excitation.

This paper presents a finite element analysis of sloshing in 3D water tanks using a pressure-based Eulerian approach. The fluid domain is discretized by isoperimetric elements (FLUID220) that exhibit a quadratic pressure behavior and are used for modeling the fluid domain. Three examples (a rectangular cavity, a square-tuned liquid column damper (TLCD), and a bidirectional-tuned liquid multicolumn damper (TMLCD)) were modeled with rigid contours and a free surface to study uncoupled liquid reservoirs. Free vibration and harmonic analysis were performed to determine dynamic parameters of the three cases. For the rectangular cavity, the numerical results are compared to analytical solutions and previous numerical and experimental studies. The numerical solutions present acceptable relative error (inferior to 0.2% relative error) when compared to analytical solutions. For the TLCD example, the numerical results were validated using experimental results and previous numerical studies, presenting acceptable errors (6% relative error). For the third case, the modal results were compared to the analytic solution and previous works returning an error of 2.75 and 3.14% relative to the experimental values and the harmonic analysis presented a reduction of 44.88% in the amplitude of displacement of the system, thus validating this approach of analysis in the development of this kind of device.

To ensure that wind turbine towers remain economically viable, they must be able to operate for prolonged periods. Therefore, analyzing the dynamic behavior of the structure is crucial to extend its lifespan and optimize its efficiency. In this study, we investigate the attenuation of vibrations in a wind turbine tower using metamaterials. For this analysis, a discrete model of the tower is considered. The finite element method (FEM) is employed in the numerical simulation using a routine developed in Python. The wind effect is described by force signals obtained through a statistical method, using Weibull Probability Distribution as random distribution and Kaimal’s power spectral density to simulate the speed wind fluctuations caused by turbulence. The action of the wind is represented by a concentrated force at the upper end of the tower, specifically concentrated at the nacelle. To reduce the tower vibration, identical metamaterials are placed in different positions along the tower and the performance is evaluated considering attenuation of the first and the fifth modes.