Nonlinear vibration absorber optimal design via asymptotic approach

This paper tackles the classical problem of Vibration Absorbers (VAs) operating in the nonlinear dynamic regime. Since traditional linear VAs suffer from the drawback of a narrow bandwith and numerous structures exhibit nonlinear behavior, nonlinear absorbers are of practical interest. The resonant dynamic behavior of a nonlinear hysteretic VA attached to a damped nonlinear structure is investigated analytically via asymptotics and numerically via path following. The response of the reduced-order model, obtained by projecting the dynamics of the primary structure onto the mode to control, is evaluated using the method of multiple scales up to the first nonlinear order beyond the resonance. Here, the asymptotic response of the two-degree-of-freedom system with a 1:1 internal resonance is shown to be in very close agreement with the results of path following analyses. The asymptotic solution lends itself to a versatile optimization based on differential evolutionary

Nonlinear cancellation of the parametric resonance in elastic beams: theory and experiment

A non-linear control strategy is applied to a simply supported uniform elastic beam subjected to an axial end force at the principal-parametric resonance frequency of the first skew-symmetric mode. The control input consists of the bending couples applied by two pairs of piezoceramic actuators attached onto both sides of the beam surfaces and symmetrically with respect to the midspan, driven by the same voltage, thus resulting into symmetric control forces. This control architecture has zero control authority, in a linear sense, onto skew-symmetric vibrations. The non-linear transfer of energy from symmetric motions to skew-symmetric modes, due to non-linear inertia and curvature effects, provides the key physical mechanism for channelling suitable control power from the actuators into the linearly uncontrollable mode. The reduced dynamics of the system, constructed with the method of multiple scales directly applied to the governing PDE’s and boundary conditions, suggest effective forms of the control law as a two-frequency input in sub-combination resonance with the parametrically driven mode. The performances of different control laws are investigated. The relative phase and frequency relationships are designed so as to render the control action the most effective. The control schemes generate non-linear controller forces which increase the threshold for the activation of the parametric resonance thus resulting into its annihilation. The theoretical predictions are compared with experimentally obtained results

Ropeway roller batteries dynamics. Modeling, identification, and full-scale validation

A parametric mechanical model based on a Lagrangian formulation is here proposed to predict the dynamic response of roller batteries during the vehicles transit across the so-called compression towers in ropeways transportation systems. The model describes the dynamic interaction between the ropeway substructures starting from the modes and frequencies of the system to the forced dynamic response caused by the vehicles transit. The analytical model is corroborated and validated via an extensive experimental campaign devoted to the dynamic characterization of the roller battery system. The data acquired on site via a custom-design sensor network allowed to identify the frequencies and damping ratios by employing the Frequency Domain Decomposition (FDD) method. The high fidelity modeling and the system identification procedure are discussed

Nonlinear Dynamic Response of Nanocomposite Microbeams Array for Multiple Mass Sensing

A nonlinear MEMS multimass sensor is numerically investigated, designed as a single input-single output (SISO) system consisting of an array of nonlinear microcantilevers clamped to a shuttle mass which, in turn, is constrained by a linear spring and a dashpot. The microcantilevers are made of a nanostructured material, a polymeric hosting matrix reinforced by aligned carbon nanotubes (CNT). The linear as well as the nonlinear detection capabilities of the device are explored by computing the shifts of the frequency response peaks caused by the mass deposition onto one or more microcantilever tips. The frequency response curves of the device are obtained by a pathfollowing algorithm applied to the reduced-order model of the system. The microcantilevers are described by a nonlinear Euler-Bernoulli inextensible beam theory, which is enriched by a meso-scale constitutive law of the nanocomposite. In particular, the microcantilever constitutive law depends on the CNT volume fraction suitably used for each cantilever to tune the frequency bandwidth of the whole device. Through an extensive numerical campaign, the mass sensor sensitivity estimated in the linear and nonlinear dynamic range shows that, for relatively large displacements, the accuracy of the added mass detectability can be improved due to the larger nonlinear frequency shifts at resonance (up to 12%). © 2023 by the authors

Payload oscillations control in harbor cranes via semi-active vibration absorbers: modeling, simulations and experimental results

Abstract Semi-active vibration absorbers (SAVAs) are proposed to suppress large amplitude oscillations in container cranes during maneu-vers and wind forcing. The SAVA design and optimization are achieved via suitable nonlinear models, numerical simulations, and laboratory as well as full-scale tests. A comprehensive nonlinear modelling, featuring a full three-dimensional crane model and the adaptive vibration control architecture, is devised. The container is modeled as a rigid body elastically suspended from the trolley traveling along the crane boom. Two identical SAVAs are studied coupling their equations of motion - which include the impact against rubberized end stops - with the container crane dynamics. Suitable parametric analyses are carried out to investigate and optimize the control devices. Full-scale experiments are performed to validate the semi-active control architecture which proves to be a feasible approach

ZEROTH-ORDER CORRECTIONS TO THE EULER-BERNOULLI BEAM MODEL

ABSTRACT This paper compares the frequency-amplitude relationship for nonlinear oscillations of a geometrically nonlinear model of a slender beam in the absence of damping with the corresponding predictions from the Mettler model for the transverse motion. In particular, the analysis shows that the Mettler model fails to account for a constant, amplitude-independent shift in the nonlinear frequency relative to the linear frequency caused by rotary inertia terms. INTRODUCTION There is widespread interest in the nonlinear dynamics of macro-beams and nano/micro-beams as they are employed as essential components of structural assemblies designed for enhanced performance (e.g., There are two main groups of analyses within the context of nonlinear planar shear-undeformable beams. One is focused on axially restrained beams, for which the beam-axis stretching is considered the dominant nonlinearity. These studies (e.g., [5, 6]) were mostly inspired by the work of Mettle

Prof D. T. Mook

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Quantifying rate dependence of hysteretic systems

Hysteresis nonlinearities are formally defined as deterministic, rate-independent operators for a great variety of systems. Rate independence frequently occurs in problems in which the time scales of interest are much longer than the intrinsic time scales of the system. In this paper we propose a measure of rate dependence and numerically evaluate the corresponding metric for two rate-dependent systems, namely, a linearly viscous damper and a class of shape memory materials exhibiting thermomechanical behavior [1]. The rate-independent extended Bouc-Wen model of hysteresis [2] is used to validate the robustness of our rate-independence criterion. On the other hand, the shown rate dependence in shape memory materials working in nonisothermal conditions is associated with the ensuing thermomechanical coupling

Sensitivity Of A Nonlinear TMD Effectiveness With Respect To Uncertainties In The Structural Parameters

Tuned mass dampers are found to be effective in enhancing structural performance of build-ings subjected to wind and seismic loads. This paper provides insights on the sensitivity of a Nonlinear Hysteretic Tuned Mass Damper (TMD) in mitigation of seismic induced vibrations under uncertainties present in structural parameters. A 2-DOF reduced ordered model of the structure and TMD is used to optimize the parameters of TMD when structure is subjected to Nonstationary excitations. A 3- dimensional 5-storey scaled down building is modeled in Opensees to have a high-fidelity model of the structure. Modified Bouc-Wen Hysteresis model is implemented in Opensees to mimic the performance of the Nonlinear TMD. Optimal design parameters of Nonlinear TMD obtained using the 2-DOF reduced ordered model are em- When structural parameters are subjected to uncertainties, the effectiveness of the optimal Non-linear TMD is studied. Various sensitivity analysis techniques are employed in ranking the pa-rameters of the structure that are effecting the performance of the TMD. It is observed that, the damping in the structure and variation in the position of additional mass in orthogonal direc-tion to direction of motion of structure are parameters that are effecting the performance of TMD

<Contributed Talk 10>Non linear phenomena in hysteretic systems

[Date] November 28 (Mon) - December 2 (Fri), 2011: [Place] Kyoto University Clock Tower Centennial Hall, Kyoto, JAPA