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Nonlinear vibration absorbers (NVA) using magnets feature ease of implementation and outstanding tunability and have attracted much interest in vibration suppression in recent years. Through configuration design and optimization, magnetic NVA can exhibit different nonlinear characteristics such as monostability, bistability and tristability. This work performs a comprehensive comparative study on the transient vibration suppression performances of the NVAs with four different magnet arrangements based on the cantilever beam design, including the NVA with two repulsive magnets (2RMNVA), two attractive magnets (2AMNVA), three repulsive magnets (3RMNVA) and three attractive magnets (3AMNVA). Based on the dipole–dipole model of magnets, the dynamic model of the system containing different magnetic NVAs is established for numerical simulation and the key parameters of each NVA are optimized under different excitation levels. The influence of parameters on different magnetic NVAs is investigated. Based on the optimization configurations, the rate of the energy dissipation from the primary structure by different magnetic NVAs is compared by wavelet transform analysis. The results show that due to the largest oscillations of crossing outmost wells, the optimized 3RMNVA and 3AMNVA are the preferred configurations for magnetic NVA under different excitation levels. Meanwhile, through the verification and comparison with reported designs, the effectiveness of the optimization method and the optimized NVAs in this paper are confirmed. This work provides the approach and guidelines to design the effective NVA to suppress transient vibrations.

The paper is devoted to a review of recent achievements in the field of dynamic analysis of structures and structural elements, such as beams and plates, with embedded viscoelastic (VE) dampers and/or layers. The general characteristics of VE materials, their rheological models, and methods of parameters identification are discussed. New formulations of dynamic problems for systems with VE elements are also reviewed. The methods of determination of dynamic characteristics, together with the methods of analysis of steady-state and transient vibrations of such systems, are also discussed. Both linear and geometrically non-linear vibrations are considered. The paper ends with a review of the methods of sensitivity and uncertainty analysis, and the methods of optimization, for structures with VE elements.

This paper presents a 2-link, 2-DOF flexible manipulator control using an inverse feedforward controller and an adaptive notch filter with a direct strain feedback controller. In the flexible manipulator, transient and residue vibrations inhibit the full potential of the manipulator. Vibrations caused by abrupt changes in the direction of the links are referred to as transient vibrations, whereas residual vibrations occur when the arm takes too long to settle after engaging in the intended task. The feedforward adaptive notch filter will reduce transient vibration caused by the manipulator arm beginning and halting suddenly, while the strain feedback will assure the quick decay of leftover vibrations. Maple, Maplesim, and MATLAB tools were used to model the manipulator and create the inverse controller and adaptive notch filter. The experiments took place in the dSPACE control desk environment. The experimental results of the spectral power of strain resulting from the two strategies are compared. From the results, the adaptive notch filter control had over an 80% improvement in the reduction in resonant frequencies that contribute to vibration. The results confirmed the feasibility of the approach, characterized by very minimal transient vibrations and a quick settling of the end effector.

In order to be able to maintain the safety ,stabilize the operation, and prolong the service life of highway engineering, it is necessary to place particular emphasis on the detection of highway engineering. In view of the current imperfection existed in operation techniques of cutting-ring method and sand replacement method.This paper puts forward to a kind of non-destructive detection method for highway engineering based on transient vibration signals.The author makes a detailed analysis and discussion on the main principle and application of the detection method.

A nonlinear energy sink (NES) passively reduces transient vibration energy of a typically impact loaded mechanical system. It is locally connected to the vibrating system through a nonlinear connecting stiffness. For a NES to perform efficiently, through targeted energy transfer (TET), the vibration levels need to exceed a well-defined threshold, below which the NES performs poorly. This threshold can be lowered by considering a NES with a bi-stable connecting stiffness. A bi-stable NES (BNES) has two stable equilibria. Besides vibrating in TET regime, a BNES can also vibrate chaotically or close to one of its equilibria, called intra-well vibrations. However, during both chaotic and intra-well vibrations, the mitigating performance of the BNES is poor. Here, a novel tuning method is developed, which finds the boundary between chaotic and TET regime, such that the BNES avoids the chaos and operates with the more performant TET. This boundary is found by numerically calculating the Lyapunov exponent, a measure for chaos. To quantify performance, two algebraic expressions, requiring no simulations, are derived in the paper expressing the speed of vibration mitigation and expressing the residual vibration energy left after TET. The result is a generic tuning methodology that not only ensures the BNES operates in the efficient TET regime, but also guarantees optimal speed of vibration mitigation. The developed performances measures in function of the NES’s parameters are to the point and easy to use. The tuned BNES shows a superior robustness w.r.t detuning compared to the linear vibration absorbers.

In vibrating mechanical systems, the targeted energy transfer mechanism (TET) of nonlinear energy sinks (NES) is employed as an alternative to linear tuned mass dampers (TMD) as passive vibrations absorbers for transient vibrations. The major advantages a NES has over a linear TMD are (1) an increased robustness to detuning and (2) the ability to dissipate multiple frequencies with only a single NES through so-called resonance capture cascading (RCC). The performance, especially the speed, of TET and RCC has rarely been a topic of research. In this research, algebraic performance measures for the speed of both TET and RCC are derived, called the pumping time and the cascading time, respectively. It shows that cascading time can be seen as a sum of single-mode pumping times, by introducing a novel modal decomposition. The strength of both measures is that they do not require numerical simulations, allowing easy optimization of the NES. The influence of different nonlinearities on the TET and RCC performance is investigated. Actual numerical simulations presented in the study validate the merit of both the pumping time and cascading time.

Introducing a time-periodicity into a system parameter leads to parametric excitation, which in general, may cause a parametric resonance with exponentially increased vibration. Applying a parametric excitation but carefully tuning its frequencies to multiple parametric anti-resonance frequencies is investigated here. The parametric excitation here is realized by an open-loop control at the system boundary that allows for an energy flow into or from the system. A parametric anti-resonance successfully triggers an energy transfer between specific vibration modes of the system and occurs in systems with at least two degrees of freedom. Such an energy transfer increases the overall dissipation of kinetic energy of a lightly damped system. This contribution presents an approach to accelerate the mitigation of transient vibrations by applying a multi-frequency parametric excitation with two or more parametric anti-resonance frequencies. The potential application in a MEMS sensor arrangement consisting of two and more coupled flexible beams exemplifies the method. Starting from the minimum system with two degrees of freedom, the averaging method is applied to analyze the transient slow flow, leading to an analytical approximation of the transition time response of a pulsed multi-frequency parametric excitation system. For a specific example, a reduction of 96.7% of the transient vibrations is achievable.

Serious transient vibrations often occur in a vertical-axis washing machine during the starting stage of the spin drying process. For solving this problem, a new type of rotational damper installed between the tub and the suspenders is designed, which can enhance lateral damping of the suspension system along radial directions. Damping force on the tub provided by the damper is derived, based on which vibration model of the washing machine is constructed. Bifurcation analyses are carried out to investigate influences of the rotational damper on stabilities of the suspension structure, and interactions between damping coefficient of the damper and several other design parameters are discussed. Variations of the unstable regions of the washer associated with the liquid balancer are studied, and the effect of the rotational damper on eliminating the unstable region induced by insufficient axial damping of the suspenders is discovered. The effectiveness of the damper for reducing transient vibrations of the tub is validated through experiments, and impacts of the damper on steady-state vibrations of the tub and the cabinet are presented. Conclusions can be drawn that the damper is not only effective for reducing transient vibrations, but also beneficial to stabilities of the washing machine.

Funding Information: The author acknowledges Fundação para a Ciência e a Tecnologia (FCT) for its financial support via the project LAETA Base Funding (DOI: 10.54499/UIDB/50022/2020). EEA grant FBR_OC2_45: SMART—Sustainable Maintenance and Rehabilitation of Railway Track is also acknowledged. Publisher Copyright: © 2025 by the author. 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.

Whole body vibrations in alpine skiing are a potential cause for frequent overuse and acute injuries. Therefore, the aim of the study was to investigate the transmissibility of vibrations from the skis to lower back and head. Attention was addressed to distinguish shocks and transient vibrations from long-lasting vibrations. Whole body vibrations were analysed in snow-plough swinging, basic swinging, short swinging and carved turns performed by eight highly skilled skiers. Power spectrum densities (PSD), running root-mean-square accelerations (RMS) and transmissibilities were estimated and analysed from 7 accelerometers positioned on skis, pelvis and head. In the measurements frequency range, vibrations were effectively transmitted from the skis to the pelvis and to the head, with the highest transmissibility occurring at frequencies below 6Hz. The highest transmissibility was observed for short swinging. The running RMS was cyclically increasing and decreasing with turning and shocks. Also, transient vibrations exhibited similar PSDs with considerably higher densities compared to overall PSDs. All form of alpine skiing were associated with random, periodic and transient vibrations. Skiing involving skidding was associated with higher vibration levels, higher transmissibilities and more pronounced shocks and transient vibrations compared to carving turns. Frequent skiers should preferably use carving instead of skidding techniques to decrease the risk for low back pain and loss of control.