Forced vibration of smart laminated viscoelastic plates by RPT finite element approach

Abstract

In this study, a finite element formulation based on the four-variable refined plate theory (RPT) is presented for forced vibration analysis of laminated viscoelastic composite plates integrated with a piezoelectric layer. To the best of the authors’ knowledge, this is the first time that the proposed approach is extended for study of the dynamic behavior of the smart viscoelastic plate. The utilized RPT which works for both thick and thin plates predicts a parabolic variation for transverse shear stresses across the plate thickness. Considering a linear viscoelastic model for the substrate material, the relaxation module is predicted by the Prony series. Using Hamilton’s principle, the weak form equation is constructed and a four-node rectangular plate element is utilized for discretizing the domain. The Newmark scheme is employed for advancing the solution in time. A MATLAB code is developed based on the formulations and several benchmark problems are solved. Comparing the findings with existing results in previous studies confirms the accuracy and efficiency of the proposed method. The dynamic response of the smart viscoelastic plates under various electromechanical loads is investigated and the results show that the vibration can be passively controlled by adding and actuating the piezoelectric layer. The damping effects of viscoelastic parameters on the results are investigated, too.