Optimum Design of a Nonlinear Vibration Absorber Coupled to a Resonant Oscillator: A Case Study

H F Abundis-Fong,A Cabrera-Amado,G Silva-Navarro,J Enríquez-Zárate

doi:10.1155/2018/2107607

Abstract

This paper presents the optimal design of a passive autoparametric cantilever beam vibration absorber for a linear mass-spring-damper system subject to harmonic external force. The design of the autoparametric vibration absorber is obtained by using an approximation of the nonlinear frequency response function, computed via the multiple scales method. Based on the solution given by the perturbation method mentioned above, a static optimization problem is formulated in order to determine the optimum parameters (mass and length) of the nonlinear absorber which minimizes the steady state amplitude of the primary mass under resonant conditions; then, a PZT actuator is cemented to the base of the beam, so the nonlinear absorber is made active, thus enabling the possibility of controlling the effective stiffness associated with the passive absorber and, as a consequence, the implementation of an active vibration control scheme able to preserve, as possible, the autoparametric interaction as well as to compensate varying excitation frequencies and parametric uncertainty. Finally, some simulations and experimental results are included to validate and illustrate the dynamic performance of the overall system.

Highlights

Vibration is a constant problem as it can impair performance and lead to fatigue, damage, and failure of a structure
Based on the solution given by the perturbation method mentioned above, a static optimization problem is formulated in order to determine the optimum parameters of the nonlinear absorber which minimizes the steady state amplitude of the primary mass under resonant conditions; a PZT actuator is cemented to the base of the beam, so the nonlinear absorber is made active, enabling the possibility of controlling the effective stiffness associated with the passive absorber and, as a consequence, the implementation of an active vibration control scheme able to preserve, as possible, the autoparametric interaction as well as to compensate varying excitation frequencies and parametric uncertainty
We have described the optimum design of a passive autoparametric vibration absorber applied to a linear mechanical system under resonant condition

Summary

Introduction

Vibration is a constant problem as it can impair performance and lead to fatigue, damage, and failure of a structure. A popular way to deal with vibration attenuation is carried out by (linear or nonlinear) passive techniques, taking advantage of the physical properties of the system itself, where the engineering approach to avoid the undesirable effects of mechanical vibrations is to modify mass, stiffness, and damping properties of structures with respect to the primary configuration of the system. Vazquez-Gonzalez and SilvaNavarro discussed the dynamic response and nonlinear frequency analysis of a damped Duffing system attached to an autoparametric pendulum absorber, operating under the external and internal resonance conditions [16]. SilvaNavarro et al described experimental studies of an active autoparametric absorber using a PZT patch actuator to attenuate resonant vibrations in a Duffing oscillator and a building-like structure [17, 18]. Approximate frequency response, parameterized in terms of the equivalent stiffness of the PZT actuator, providing a mechanism to asymptotically tune an optimal and stable attenuation solution

System Description

System with Autoparametric Absorber

Optimum Nonlinear Vibration Absorber

System with Active Nonlinear Absorber

Conclusions