Three-dimensional analysis for the free vibration of finite-length orthotropic piezoelectric circular cylindrical shells

An exact elasticity study of the free vibration of a simply-supported cross-ply cylindrical shell containing a piezoelectric layer is presented. The solution of the derived governing differential equations is obtained through the power series expansion method. Both the direct and inverse piezoelectric effects are investigated. Results presented here provide an understand of the behavior of piezoelectric materials when acted as smart materials and cart be used to assess various numerical results obtained from approximate shell theories.