The refined theory of torsional deformation of transversely isotropic piezoelectric circular shaft

Summary form only given. The refined theory and the decomposed theorem of plates are converted into the refined theory of the torsional deformation of transversely isotropic piezoelectric circular shaft by using Bessel Function´s Operator Method from equation of transversely isotropic piezoelasticity for torsional problem without ad hoc assumptions. Firstly, the problem of deducing one-dimensional theory from three-dimensional theory for transversely isotropic piezoelastic shaft is investigated. Expressions are obtained for all the displacements and stress components in term of one function on the neutral axis. Secondly, based on the refined theory of piezoelectric circular shaft, the exact equations for homogeneous boundary conditions are derived, which consist of two governing differential equations: 2-orders equation and the transcendental equation. Lastly, the approximate governing equations are accurate up to the high-order terms with respect to radius of shaft in the case of non-homogenous boundary conditions.