Surface energy effect on nonlinear free vibration behavior of orthotropic piezoelectric cylindrical nano-shells

In this paper, the electro-elastic surface/interface model is introduced to investigate the surface energy effect on the nonlinear free vibration behavior of orthotropic piezoelectric cylindrical nano-shells. On the basis of classical shell theory and von-Karman-Donnell-type geometric nonlinearity, the fundamental equations for vibration are given. By considering the constitute relations for surfaces, the total energy of the orthotropic piezoelectric cylindrical nano-shell is obtained. The governing equations of motion are derived from Hamilton's principle and solved by using the homotopy perturbation method (HPM). Afterwards, the results without surface effect are compared and validated with the datum available in the literature, and the influences of surface parameters and geometric characteristics on the nonlinear free vibration of the orthotropic piezoelectric cylindrical nano-shell are examined.