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Dynamic stress analysis on nonlinear vibration of a stiffened plate with initial stresses and geometric imperfections considering different resonance conditions

Niu-Jing Ma (School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, China and State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu, China)
Li-Xiong Gu (School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, China)
Long Piao (School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, China and Zhejiang Hang-Shao-Yong expressway Co. LTD, Hangzhou, China)
Xing-Zhi Zhang (Zhejiang Hang-Shao-Yong expressway Co. LTD, Hangzhou, China)

Engineering Computations

ISSN: 0264-4401

Article publication date: 6 August 2020

Issue publication date: 8 February 2021

141

Abstract

Purpose

Stiffened plates have been widely used in civil, marine, aerospace engineering. As a kind of thin-walled structure operating in complex environment, stiffened plates mostly undergo a variety of dynamic loads, which may sometimes result in large-amplitude vibration. Additionally, initial stresses and geometric imperfections are widespread in this type of structure. Furthermore, it is universally known that initial stresses and geometric imperfections may affect mechanical behavior of structures severely, particularly in dynamic analysis. Thus, the purpose of this paper is to study the stress variation rule of a stiffened plate during large-amplitude vibration considering initial stresses and geometric imperfections.

Design/methodology/approach

The initial stresses are represented in the form of initial bending moments applying to the stiffened plate, while the initial geometric imperfections are considered by means of trigonometric series, and they are assumed existing in the plate along the z-direction exclusively. Then, the dynamic equilibrium equations of the stiffened plate are established using Lagrange’s equation as well as aforementioned conditions. The nonlinear differential equations of motion are simplified as a two-degree-of-freedom system by considering 1:2 and 1:3 internal resonances, respectively, and the multiscale method is applied to solve the equations.

Findings

The influence of initial stresses on the plate, stresses during internal resonance is remarkable, while that is moderate for initial geometric imperfections. (Upon considering the existence of initial stresses or geometric imperfections, the stresses of motivated modes are less than the primary mode for both and internal resonances). The influence of bidirectional initial stresses on the plate’s stresses during internal resonance is more remarkable than that of unidirectional initial stresses. The coupled vibration in 1%3A2 internal resonance is fiercer than that in internal resonance.

Originality/value

Stiffened plates are widely used in engineering structures. However, as a type of thin-walled structure, stiffened plates vibrate with large amplitude in most cases owning to their complicated operation circumstance. In addition, stiffened plates usually contain initial stresses and geometric imperfections, which may result in the variation of their mechanical behavior, especially dynamical behavior. Based on the above consideration, this paper studies the nonlinear dynamical behavior of stiffened plates with initial stresses and geometrical imperfections under different internal resonances, which is the originality of this work. Furthermore, the research findings can provide references for engineering design and application.

Keywords

Acknowledgements

The authors gratefully acknowledge the support of State Key Laboratory of Traction Power, Southwest Jiaotong University (No. TPL1802), Pearl River Science and Technology Nova Program of Guangzhou (No.201906010009), Fundamental Research Funds for the Central Universities, South China University of Technology (No.2019MS118) and National Natural Science Foundation of China (No. 51678247, No. 51878295).

Citation

Ma, N.-J., Gu, L.-X., Piao, L. and Zhang, X.-Z. (2021), "Dynamic stress analysis on nonlinear vibration of a stiffened plate with initial stresses and geometric imperfections considering different resonance conditions", Engineering Computations, Vol. 38 No. 2, pp. 720-744. https://doi.org/10.1108/EC-03-2020-0147

Publisher

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Emerald Publishing Limited

Copyright © 2020, Emerald Publishing Limited

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