Eur. Phys. J. Plus (2019) 134: 486
https://doi.org/10.1140/epjp/i2019-12852-2

Regular Article

Nonlinear free vibration of functionally graded viscoelastic piezoelectric doubly curved nanoshells with surface effects

¹ School of Civil Engineering, Shijiazhuang Tiedao University, 050043, Shijiazhuang, China
² Department of Engineering Mechanics, Shijiazhuang Tiedao University, 050043, Shijiazhuang, China
³ State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, 050043, Shijiazhuang, China
⁴ School of Mechanical Engineering, Shijiazhuang Tiedao University, 050043, Shijiazhuang, China

^* e-mail: stduxfang@yeah.net

Received: 24 April 2019
Accepted: 27 June 2019
Published online: 2 October 2019

Abstract

In this paper, the size-dependent nonlinear free vibration of functionally graded viscoelastic piezoelectric (FGVP) doubly curved nanoshells is investigated by using the surface piezoelectricity theory. The viscoelasticity and nonlinearity of FGVP doubly curved nanoshells are described by means of the Kelvin-Voigt viscoelastic model and Donnell’s strain-displacement relationships, respectively. Based on the constitutive equations and geometrical relationships, the elastic potential energy, kinetic energy and virtual work done by the viscous dissipative force are all presented. The nonlinear governing differential equations are derived from the generalized Hamilton’s principle, and then these equations are solved by employing the harmonic balance method. To validate the present results, three sets of comparison are carried out. The effects of the surface parameter, viscous damping coefficient, applied voltage, initial displacement and power law index on the nonlinear displacement and natural frequency of FGVP doubly curved nanoshells are discussed in detail. The current results reveal that the surface energy plays a significant role in the nonlinear vibration behaviors of FGVP doubly curved nanoshells.