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

  • Changsong Zhu
  • Xueqian FangEmail author
  • Shaopu Yang
Regular Article
  • 13 Downloads

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.

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Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Civil EngineeringShijiazhuang Tiedao UniversityShijiazhuangChina
  2. 2.Department of Engineering MechanicsShijiazhuang Tiedao UniversityShijiazhuangChina
  3. 3.State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering StructuresShijiazhuang Tiedao UniversityShijiazhuangChina
  4. 4.School of Mechanical EngineeringShijiazhuang Tiedao UniversityShijiazhuangChina

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