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

• Published in: European physical journal plus Vol. 134; no. 10; p. 486
• Main Authors: Zhu, Changsong, Fang, Xueqian, Yang, Shaopu
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2019; Springer Nature B.V
• Subjects: Applied and Technical Physics; Atomic; Complex Systems; Condensed Matter Physics; Constitutive equations; Constitutive relationships; Differential equations; Free vibration; Hamilton's principle; Harmonic balance method; Kinetic energy; Mathematical and Computational Physics; Molecular; Nonlinearity; Optical and Plasma Physics; Physics; Physics and Astronomy; Piezoelectricity; Potential energy; Regular Article; Resonant frequencies; Surface energy; Theoretical; Vibration; Viscoelasticity; Viscous damping
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/i2019-12852-2

. 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.