Frequency shifts in a piezoelectric body due to a surface mass layer with consideration of the layer stiffness

Shifts of resonant frequencies of a three-dimensional piezoelectric body of an arbitrary shape due to the addition of a thin layer of mass to its surface are studied. A first-order perturbation integral is obtained for the frequency shifts. The result generalizes that of a previous paper by considering the effect of the stiffness of the mass layer, in addition to its inertial effect.