Resonant Properties of Piezoelectric Ceramic Rectangular Parallelepipeds

This paper is concerned with the resonant properties of free, piezoelectric ceramic rectangular parallelepipeds, such as cubes. By means of the calculus of variations, the electroelastic differential equations are transformed into an approximate matrix characteristic value problem. Solution of this problem yields the resonant frequencies, the particle displacement patterns at resonance, and the equivalent circuit parameters such as the motional capacitances. Structures of the present type possess eight distinct symmetry families of modes; however, only one of these is excitable piezoelectrically with two opposite faces completely electroded. The resonant frequencies of the first 50 modes of this family are presented graphically versus Poisson's ratio for the special case of an isotropic cube. The frequency and dynamic capacitance of the first 30 modes of the same family are given for a piezoelectric ceramic square cylinder as the thickness-to-width ratio is varied from zero (thin square plate case) to unity (cube case). This result demonstrates the fact that the so-called thickness mode of a thin plate is actually a composite of many high contour-extensional overtones. Numerous modal displacement patterns are sketched for the square cylinder and cube special cases. Lastly, experimental results are reported that correspond reasonably well with the theory: Agreement is on the order of 3% for resonant frequency values and 20% for other quantities.