An analytical treatment for pull-in instability of circular nanoplates based on the nonlocal strain gradient theory with clamped boundary condition

This paper is interested in the development of an analytical model for describing the dynamic pull-in instability of circular nanoplates based on the nonlocal strain gradient theory (NSGT). Herein, Kirchhoff's thin plate theory is accommodated with the NSGT theory; hence the governing equation of motion is procured according to Hamilton's principle. For this goal, the Galerkin method (GM) is used to reduce the governing equation in spatial domain considering clamped boundary condition (BC), and then it is discretized via homotopy analysis method (HAM). Finally, the effects of nonlocal and length scale parameters on the non-dimensional fundamental frequency against electrostatic, hydrostatic, and thermal forces are relatively illuminated.