Higher-order effects of initial deformation on the vibrations of crystal plates

A system of plate equations for the thickness_shear and flexural vibrations superposed on large initial deflection due to bending is derived; in the stress–strain relations the terms associated with the fourth_order elastic stiffness coefficients are retained. An explicit formula for the change in the fundamental cutoff thickness shear frequency is obtained and the effects of the terms associated with the fourth_order constraints appear to be significant for large gradients of the rotation angles.