Practical design of a nonlinear tuned vibration absorber

The aim of the paper is to develop a new nonlinear tuned vibration absorber (NLTVA) capable of mitigating the vibrations of nonlinear systems which are known to exhibit frequency-energy-dependent oscillations. A nonlinear generalization of Den Hartog’s equal-peak method is proposed to ensure equal peaks in the nonlinear frequency response for a large range of forcing amplitudes. An analytical tuning procedure is developed and provides the load-deflection characteristic of the NLTVA. Based on this prescribed relation, the NLTVA design is performed by two different approaches, namely thanks to (i) analytical formulas of uniform cantilever and doubly-clamped beams and (ii) numerical shape optimization of beams with varying width and thickness. A primary system composed of a cantilever beam with a geometrically nonlinear component at its free end serves to illustrate the proposed methodology.ERC Starting Grant NoVib 307265; ERC Starting Grant INNODY

O referendumskih vrednotah in vrlinah

peer reviewedThe harmonic balance (HB) method has been widely used in the past few years, as a numerical tool for the study of nonlinear models. However, in its classical formulation the HB method is limited to the approximation of periodic solutions. The present paper proposes to extend the method to the detection and tracking of bifurcations in the codimension-2 system parameters space. To validate the methodology, the forced response of a real spacecraft is examined. The paper first provides some numerical evidence of the presence of quasiperiodic oscillations and isolated solutions. It then demonstrates how the tracking of Neimark-Sacker and fold bifurcations can help get a deeper understanding of these attractors

Prediction of isolated resonance curves using nonlinear normal modes

Isolated resonance curves are separate from the main nonlinear forced-response branch, so they can easily be missed by a continuation algorithm and the resonant response might be underpredicted. The present work explores the connection between these isolated resonances and the nonlinear normal modes of the system and adapts an energy balance criterion to connect the two. This approach provides new insights into the occurrence of isolated resonances as well as a method to find an initial guess to compute the isolated resonance curve using numerical continuation. The concepts are illustrated on a finite element model of a cantilever beam with a nonlinear spring at its tip. This system presents jumps in both frequency and amplitude in its response to a swept sinusoidal excitation. The jumps are found to be the result of a modal interaction that creates an isolated resonance curve that eventually merges with the main resonance branch as the excitation force increases. Excellent insight into the observed dynamics is provided with the NNM theory, which supports that NNMs can also be a useful tool for predicting isolated resonance curves and other behaviors in the damped, forced response.</jats:p

A Multimodal Nonlinear Tuned Vibration Absorber

peer reviewedThis paper presents a tuning methodology to design a vibration absorber able to mitigate the vibratory amplitude of multiple resonances of a nonlinear structure. The linear characteristics of the absorber are first tuned to obtain the equal-peak design on every mode to be controlled when the structure is behaving linearly. Nonlinearities are then introduced intentionally in the absorber to counteract the effect of the nonlinearities inside the host structure. Their functional formis chosen according to a principle of similarity, and their coefficients are determined to enforce equal peaks in the nonlinear regime

The harmonic balance method for advanced analysis and design of nonlinear mechanical systems

As a tool for analyzing nonlinear large-scale structures, the harmonic balance (HB) method has recently received increasing attention in the structural dynamics community. However, its use was so far limited to the approximation and study of periodic solutions, and other methods as the shooting and orthogonal collocation techniques were usually preferred to further analyze these solutions and to study their bifurcations. This is why the present paper intends to demonstrate how one can take advantage of the HB method as an efficient alternative to the cited techniques. Two different applications are studied, namely the normal modes of a spacecraft and the optimization of the design of a vibration absorber. The interesting filtering feature of the HB method and the implementation of an efficient bifurcation tracking extension are illustrated

O "zvezni" pristojnosti ali Prevzetnost in prilastitev

Because nowadays structural engineers are willing to use or at least understand nonlinearities instead of simply avoiding them, there is a need for numerical tools performing analysis of nonlinear large-scale structures. Among these techniques, the harmonic balance (HB) method is certainly one of the most commonly used to study finite element models with reasonably complex nonlinearities. However, in its classical formulation the HB method is limited to the approximation of periodic solutions. For this reason, the present paper proposes to extend the method to the detection and tracking of codimension-1 bifurcations in the system parameters space. As an application, the frequency response of a spacecraft is studied, together with two nonlinear phenomena, namely quasiperiodic oscillations and detached resonance curves. This example illustrates how bifurcation tracking using the HB method can be employed as a promising design tool for detecting and eliminating such undesired behaviors