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<p>Nonlinear vibrations of an axially moving functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plate are numerically and analytically investigated on the steady-state responses in the presence of 1:3 internal resonances. Based on Reddy’s third-order shear deformation theory, nonlinear partial differential equations of motion for axially moving FG-CNTRC plates are derived by Hamilton’s principle and subsequently discretized through the Galerkin method. Nonlinear differential equations of motion are solved by means of Runge–Kutta method and method of multiple scales, and then dynamic response of the internal resonance system is analyzed. Lyapunov’s first-order approximation theory is employed to determine the stabilities of the steady-state response. The effects of excitation amplitude, detuning parameters, axial velocity and location of excitation force on nonlinear dynamic behavior of the system are investigated and discussed in detail. </p>

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Internal resonance of axially moving functionally graded carbon nanotube-reinforced composite plates

  • 期刊论文

  • 发表日期：

    2025年6月5日

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  • Hong Ying Li,
  • Ming Yao Zhang,
  • Qin Jing Ji,
  • Jian Li

摘要

Nonlinear vibrations of an axially moving functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plate are numerically and analytically investigated on the steady-state responses in the presence of 1:3 internal resonances. Based on Reddy’s third-order shear deformation theory, nonlinear partial differential equations of motion for axially moving FG-CNTRC plates are derived by Hamilton’s principle and subsequently discretized through the Galerkin method. Nonlinear differential equations of motion are solved by means of Runge–Kutta method and method of multiple scales, and then dynamic response of the internal resonance system is analyzed. Lyapunov’s first-order approximation theory is employed to determine the stabilities of the steady-state response. The effects of excitation amplitude, detuning parameters, axial velocity and location of excitation force on nonlinear dynamic behavior of the system are investigated and discussed in detail.