title: Nonlinear torsional vibration of a circular cylindrical piezoelectric rod with relatively large shear deformation.
abstract: We show that, in a circular cylindrical rod, torsional modes are coupling to extension when the shear deformation associated with the torsional modes is no longer infinitesimal. A set of a couple equations is derived with which the effect of extension on the torsional frequency is examined. The results are useful to the understanding and design of devices operating with torsional modes.
authors: Jiashi
authors: J
authors: Yang