Piezoelectric, laminated composite plate theory for thin-film resonators

A piezoelectric, laminated composite plate theory is developed and presented for the purpose of modeling and analyzing piezoelectric thin-film resonators and filters. The laminated plate equations are extensions of anisotropic composite plate theories by P.C. Yang (1966) and J.M. Whitney and N.J. Pagano (1970) to include piezoelectric effects and capabilities for modeling harmonic overtones of thickness-shear vibrations. Two-dimensional equations of motion of piezoelectric laminates were deduced from the three-dimensional equations of linear piezoelectricity by expanding mechanical displacement u_i and electric potential φ in a series of trigonometric functions for elastic, isotropic plates. The laminated plate equations are applied to a zinc-oxide-silicon bilayer strip without electrodes and solved for straight crested waves. Dispersion relations and mode shapes of the fundamental thickness-shear are presented for different ratios of zinc-oxide to silicon thickness