An analytical solution for free and forced vibration of a piezoelectric laminated plate coupled with an acoustic enclosure

This paper deals with analytical vibro-acoustic modeling of a three-layered piezoelectric laminate coupled with an acoustic enclosure. Equation of the motion of the simply supported laminate is derived using the classical lamination theory (CLT) and pressure distribution inside the enclosure is obtained from the linear acoustic wave equation. Piezoelectric layers are assumed to be fully electroded and electric potential distribution in the piezoelectric layers satisfies both Maxwell’s equation and closed circuit condition on major surfaces of the piezoelectric layers. In order to study the free and forced vibratory characteristics of the coupled system, the time dependent motion equation of the coupled system transformed into frequency domain and Laplace domain and reduced to a set of ordinary differential equations, based on the eigenfunction expansion method. Afterwards, the effect of the cavity depth upon natural frequencies and dynamic response of the presented model is examined. To ensure the accuracy of the presented model, results are compared with those obtained from commercial finite element analysis software.