An iterative simulation algorithm for large oscillation of the applicable 2D-electrical system on a complex nonlinear substrate

An iterative algorithm is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the nth approximation is derived from the previous ones. As a first endeavor, the nonlinear dynamic instability performance of the electrical plate on the nonlinear elastic substrate using an iterative algorithm is scrutinized in this research. A nonlinear elastic foundation is assumed to be in contact with the electrical plate during deformation. The nonlinear coupled dynamic equations governing the transverse and longitudinal motions of the electrical plate are derived using Hamilton's principle method, the von Karman geometric nonlinearity, and improved higher-order shear deformation theory. The iterative algorithm based generalized differential quadrature method (IAB-GDQM) is applied for solving the nonlinear equations with the aid of nonlinear boundary domains. Parametric studies are implemented to explore the impacts of the applied voltage, geometry of the plate, and nonlinear factor on large amplitude motion, and nonlinear dynamics of the presented system for various boundary domains. Results show that the nonlinear dynamic depends on nonlinear elastic foundation effects and the applied voltage, which can be used to design the electrically structures in different environmental conditions accurately.

Automated summary

This study investigates the nonlinear dynamic instability performance of an electrical plate on a nonlinear elastic foundation using an iterative algorithm. The results show that the nonlinear dynamics depend on the effects of the nonlinear elastic foundation and applied voltage, providing valuable insights for accurately designing electric structures in different environmental conditions.