TORSIONAL VIBRATIONS OF A FINITE PIEZOELECTRIC BONE

Torsional vibrations of a piezoelectric solid circular cylinder of fin ite length belonging to crystal class 6 (bone) or 622 (beta-quartz) ar e investigated. Curved surface and the plane ends of the cylinder are free from traction and electric potential. A series solution is found in which shear stress on plane ends is satisfied term by term and shea r stress on the cylindrical surface and electric potential on both sur faces are satisfied approximately by an orthogonalization procedure. N atural frequencies of first four even and odd modes for bone are calcu lated. Shear stress and electric potential are presented graphically f or beta-quartz. It is observed that the series converges with few term s.