Modelagem numérica e projeto ótimo de sistemas de amortecimento viscoelásticos aplicados a placas retangulares

Abstract

Viscoelastic materiais have been extensively used for the passive control of sound and vibration. They can be deployed either as discrete devices (mountings, for instance) or as surface treatments. In this last case, the damping effectiveness can be significantly increased by using the so-called passive constraining layer damping (PCLD), which is obtained by inserting a viscoelastic layer between the base structure and a thin metal sheet. Such procedure enables to increase the shear strain of the viscoelastic core, thus increasing the amount of dissipated energy. Additionally, hybrid active-passive control methodologies have also been developed recently, based on the use of piezoelectric patches combined with viscoelastic films. Such combination has been named active constraining layer damping (ACLD). The present work is devoted to various aspects of numerical modeling, analysis and design of rectangular plates treated with PCLD and ACLD. Finite element models of laminated plates are developed, considering both a three-layer non-symmetric and a five-layer symmetric configurations. Both models are adapted to include the direct and inverse piezoelectric effects, enabling to represent the sensing and actuation capabilities of ACLD systems. The typical dependency of the viscoelastic behavior with respect to the vibration frequency is introduced into the modeling procedure by means of three different viscoelastic models, namely: the Golla-Hughes-MacTavish (GHM) model, the Anelastic Displacement Field model (ADF) and the Fractional Derivative model. The modeling procedure is validated through the comparision of finite element-predicted dynamic responses and the experimentally derived counterparts. Based on the validated models, it is carried-out a study about the influence of some design parameters on the damping effectiveness of PCLD systems. Aiming at reducing the high computation cost involved in the numerical processing of the systems of equations of motion, a model reduction technique based on the modal transformation is evaluated. It is also suggested a methodology for the optimal placement of partial PCLD treatments based on Genetic Algorithms. Finally, it is developed a technique of sensitivity analysis of complex eigenvalues and frequency response functions with respect to design parameters of PCLD systems. It is also addressed the sensitivity analysis of frequency response functions with respect to the temperature. This last procedure is illustrated by means of numerical simulations.