A theory of high frequency vibrations of piezoelectric cyrstal bars

This paper presents a higher order, linear theory of piezoelectric crystal bars as in the same spirit as that of Mindlin. First, a power series representation in aerial coordinates is employed for both the mechanical displacement and electric potential fields. Next, with the help of a variational theorem deduced from Hamilton's principle, together with these series, the theory is established consistently. A hierarchy of 1-dimensional approximate equations of motion, charge equations of electrostatics, initial and boundary conditions, strain-displacement and electric field-electric potential relations, and macroscopic constitutive equations constitutes the theory, and it governs all the types of motions of piezoelectric crystal bars of uniform cross-section. Further, special cases of interest are pointed out. The solutions of the initial mixed boundary-value problems defined by this theory are proven to be unique.