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Refined Approach to Electrically Excited Vibration of a Rectangular Plate with Piezoelectric Layers

Tylikowski A.

Machine Dynamics Problems

2006

Vol. 30, No. 1

97-111

The purpose of this analytical work is to present a general model of the electro-mechanical response of a simply supported laminated plate to excitation by piezoelectric embedded actuators. The dynamic plate transverse displacement and the electric field to the excitation by the applied voltage term are determined from the solution of boundary value problem. The distribution of the piezoelectric potential is obtained by including the Maxwell electrostatics equation in the formulation. Coupled dynamics equations with respect to a plate displacement and an electric field are derived using Hamilton principle. Dynamic equations, joints conditions between sections with and without active layers as well as the mechanical and electrical boundary conditions at the plate edges form the boundary value problems. The steady-state frequency and space characteristics due to sinusoidal voltage applied to actuators are presented. The analysis generalizes previous results obtained under neglecting the in-plane components of electric displacement.