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A common format is developed for a mass and an inerter-based resonant vibration absorber device, operating on the absolute motion and the relative motion at the location of the device, respectively. When using a resonant absorber a specific mode is targeted, but in the calibration of the device it may be important to include the effect of other non-resonant modes. The classic concept of a quasi-static correction term is here generalized to a quasi-dynamic correction with a background inertia term as well as a flexibility term. An explicit design procedure is developed, in which the background effects are included via a flexibility and an inertia coefficient, accounting for the effect of the non-resonant modes. The design procedure starts from a selected level of dynamic amplification and then determines the device parameters for an equivalent dynamic system, in which the background flexibility and inertia effects are introduced subsequently. The inclusion of background effect of the non-resonant modes leads to larger mass, stiffness and damping parameter of the device. Examples illustrate the relation between resonant absorbers based on a tuned mass or a tuned inerter element, and demonstrate the ability to attain balanced calibration of resonant absorbers also for higher modes.

Dynamical and structural systems are susceptible to sudden excitations and loadings such as wind gusts, blasts, earthquakes, and others which may cause destructive vibration amplitudes and lead to catastrophic impact on human lives and economy. Therefore, various vibration absorbers of linear and nonlinear coupling dynamics have been widely studied in plenty of publications where some have been applied in real-world practical applications. Firstly, the tuned-mass-damper (TMD), the first well-known linear vibration absorber that has been well-studied in the literature and applied with various structural and dynamical systems, is discussed. The linear vibration absorbers such as TMDs are widely used in real-life small- and large-scale structures due to their robust performance in vibration suppression of the low natural frequency structural modes. However, the TMD performs efficiently at narrowband frequency range where its performance is deteriorated by any changes in the frequency content in the structure and the TMD itself. Therefore, the targeted-energy-transfer mechanism which is found to be achieved by nonlinear energy sinks (NESs) has ignited the interest in passive nonlinear vibration suppression. Unlike TMDs, the NESs are dynamical vibration absorbers that achieve vibration suppression for wide range of frequency-energy levels. Given the very rapid growth in this field and the extensive research studies supporting the robustness of the NESs, this paper presents the different types of NESs and their applications with main emphasis on the rotary-based and impact-based NESs since they are of high impact in the literature due to their strong nonlinear dynamical behavior and robust targeted energy transfer.

A bistable nonlinear energy sink conceived to mitigate the vibrations of host structural systems is considered in this paper. The hosting structure consists of two coupled symmetric linear oscillators (LOs), and the nonlinear energy sink (NES) is connected to one of them. The peculiar nonlinear dynamics of the resulting three-degree-of-freedom system is analytically described by means of its slow invariant manifold derived from a suitable rescaling, coupled with a harmonic balance procedure, applied to the governing equations transformed in modal coordinates. On the basis of the first-order reduced model, the absorber is tuned and optimized to mitigate both modes for a broad range of impulsive load magnitudes applied to the LOs. On the one hand, for low-amplitude, in-well, oscillations, the parameters governing the bistable NES are tuned in order to make it functioning as a linear tuned mass damper (TMD); on the other, for high-amplitude, cross-well, oscillations, the absorber is optimized on the basis of the invariant manifolds features. The analytically predicted performance of the resulting tuned bistable nonlinear energy sink (TBNES) is numerically validated in terms of dissipation time; the absorption capabilities are eventually compared with either a TMD and a purely cubic NES. It is shown that, for a wide range of impulse amplitudes, the TBNES allows the most efficient absorption even for the detuned mode, where a single TMD cannot be effective.

The implementation of the nonlinear tuned vibration absorber (NLTVA) for the suppression of shimmy vibration in towed wheels is addressed in this study. We adopt a modified straight tangent tyre model of a single-degree-of-freedom towed wheel system with an attached NLTVA. Stability analysis illustrated that the NLTVA can significantly improve the stability of the equilibrium of the wheel. Bifurcation analysis highlighted the existence of large bistable regions, which undermines the system’s safety. However, numerical continuation analysis, coupled with a dynamical integrity investigation, revealed that the addition of an intentional softening nonlinearity in the absorber restoring force characteristic enables the complete suppression of the bistable regions, also reducing the amplitude of shimmy oscillations in the unstable region. Quasiperiodic motions were also identified; however, their practical relevance seems marginal.

The dynamics of a nonlinear passive vibration absorber conceived to mitigate vibrations of a nonlinear host structure is considered in this paper. The system under study is composed of a primary system, consisting of an undamped nonlinear oscillator of Duffing type, and a nonlinear dynamic vibration absorber, denominated nonlinear tuned vibration absorber (NLTVA). The NLTVA consists of a small mass, attached to the host structure through a linear damper, a linear and a cubic spring. The host structure is subject to free vibrations and the performance of the NLTVA is evaluated with respect to the minimal time required to dissipate a specific amount of the mechanical energy of the system. In order to characterize the dynamics of the system, a combination of numerical and analytical techniques is implemented. In particular, on the basis of the first-order reduced model, slow invariant manifolds of the transient dynamics are identified, which enable to estimate the absorber performance. Results illustrate that two different dynamical paths exist and the system can undergo either of them, depending on the initial conditions and on the value of the absorber nonlinear stiffness coefficient. One path leads to a very fast vibration mitigation, and therefore to a favorable behavior, while the other one causes a very slow energy dissipation.

Parametric excitation in the pitch/roll degrees of freedom (DoFs) can induce dynamic instability in floating cylinder-type structures such as spar buoys, floating offshore wind or wave energy converters. At certain frequency and amplitude ranges of the input waves, parametric coupling between the heave and pitch/roll DoFs results in undesirable large amplitude rotational motion. One possible remedy to mitigate the existence of parametric resonance is the use of dynamic vibration absorbers. Two prominent types of dynamic vibration absorbers are tuned mass dampers (TMDs) and nonlinear energy sinks (NESs), which have contrasting properties with regard to their amplitude and frequency dependencies when absorbing kinetic energy from oscillating bodies. This paper investigates the suppression of parametric resonance in floating bodies utilizing dynamic vibration absorbers, comparing the performance of TMDs against NESs for a test case considering a floating vertical cylinder. In addition to the type of dynamic vibration absorber utilized, the paper also examines the DoF which it acts on, comparing the benefits between attaching the vibration absorber to the primary (heave) DoF or the secondary (pitch) DoF. The results show that the TMD outperforms the NES and that it is more effective to attach the vibration absorber to the heave DoF when eliminating parametric resonance in the pitch DoF.

The design and characterisation of a magnetic vibration absorber (MVA), completely relying on magnetic forces, is addressed. A distinctive feature of the absorber is the ability of tuning the linear stiffness together with the nonlinear cubic and quintic stiffnesses by means of repulsive magnets located in the axis of the main vibrating magnetic mass, together with a set of corrective magnets located off the main axis. The tuning methodology is passive and relies only on three geometrical parameters. Consequently, the MVA can be adjusted to design either a nonlinear tuned vibration absorber, a nonlinear energy sink or a bi-stable absorber with negative linear stiffness. The expressions of the stiffnesses are given from a multipole expansion of the magnetic fields of repulsive and corrective magnets. A complete static and dynamic characterisation is performed, showing the robustness of the modelling together with the ability of the MVA to work properly in different vibratory regimes, thus making it a suitable candidate for passive vibration mitigation in a wide variety of contexts.

Attenuation of mechanical vibrations is an ongoing field of research in engineering aiming at reducing damage and improving performance in the presence of dynamical forces. Different alternatives have been proposed over time; the active vibration absorber can be highlighted as an alternative which can absorb the vibration from system in real time. In this study, an active vibration absorber was modelled as an electromechanical device. It was applied to a cantilever beam, mathematically modelled as a continuous beam. A set of differential equations representing the dynamical behaviour of the cantilever beam and active vibration absorber was obtained and it was simulated in Matlab Simulink®. Results indicated that the active vibration absorber is able to significantly reduce the vibration amplitudes of a system, especially in resonance conditions. The analytical model and procedure developed here can easily spread to any more complex system.

The study presents a new configuration of nonlinear energy sinks (NESs) which is adaptable to function as either stable or bistable NES. The proposed NES is based on the spring-loaded inverted pendulum (SLIP) in which a torsional stiffness element couples the SLIP to the linear oscillator (LO). The bistable configuration provides a critically stable position when the SLIP is vertically aligned with respect to the LO motion. At this critical stability position, the SLIP NES incorporates pre-stored potential energy which generates the bistability characteristics resembling that of a stiffness-based bistable NES. The equations of motion of the coupled LO with the SLIP NES are derived based on the Euler–Lagrange method in non-dimensional form. The parameters of the considered SLIP NESs are optimized to achieve an optimum energy absorption from the LO. The proposed B-SLIP NES is also applied to suppress seismic ground motion and forced torsional vibrations. The obtained numerical simulation and analytical response results verify the robustness of the B-SLIP NES in vibration suppression performance compared with the tuned mass damper and the cubic stiffness NES.

This paper first presents a multi‐objective optimization problem formulation for the design of a tuned mass damper (TMD) for either a base excitation or an external load. The optimization seeks to simultaneously minimize structural responses, the TMD mass and the TMD stroke. A white noise input is adopted to represent the base acceleration or the external load. Alternatively, a filtered white noise could be used. Furthermore, the TMD is assumed to be tuned to dampen one of the modes of the structure, typically the first mode. Two approaches for the solution of the problem are then presented. The first approach directly solves the problem while considering the full multi‐degree‐of‐freedom system and the TMD equations. Using the second approach, the multimodal response of the structure is first approximately decomposed to its modal contributions. The modal contribution of the damped mode could thus be analyzed as a single‐degree‐of‐freedom system with a TMD. An intensive parametric study, where the response of a single‐degree‐of‐freedom system equipped with a TMD is optimized in a multi‐objective sense, is then performed. This parametric study enables gaining insight to the behavior of the problem. Furthermore, its results assist in executing the second optimization approach without having to actually run the optimization algorithm. The second approach is also implemented in an Excel spreadsheet that is attached as “Supporting Information.”