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

• Published in: Engineering with computers Vol. 38; no. 4; pp. 3137 - 3149
• Main Authors: Huang, Xiaoping, Zhu, Yufang, Vafaei, Paniz, Moradi, Zohre, Davoudi, Mohsen
• Format: Journal Article
• Language: English
• Published: London Springer London 01.08.2022; Springer Nature B.V
• Subjects: Algorithms; CAE) and Design; Calculus of Variations and Optimal Control; Optimization; Classical Mechanics; Computer Science; Computer-Aided Engineering (CAD; Control; Differential equations; Domains; Dynamic stability; Dynamical systems; Elastic foundations; Electric contacts; Electric potential; Generalized differential quadrature method; Geometric nonlinearity; Hamilton's principle; Iterative algorithms; Iterative methods; Math. Applications in Chemistry; Mathematical analysis; Mathematical and Computational Engineering; Nonlinear dynamics; Nonlinear equations; Original Article; Quadratures; Shear deformation; Substrates; Systems Theory; Voltage; Nonlinear simulation; IAB-GDQM; Hamilton’s principle; von Kármán geometric nonlinearity; Electrically plate
• ISSN: 0177-0667; 1435-5663
• DOI: 10.1007/s00366-021-01320-y

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 n th 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 Kármán 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.