Theory of piezoelectric laminated plates as an asymptotic approximation of the three-dimensional problem

A theory of laminated plates, whose central plane coincides with the symmetry plane of the plate, has been constructed by the asymptotic method of reducing the three-dimensional equations of piezoelectricity to the two-dimensional equations of piezoelectric plates without the use of any hypotheses. The plate contains both elastic and piezoelectric layers. The constructed theory is compared with the theories of other authors. As an example, a numerical calculation has been carried out of the piezoelectric state of a circular three-layer plate performing induced harmonic vibrations.