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Multimodal Resonance Response of Incompressible Hyperelastic Moderately Thick Cylindrical Shells

Zhentao Zhao

College of Mechanical and Electronic Engineering, Dalian Minzu University, Dalian 116600, P. R. China

E-mail Address: zhaozhentao@dlnu.edu.cn

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Jiayan Lin

College of Mathematics and Information, North Minzu University, Yinchuan 750021, P. R. China

E-mail Address: LY5425426@163.com

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Jie Xu

College of Mechanical and Electronic Engineering, Dalian Minzu University, Dalian 116600, P. R. China

E-mail Address: xjxujie1992@163.com

Corresponding author.

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, and

Xuegang Yuan

School of Science, Dalian Minzu University, Dalian 116600, P. R. China

E-mail Address: yxg1971@163.com

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https://doi.org/10.1142/S0219455425500282Cited by:0 (Source: Crossref)

Abstract

Based on the modified third-order shear deformation theory, the harmonic balance method, and the pseudo-arclength continuation method with two-point prediction, the nonlinear forced vibration response of incompressible hyperelastic moderately thick cylindrical shells subjected to a concentrated harmonic load at mid-span and simply supported boundary conditions at both ends is investigated. The algorithmic procedure for solving steady-state periodic solutions of strongly nonlinear systems of differential equations is presented. The structural response characteristics of shells under different excitation amplitudes and structural parameters are analyzed. The numerical results indicate that the aspect ratio of moderately thick hyperelastic cylindrical shells has a significant effect on the natural frequency ratio. Different frequency ratios lead to varying nonlinear mode coupling effects. The coupling effects among modes result in complex nonlinear behavior in the vibration response of each mode, leading to abundant multi-valued phenomena in the response curve.

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