Nonlinear Dynamic Stability Analysis of Axially Moving CNTRC Piezoelectric Viscoelastic Nano/Micro Plate Based on MCST

Document Type : Research Paper


1 Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran

2 Institute of Nanoscience & Nanotechnology University of Kashan, Kashan, Iran

3 Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr/Isfahan, Iran


Analyzing the nonlinear dynamic stability of axially moving carbon nanotube reinforced composite (CNTRC) piezoelectric viscoelastic nano/micro plate under time dependent harmonic biaxial loading is the purpose of the present study. The nano/micro plate is made from Polyvinylidene Fluoride (PVDF). It moves in the positive direction of the x-axis at a constant velocity and supported by a nonlinear viscoelastic piezoelectric foundation (Zinc Oxide). A viscoelastic material is assumed in the Kelvin-Voigt model. Nano/micro plate is exposed to electric potential, 2D magnetic field and uniform thermal gradient. Maxwell's relations are used to integrate magnetic field effects. The nano/micro plate as well as smart foundation are subjected to electric potential in thickness direction. The effective elastic properties are estimated using the Eshelby-Mori-Tanaka approach. Von-Kármán's theory provides the basis for the nonlinear strain-displacement relationship. According to various shear deformation plate theories, a novel formulation is presented that incorporates surface stress effects via Gurtin-Murdoch elasticity theory. A modified couple stress theory (MCST) is used in order to consider small scale parameter. It is possible to derive the governing equations by using the energy method and Hamilton's principle. An analysis is conducted using Galerkin procedure and finally the incremental harmonic balance method (IHBM) to obtain the dynamic instability region (DIR). Among the parameters that will be examined are small-scale parameter, alternating and direct applied voltages, magnetic field intensity, surface effects as well as axially moving speed. The results demonstrate that increasing the axial speed of the nano/micro plate causes the system to become more unstable. As a result, if the smart foundation is considered, in addition to increasing the excitation frequency, the area of the instability zone will also decrease by at least 50%. It is estimated that in a static state (not moving), the area of the instability zone is reduced by more than 70%.


Main Subjects

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Volume 55, Issue 2
April 2024
Pages 242-274
  • Receive Date: 30 October 2023
  • Revise Date: 27 December 2023
  • Accept Date: 23 November 2023