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Nonlinear vibration analysis of third-order shear deformable functionally graded beams by a new method based on direct numerical integration technique

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Abstract

This study investigates the nonlinear vibration and dynamic response of a beam made of functionally graded material (FGM) within the framework of the improved third-order shear deformable theory. The beam is subjected to a concentrated moving load, and the included angle of the load direction and axial direction varies with time. Considering the von Kármán geometric nonlinearity, the nonlinear formulations of the FGM beam is derived. The Newmark method in conjunction with the Newton–Raphson iteration is adopted to analyze the dynamic response of the beam. A new method, based on a direct numerical integration technique for the matrix form motion equation, is presented to study the nonlinear vibration of the FGM beam. The proposed method overcomes the problem of signal determination for the solution of the eigenvector equation that often leads to nonconvergence or a false result of the nonlinear eigenvalue equation. In relation to the numerical results, the effects of material property distribution, vibration amplitude on the nonlinear dynamic behavior of the FGM beams, and the energy transference phenomenon are discussed in this paper.

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Authors and Affiliations

  1. Institute of Systems Engineering, China Academy of Engineering Physics, Mianyang, 621900, Sichuan, China

    Ke Xie

  2. Shock and Vibration of Engineering Material and Structures Key Laboratory of Sichuan Province, Mianyang, 621900, Sichuan, China

    Ke Xie

  3. Department of Energy and Power Engineering, Tsinghua University, Beijing, 100084, China

    Yuewu Wang & Tairan Fu

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  1. Ke Xie
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  2. Yuewu Wang
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  3. Tairan Fu
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Correspondence to Ke Xie.

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Xie, K., Wang, Y. & Fu, T. Nonlinear vibration analysis of third-order shear deformable functionally graded beams by a new method based on direct numerical integration technique. Int J Mech Mater Des 16, 839–855 (2020). https://doi.org/10.1007/s10999-020-09493-y

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  • DOI: https://doi.org/10.1007/s10999-020-09493-y

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