Free Vibration Analysis of Piezoelectric Cylindrical Nanoshell: Nonlocal and Surface Elasticity Effects

Vibration analysis of piezoelectric cylindrical nanoshell subjected to visco-Pasternak medium with arbitrary boundary conditions is investigated. In these analysis simultaneous effects of the nonlocal, surface elasticity and the different material scale parameter are considered. To this end, Eringen nonlocal theory and Gurtin–Murdoch surface/interface theory considering Donnell's shell theory are used. The governing equations and boundary conditions are derived using Hamilton’s principle and the assumed mode method combined with Euler–Lagrange method is used for discretizing the equations of motion. The viscoelastic nanoshell medium is modeled as Visco-Pasternak foundation. A variety of new vibration results including frequencies and mode shapes for piezoelectric cylindrical nano-shell with non-classical restraints as well as different material parameters are presented. The convergence, accuracy and reliability of the current formulation are validated by comparisons with existing experimental and numerical results. Also, the effects of nonlocality, surface energy, nanoshell radius, circumferential wavenumber, nanoshell damping coefficient, and foundation damping are accurately studied on frequencies and mode shapes of piezoelectric cylindrical nanoshell.