A coupled Galerkin and Newmark techniques for resonance simulation of the electrically single-curved system under low-velocity impact

• Published in: Engineering with computers Vol. 38; no. Suppl 4; pp. 3153 - 3170
• Main Authors: Zhang, Chunliang, Long, Shangbin, Mohammadi, Alireza, Bagh, Farzaneh Sharifi, Selmi, Abdellatif, Khan, Afrasyab
• Format: Journal Article
• Language: English
• Published: London Springer London 01.10.2022; Springer Nature B.V
• Subjects: CAE) and Design; Calculus of Variations and Optimal Control; Optimization; Classical Mechanics; Computer Science; Computer-Aided Engineering (CAD; Contact force; Control; Domains; Dynamic stability; Electric contacts; Energy methods; Galerkin method; Low speed; Math. Applications in Chemistry; Mathematical analysis; Mathematical and Computational Engineering; Operators (mathematics); Original Article; Physical factors; Piezoelectricity; Potential energy; Stability analysis; Systems Theory; Velocity; Coupled Galerkin and Newmark methods; External excitation; Curved open-type shell; Hertz contact theory; Dynamic stability
• ISSN: 0177-0667; 1435-5663
• DOI: 10.1007/s00366-021-01450-3

The purpose of this paper is to study the stability analysis of the curved system made of piezoelectric materials under low-velocity impact. To examine the contact force through the impactor and structure, the Hertz contact model has been taken into account. The minimum potential energy method is applied for achieving the structure’s boundary and governing equations subject to a low-speed impact. In the numerical investigation’s step, the Galerkin approach could be considered as a class of techniques to changing an operator of a continuous problem to a discrete one in the displacement domains. Newmark method is presented for solving the problem in the time domains. After this, by coupling these two approaches (Galerkin and Newmark), the electrically curved system’s governing equations have been solved subjected to external loads for achieving the responses of low-velocity impact and dynamics. The results show that some geometrical and physical factors contribute considerably to the dynamic stability information of the electrically curved system under low-speed impact. The results show that the convergence study of the Galerkin method appears when the circumferential and axial mode numbers are more than 8. This study’s outcomes are likely to be employed can be used in the aircraft industries.