FREE VIBRATION OF SIMPLY-SUPPORTED TRANSVERSELY ISOTROPIC PYROELECTRIC RECTANGULAR PLATES
横观各向同性热电材料简支矩形板的自由振动

Free vibration of rectangulax pyroelectric plates of transverse isotropy is analyzed based on the three-dimensional coupled piezothermoelasticity theory.It has been proved that there exist two classes of vibrations for a pyroelectric plate of this type, that is, the uncoupled first class of vibration and the coupled second class of vibration. The first class of vibration includes the thickness-shear motion. If the structure of the plate and boundary conditions on the top and bottom surfaces are symmetric about the middle plane, the second class of vibration can be further decomposed into symmetric vibration and antisymmetric vibration. Three dimensional exact solutions are obtained for free vibration of rectangular pyroelectric plates. Monte Carlo method is utilized to overcome the difficulty of solving transcendental equations for complex roots.Numerical results are presented for a rectangular PZT-4 plate. The results of calculation show good agreement with those given by other researchers. The results also show that frequencies for vibration of the first class are always real while frequencies for the second class axe complex when thermo-mechanical and electro-thermal coupling effects are accounted. The imaginary parts of complex frequencies, which represent thermal damping, are all very small over the low and medium frequency range, which is commonly encountered in engineering. The effects of thermomechanical and electro-thermal coupling on natural frequencies are discussed. It is observed that the frequencies obtained in the open condition are still higher that those in closed condition when thermo-mechanical and electro-thermal coupling effects are considered. In addition, in the second class vibration frequencies of antisymmetric mode are higher than those of symmetric mode. Although numerical calculation is only carried out on a single-layer PZT-4 plate, the method proposed in this paper is also applicable for laminated pyroelectric plates.