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<p>It is widely recognized that axial velocity disturbance and voltage disturbance can induce parametric resonance in shell structures, while external excitation leads to transverse vibrations. However, the prediction of nonlinear dynamic responses for functionally graded piezoelectric material (FGPM) shells under coupled parametric and external excitations remains insufficiently explored. Therefore, this paper investigates super- and sub-threshold parametrically excited responses to analyze the nonlinear vibrations of FGPM shells under a typical tuning condition (with a frequency ratio of exactly 2:2:1). A Duffing–Mathieu equation with cubic nonlinearity is established based on von Karman geometric nonlinearity, and approximate analytical solutions are derived using the method of varying amplitudes (MVA) and the Jacobian matrix. Subsequently, the accuracy of the MVA is validated, showing minimal deviation from numerical solutions obtained via MATLAB numerical integration. Analytical expressions for typical tuned coupled resonance are formulated, and parametric studies are conducted. Notably, the parametric excitation originates from velocity disturbance and voltage disturbance. And by changing the values of these parameters, the super- or sub-threshold parametrically excited responses may occur. The super-threshold parametrically excited response exhibits double jumps and bi-stability, contrasting sharply with the sub-threshold parametric excitation case.</p>

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Electrothermal coupling in the parametrically excited nonlinear dynamics of axially moving piezoelectric cylindrical shells

  • 期刊论文

  • 发表日期：

    2025年7月29日

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  • Yi-Wen Zhang,
  • Gui-Lin She,
  • Cheng Li

摘要

It is widely recognized that axial velocity disturbance and voltage disturbance can induce parametric resonance in shell structures, while external excitation leads to transverse vibrations. However, the prediction of nonlinear dynamic responses for functionally graded piezoelectric material (FGPM) shells under coupled parametric and external excitations remains insufficiently explored. Therefore, this paper investigates super- and sub-threshold parametrically excited responses to analyze the nonlinear vibrations of FGPM shells under a typical tuning condition (with a frequency ratio of exactly 2:2:1). A Duffing–Mathieu equation with cubic nonlinearity is established based on von Karman geometric nonlinearity, and approximate analytical solutions are derived using the method of varying amplitudes (MVA) and the Jacobian matrix. Subsequently, the accuracy of the MVA is validated, showing minimal deviation from numerical solutions obtained via MATLAB numerical integration. Analytical expressions for typical tuned coupled resonance are formulated, and parametric studies are conducted. Notably, the parametric excitation originates from velocity disturbance and voltage disturbance. And by changing the values of these parameters, the super- or sub-threshold parametrically excited responses may occur. The super-threshold parametrically excited response exhibits double jumps and bi-stability, contrasting sharply with the sub-threshold parametric excitation case.