The effect of radial force on pull-in instability and frequency of rigid core circular and annular plates subjected to electrostatic field

In this work static pull-in instability and frequency analysis of circular and annular plates in electrical field was studied. The plate is modeled based on classical plate theory with nonlinear Von Kármán strain-displacement field. The governing equation of motion and boundary conditions were obtained using Hamilton principle. For this purpose potential and kinetic energies and the work done by radial and electrostatic force are obtained. Governing partial differential equations were reduced to ordinary differential equations by Galerkin's method. Then, static pull-in instabilities of clamped circular plate and annular plate with clamped-clamped and clamped-simply boundary conditions were analyzed by arc-length continuation method. The effect of rigid core, radial load, geometric nonlinearity, inner radius and boundary conditions on pull-in instability and frequency of the plate has been studied.