Theory of vibrations of coated, thermopiezoelectric laminae

In this paper, we aim to construct a theory of vibrations of coated laminae in which there is coupling between elastic and electric as well as thermal fields. The laminas coated completely with perfectly conducting electrodes on both faces may comprise an arbitrary number of bonded layers, each with a distinct but uniform thickness, density and electromechanical properties. Within the framework of 3‐D thermopiezoelectricity, we first develop a generalized variational theorem [cf. M. C. Dökmeci L. Al Nuovo Cimento 7, 449–454 (1973)]. Next, following Mindlin [R. D. Mindlin, Int. J. Solids Struct. 10, 625–637 (1974)] and using this theorem, we construct a system of 2‐D approximate governing equations of the coated laminae for the case when the mechanical displacement, electric potential and thermal field vary linearly across the laminas thickness. The effects of elastic stiffnesses of, and the interactions between, layers of the laminae and its electrodes are all taken into account. Lastly, we present theorems of uniqueness in the governing equations of the theory. And we examine special cases of interest. [Work supported by the Scientific and Technical Research Council of Turkey.]