Vibration

The vibration control in structural design has long been a critical area of study, particularly in mitigating undesirable resonant vibrations using dynamic vibration absorbers (DVAs). Traditional approaches to tuning DVAs have relied on complex mathematical models based on Newtonian or Euler–Lagrange equations, often leading to intricate systems requiring simplification of the analysis of multi-degree-of-freedom structures. This paper introduces a novel modeling approach for analyzing DVAs based on the concept of global admittance, which stems from mechanical admittance and network simplifications. This model streamlines the representation of structures with DVAs as one-degree-of-freedom systems coupled with a global admittance function, which emulates additional damping coupled to the primary structure. In this work, global admittance functions are determined by the independent analysis of the mechanical networks of the DVA, restructuring the process of obtaining the system’s transfer function. The model was validated using different classical DVA configurations, demonstrating total accuracy in its applicability across designs concerning conventional modeling. Our most remarkable finding was that the dimensionless function, ${\gamma }_g\left(\mathsf{\Omega }\right)$, resulting from the global admittance, partially decouples the dynamics of the DVAs from the primary structure, facilitating the implementation of passive vibration control strategies in more realistic structural models. Additionally, this work establishes a significant advancement in vibration control analysis, providing a flexible tool for control strategies in real-world structural systems. Full article

Noise, vibration and harshness analyses are of great interest for the latest developments of the gearboxes of electric vehicles. Gearboxes are now the main source of vibrations, since electric powertrains are much quieter than internal combustion engines. Traditionally, the simulation of the non-linear gear dynamics is studied by first performing a series of preliminary static analyses to compute the static transmission error (STE). The STE (i.e., in the form of varying mesh stiffness) is then accepted as the system’s excitation source to compute the dynamic transmission error (DTE). This paper presents a novel approach to analyze the non-linear dynamics of gears which does not require any preliminary static analyses. The method consists of a frequency–domain approach based on the Harmonic Balance Method (HBM) and the Alternating Frequency–Time (AFT) scheme, allowing for much faster simulations when compared to the widely used direct–time integration (DTI). The contact between the teeth is modeled as intermittent and penalty based with a varying gap. The time–varying gap between the teeth is initially approximated to a step function that guarantees the design contact ratio. The methodology introduced is tested on a lumped parameter model of a spur–gear pair already proposed and simulated in the literature. The results obtained with the novel approach are compared with the DTI simulation of the model as a reference. The excellent match between the different approaches validates the reliability of developed methodology. Full article

Driven piles are a common geotechnical solution for foundations in weak soil profiles. However, hammer impacts during the driving process can generate excessive levels of ground vibration, which, in extreme cases, can affect nearby structures and people. Due to the complexity of wave propagation in soils, the accurate prediction of these vibrations typically requires advanced numerical modeling approaches. To address this challenge, a surrogate modeling framework was developed by integrating Artificial Neural Networks (ANNs) and Extreme Gradient Boosting (XGBoost), trained on a synthetic dataset generated from an experimentally validated numerical model. The proposed surrogate model enables the rapid prediction of ground vibration characteristics, including peak particle velocity (PPV) and frequency content, across a broad range of soil, pile, and hammer conditions. In addition to its predictive capabilities, the tool allows users to design a specific mitigation measure (open trench) and compare the vibration levels with international standards. Experimental validation confirmed the model’s ability to replicate field measurements with acceptable accuracy. The expedited prediction tool is available as supplemental data and can be used by other researchers and technicians for quick and accurate ground vibration predictions. Full article

A new frequency–amplitude formula by improving an ancient Chinese mathematics method results in a modification of He’s formula. The Chinese mathematics method that expresses via a fixed-point Newton form is proven to be equivalent to the original nonlinear frequency equation. We modify the fixed-point Newton method by adding a term in the denominator, and then a new frequency–amplitude formula including a parameter is derived. Upon using the new frequency formula with the parameter by minimizing the absolute error of the periodicity condition, one can significantly raise the accuracy of the frequency several orders. The innovative idea of a linearly perturbed frequency equation is a simple extension of the original frequency equation, which is supplemented by a linear term to acquire a highly precise frequency for the nonlinear oscillators. In terms of a differentiable weight function, an integral-type formula is coined to expeditiously estimate the frequency; it is a generalized conservation law for the damped nonlinear oscillator. To seek second-order periodic solutions of nonlinear oscillators, a linearized residual Galerkin method (LRGM) is developed whose process to find the second-order periodic solution and the vibrational frequency is quite simple. A hybrid method is achieved through a combination of the linearly perturbed frequency equation and the LRGM; very accurate frequency and second-order periodic solutions can be obtained. Examples reveal high efficacy and accuracy of the proposed methods; the mathematical reliability of these methods is clarified. Full article

This study proposes a piezoelectric device for vibration damping in satellite solar panels. The design features a structural arrangement with piezoelectric stacks configured in a V-shape and hinged to the main yoke structure. The satellite structure is modeled using an Euler–Bernoulli beam finite element framework, incorporating the electro-mechanical coupling of active elements through equivalent nodal piezoelectric loads. Various shunt circuits are designed to mitigate vibrations, with a parametric study conducted to optimize the key circuit parameters. Additionally, a filtered PID active suppression system is developed and tuned using a meta-heuristic algorithm to determine optimal controller gains. Numerical simulations are performed to evaluate and compare the effectiveness of the proposed vibration suppression systems, demonstrating the efficiency of the smart structure configuration and providing performance analysis. Full article

This research explores the dynamic characteristics of composite nano-beams with a hybrid cellular structure (HCS) core, composed of two segments with distinct unit cell configurations, and face sheets reinforced with carbon nanotube (CNT) composites. By considering three-layered sandwich beams with aluminum cores of varying unit cell angles, the study explores a broad spectrum of achievable Poisson’s ratios. The top and bottom face sheets incorporate CNTs, distributed either uniformly or in a functionally graded manner. The governing equations are derived using Eringen’s nonlocal elasticity framework and the modified theory of shear deformation, with solutions obtained via the Galerkin method. A detailed parametric analysis is conducted to evaluate the effects of CNT content, arrangement configurations, hybrid core cellular angles, nonlocal parameters, and slenderness ratio (L/h) on the dimensionless natural frequencies of sandwich nanobeams with hybrid cellular cores. A key contribution of this study is the presentation of natural frequencies for nanobeams with hybrid cellular cores and composite face sheets reinforced with functionally graded CNTs, derived from advanced theoretical formulations. These findings offer new insights into design optimization and highlight the potential applications of hybrid cellular sandwich nanobeams in cutting-edge engineering systems. Full article

This paper analyzes vibrations induced by a moving bogie passing through a single-layer railway track model. The emphasis is placed on the possibility of unstable behavior in the subcritical velocity range. All results are presented in dimensionless form to encompass a wide range of possible scenarios. The results are obtained semi-analytically, however, the only numerical step involves solving the roots of polynomial expressions. No numerical integration is used, allowing for the straightforward solution of completely undamped scenarios, as damping is not required for numerical stability. The vibration shapes are presented in the time domain in closed form. It is concluded that increased foundation damping worsens the situation. However, in general, the risk of instability in the subcritical velocity range for a moving bogie is lower than that of two moving masses, particularly for higher mass moments of inertia of the bogie bar and primary suspension damping. The study also examines how the results change when a Timoshenko-Rayleigh beam is considered instead of an Euler-Bernoulli beam. Although some cases may appear academic, it is demonstrated that instability in the supercritical velocity range cannot be assumed to be guaranteed. Full article

Rhythm is fundamental in many physical and biological systems. Rhythm is relevant to a broad range of phenomena across different fields, including animal bioacoustics, speech sciences, and music cognition. As a result, the interest in developing consistent quantitative measures for cross-disciplinary rhythmic analysis is growing. Two quantitative measures that can be directly applied to any temporal structure are the normalized pairwise variability index (nPVI) and rhythm ratios (r_k). The nPVI summarizes the overall isochrony of a sequence, i.e., how regularly spaced a sequence’s events are, as a single value. Meanwhile, r_k quantifies ratios between a sequence’s adjacent intervals and is often used for identifying rhythmic categories. Here, we show that these two rhythmic measures are fundamentally connected: the nPVI is a summary static of the r_k values of a temporal sequence. This result offers a deeper understanding of how these measures are applied. It also opens the door for creating novel, custom measures to quantify rhythmic patterns based on a sequence’s r_k distribution and compare rhythmic patterns across different domains. The explicit connection between nPVI and r_k is one further step towards a common quantitative toolkit for rhythm research across disciplines. Full article

The objective of this study was to examine the seismic behavior of steel buildings equipped with linear and nonlinear viscous dampers that may exhibit variable capacity. More specifically, nonlinear time history analyses were conducted on two three-dimensional steel buildings utilizing a number of recorded seismic motions. Initially, it was assumed that the distribution of viscous dampers was uniform along the height of the building and, thus, the damping coefficients used to size the viscous dampers were derived. Subsequently, nonlinear time history analyses were performed assuming either linear or nonlinear viscous dampers, which may operate at 80%, 100%, and 120% of their capacity. The response parameters extracted by these analyses included the base shear (structural and inertial), the inter-story drift ratio (IDR), the residual inter-story drift ratio (RIDR), the absolute floor accelerations, the formation of plastic hinges, and the forces experienced by the dampers. On the basis of these response parameters, the most appropriate type of viscous dampers was indicated. Full article

To cut a clod of soil containing the roots of trees in nurseries, a semi-circular vibrating blade digging machine with diameters up to 1.2 m is increasingly used. The heart of the machine is the mechanical oscillator that produces an excitation torque supplied to the blade together with the cutting torque of the soil. The advantage of the vibrating blade is a reduction in the cutting torque up to 70%. This advantage led to the present study of the extension to blades of even 1.8 m for the digging of very large trees. To build an oscillator suitable for all blade sizes (from 0.6 to 1.8 m), it was necessary to equip it with nonlinear (quadratic) springs, since with traditional linear springs, it would not be versatile. The design and simulation of its operation required the development of a new mathematical model. Therefore, an approximate solution of the differential equation of the forced vibration with quadratic springs and dry friction between the blade and soil was developed, aimed at calculating the maximum blade displacement and the phase lag. These quantities, together with the cutting time, had to satisfy certain values to ensure the maximum reduction in the cutting torque (−70%). After the construction of the oscillator, it was coupled with all the blades (0.6, 0.9, 1.2, and 1.8 m) for experimental tests. For all diameters, the oscillator was able to optimally vibrate the blades, preventing the springs from reaching the end of the stroke when cutting the soil. Measuring the maximum blade displacement compared with the calculated one provided a good accuracy of the mathematical modeling, resulting in a mean error of 5.6% and a maximum error of 7.2%. Full article

This paper is the first to offer a digital-twin of the Energy Rebound Testing Device, which is specified by the National Collegiate Athletic Association for the sport of basketball. This digital-twin replicates the physical ERTD, which was previously studied empirically. This paper merges the original finite element analysis of a basketball rim and backboard with the finite element analysis of the Energy Rebound Testing Device, using the ANSYS Workbench 2024R2, student edition. The first modal model was of the ERTD in isolation in the Workbench Modal Analysis system, and the natural frequency modeled via finite element analysis, 12.776 Hz, compared favorably with the empirical modal analysis value of 12.72 Hz. The second modal model, also in the Workbench Modal Analysis system, was of the ERTD rotatably attached to a basketball rim and backboard. This second model was then imported into the Transient Structural Analysis system and first used to confirm the hypothesis that the ERTD did indeed transfer kinetic energy from its drop-mass to the basketball rim and backboard. Then, an energy transfer surface was used to confirm the hypothesis that this kinetic energy transfer was responsive to changes in rim and backboard stiffness via changes in the respective Young’s moduli. Finally, a second-generation ERTD was proposed, where the control box transmits its energy readings to “the cloud” via the WiFi capabilities of the Arduino UNO R4 WiFi. Full article

Based on a reduced model of a linear section of a steel gas pipeline between four supports and with a crack-like through defect, ANSYS FE software is used in this study to develop numerical approaches regarding three key parameters of a composite bandage in the form of a circular lining: the type of composite material and the length and thickness of the composite lining. The approach for assessing the static strength of a damaged section of a steel pipeline with a composite lining that is subjected to internal pressure allows for the determination of the optimal thickness of the composite lining itself, which is equal to the indicator “50.0% to 62.5%” of the pipe thickness. Furthermore, the approach for assessing the dynamic strength and analyzing the possible destruction of the reinforced damaged section of a pipeline experiencing an increase in internal pressure allows for the determination of the optimal length of the composite lining, which, in turn, should be at least 241.2 mm. This work also considers cases when there is no internal pressure and the steel pipeline is subjected to critical pressure. It is found that the frequency spectrum of pipeline oscillations without a composite lining is higher than that with a composite lining. The difference between the corresponding dynamic oscillations increases with the thickness or the length of the composite lining. In the absence of internal pressure, all frequencies of the steel pipeline with a crack closed by a composite lining are paired. This pairing is disrupted when the pipeline is subjected to critical internal pressure, and the difference between its oscillation frequency spectrum without and with a composite lining increases. In this case, the oscillation modes significantly differ from those of the same pipeline structure when unloaded. The results ensure the optimal stress distribution in the defect area of a steel pipeline wall and improve the reliability and safety of pipelines under seismic actions. The approach for increasing dynamic strength and eliminating defects can be applied to pipelines with a large diameter regardless of the causes and geometric dimensions of the defects. Moreover, this approach to increasing the strength can be used by various industries and/or institutes which work on the design of new, earthquake-resistant, reinforced pipelines. Full article

This paper proposes a unified reliability analysis framework for mechanical and structural systems equipped with Tuned Mass Dampers (TMDs), encompassing single-degree-of-freedom (1-DOF), two-degrees-of-freedom (2-DOF), and ten-degrees-of-freedom (10-DOF) configurations. The methodology integrates four main components: (i) probabilistic uncertainty modeling for mass, damping, and stiffness, (ii) Latin Hypercube Sampling (LHS) to efficiently explore parameter variations, (iii) Monte Carlo simulation (MCS) for estimating failure probabilities under stochastic excitations, and (iv) machine learning models, including Random Forest (RF), Gradient Boosting (GB), Extreme Gradient Boosting (XGBoost), and Neural Networks (NNs), to predict structural responses and failure probabilities. The results demonstrate that ensemble methods, such as RF and XGBoost, provide high accuracy and can effectively identify important features. Neural Networks perform well for capturing nonlinear behavior, although careful tuning is required to prevent overfitting. The framework is further extended to a 10-DOF structure, and the simulation results confirm that machine learning-based models are highly effective for large-scale reliability analysis. These findings highlight the synergy between simulation methods and data-driven models in enhancing the reliability of TMD systems under uncertain inputs. Full article

To quantify the effect of frequency-range-specific hand–arm vibration (FRS-HAV) exposure on the risk of musculoskeletal disorders of the upper limb (UMSDs), we performed an analysis among the study sample of the German Hand–Arm Vibration Study. In total, 206 cases and 609 controls were included in this analysis. Cases were new patients with UMSDs. Controls were a random sample of people with compensable occupational injuries. Standardized personal interviews were performed among cases and controls. In addition to leisure activities and comorbidities, detailed work histories were obtained from all participants. To quantify FRS-HAV exposures, a database of vibration measurements of over 700 power tools was used. This database allows detailed quantification of vibration exposure over long periods of time. A dose–response relationship between FRS-HAV exposure and UMSDs was quantified using conditional logistic regression analyses. After adjustment for relevant confounders, consistent and statistically significant exposure–response relationships were observed between cumulative vibration exposure and UMSDs. The effect of vibration exposure on the risk of UMSDs is mainly concentrated in the frequency range ≤ 50 Hz. This suggests that the current ISO frequency-weighting curve for quantifying hand–arm vibration exposure is reasonable and can be used for vibration-related risk assessment, especially for musculoskeletal disorders. Full article

In many tasks of railway vibration, the structure, that is, the track, a bridge, and a nearby building and its floors, is coupled to the soil, and the soil–structure interaction and the damping by the soil should be included in the analysis to obtain realistic resonance frequencies and amplitudes. The stiffness and damping of a variety of foundations is calculated by an indirect boundary element method which uses fundamental solutions, is meshless, uses collocation points on the boundary, and solves the singularity by an appropriate averaging over a part of the surface. The boundary element method is coupled with the finite element method in the case of flexible foundations such as beams, plates, piles, and railway tracks. The results, the frequency-dependent stiffness and damping of single and groups of rigid foundations on homogeneous and layered soil and the amplitude and phase of the dynamic compliance of flexible foundations, show that the simple constant stiffness and damping values of a rigid footing on homogeneous soil are often misleading and do not represent well the reality. The damping may be higher in some special cases, but, in most cases, the damping is lower than expected from the simple theory. Some applications and measurements demonstrate the importance of the correct damping by the soil. Full article

Flexure-based Stirling cryocooler compressors are a critical technology in providing cryogenic temperatures in various advanced engineering fields, such as aerospace, defense, and medical imaging. The most challenging problem in the design of this type of compressor is achieving a precise alignment that preserves small gaps between the components moving relative to each other and avoids severe friction and wear. This paper introduces a novel experimental procedure for designing Stirling cryocooler compressors, leveraging a recently developed nonlinear experimental modal analysis method known as response-controlled stepped-sine testing (RCT). The alignment in a compressor prototype was significantly improved in light of a series of RCT with base excitation. The enhanced compressor design was subsequently validated though a series of constant-current tests, which confirmed the elimination of the sticking/locking phenomenon observed in the initial design. Furthermore, an indirect harmonic force surface (HFS)-based approach proposed for weakly nonlinear systems was extended to identify the high and nonlinear damping (up to a 65% hysteretic modal damping ratio) observed in the enhanced compressor design due to excessive friction. As another contribution, it was shown that the extrapolation of the HFS gives accurate results in the prediction of the nonlinear modal parameters at response levels where no experimental data are available. In light of these findings, it was concluded that the enhanced design needs further design modifications to further decrease the friction and wear between the moving parts. Overall, this study provides valuable insights for designing cryocooler compressors, with implications for aerospace and medical applications. Full article

In mechanical engineering, the building industry, and many other branches of industry, vibration machines are widely used, in which circular and directed oscillations predominate in the form of movement of the working equipment. This article examines methods for generating asymmetric oscillations, which are estimated by a numerical parameter, namely by the coefficient of asymmetry of the magnitude of the driving force when changing the direction of action in a directed motion within each period of oscillations. It is shown that for generating asymmetric mechanical vibrations, vibration devices are used, consisting of vibrators of directed vibrations, called stages. These stages form the total asymmetric driving force. The behavior of the total driving force of asymmetric vibrations and the working equipment of the vibration machine are described by analytical equations, which represent certain laws of motion of the mechanical system. This article presents a numerical analysis of methods for obtaining laws of motion for a two-stage, three-stage, and four-stage vibration device with asymmetric oscillations. An analysis of the methodology for obtaining a generalized law of motion for a vibration device with asymmetric oscillations is performed based on the application of polyharmonic oscillation synthesis methods. It is shown that the method of forming the total driving force of a vibration device based on the coefficients of the terms of the Fourier series has limited capabilities. This article develops, substantiates, and presents a generalized method for calculating and designing a vibration device with asymmetric oscillations by the value of the total driving force and a given value of the asymmetry coefficient in a wide range of rational designs of vibration machines. The proposed method is accompanied by a numerical example for a vibration device with an asymmetry coefficient of the total driving force equal to 10. Full article

Different additive manufacturing modalities enable the production of multi-material components which can be used in a wide range of industrial applications. The prediction of the mechanical properties of these components via finite element modelling rather than through testing is critical in terms of cost and time. However, due to the higher computational time spent on the modelling of lattice structures, different methods have been investigated to accurately predict mechanical properties. For this purpose, this study proposes the use of a homogenization method in the two most common types of multi-material lattices: honeycomb and re-entrant auxetics. Modal analyses were performed, and the first six mode shapes were extracted from explicit and implicit models. The results were compared in terms of mode shapes and natural frequencies. The results showed that homogenization can be successfully applied to multi-material honeycomb and re-entrant auxetic lattices without compromising the accuracy. It was shown that the implicit models predict the natural frequencies with an error range of less than 6.5% when compared with the explicit models in all of the mode shapes for both honeycomb and re-entrant auxetic lattices. The Modal Assurance Criteria, which is an indication of the degree of similarity between the mode shapes of explicit and implicit models, was found to be higher than 0.996, indicating very high similarity. Full article

This paper examines the performance of Bayesian filtering system identification in the context of nonlinear structural and mechanical systems. The objective is to assess the accuracy and limitations of the four most well-established filtering-based parameter estimation methods: the extended Kalman filter, the unscented Kalman filter, the ensemble Kalman filter, and the particle filter. The four methods are applied to estimate the parameters and the response of benchmark dynamical systems used in structural mechanics, including a Duffing oscillator, a hysteretic Bouc–Wen oscillator, and a hysteretic Bouc–Wen chain system. Based on the performance, accuracy, and computational efficiency of the methods under different operating conditions, it is concluded that the unscented Kalman filter is the most effective filtering system identification method for the systems considered, with the other filters showing large estimation errors or divergence, high computational cost, and/or curse of dimensionality as the dimension of the system and the number of uncertain parameters increased. Full article