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<p>This study investigates the nonlinear vibration response of isotropic rectangular plates with partial cracks and non-uniform thickness when coupled with a fluid medium. Classical plate theory is used to derive the governing equation, and a simplified line spring model is incorporated to model a central crack. The virtual added mass from the surrounding fluid is introduced for horizontal and vertical plate immersion. Linear and parabolic thickness variations are considered, and Galerkin’s method transforms the governing equation into time-dependent modal coordinates. Nonlinearity is introduced using Berger’s method, and the method of multiple scales provides an approximate solution. Results highlight the effects of crack lengths, thickness variations, crack location, fluid levels, and immersion depth under different boundary conditions (SSSS and CCSS). Additionally, the study explores the influence of taper constant and depth of submergence on nonlinearity response, offering insights into bending–hardening and bending–softening phenomena. The present analytical model is also validated with the experimental results.</p>

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Nonlinear vibration analysis of a cracked isotropic plate with varying thickness coupled with fluid

  • 期刊论文

  • 发表日期：

    2025年5月27日

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  • Bhupesh Kumar Chandrakar,
  • N. K. Jain,
  • Ankur Gupta

摘要

This study investigates the nonlinear vibration response of isotropic rectangular plates with partial cracks and non-uniform thickness when coupled with a fluid medium. Classical plate theory is used to derive the governing equation, and a simplified line spring model is incorporated to model a central crack. The virtual added mass from the surrounding fluid is introduced for horizontal and vertical plate immersion. Linear and parabolic thickness variations are considered, and Galerkin’s method transforms the governing equation into time-dependent modal coordinates. Nonlinearity is introduced using Berger’s method, and the method of multiple scales provides an approximate solution. Results highlight the effects of crack lengths, thickness variations, crack location, fluid levels, and immersion depth under different boundary conditions (SSSS and CCSS). Additionally, the study explores the influence of taper constant and depth of submergence on nonlinearity response, offering insights into bending–hardening and bending–softening phenomena. The present analytical model is also validated with the experimental results.