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Nonlinear vibration of edged cracked FGM beams using differential quadrature method

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Abstract

This paper investigated the nonlinear vibration of functionally graded beams containing an open edge crack based on Timoshenko beam theory. The cracked section is modeled by a massless elastic rotational spring. It is assumed that material properties follow exponential distributions through the beam thickness. The differential quadrature (DQ) method is employed to discretize the nonlinear governing equations which are then solved by a direct iterative method to obtain the nonlinear vibration frequencies of beams with different boundary conditions. The effects of the material gradient, crack depth and boundary conditions on nonlinear free vibration characteristics of the cracked FGM beams are studied in detail.

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Authors and Affiliations

  1. Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing, 100044, China

    LiaoLiang Ke & YueSheng Wang

  2. School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, PO Box 71, Bundoora, Victoria, 3083, Australia

    Jie Yang & Firoz Alam

  3. Department of Building and Construction, City University of Hong Kong, Kowloon, Hong Kong, China

    Sritawat Kitipornchai

Authors
  1. LiaoLiang Ke
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  2. YueSheng Wang
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  3. Jie Yang
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  4. Sritawat Kitipornchai
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  5. Firoz Alam
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Correspondence to LiaoLiang Ke.

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Ke, L., Wang, Y., Yang, J. et al. Nonlinear vibration of edged cracked FGM beams using differential quadrature method. Sci. China Phys. Mech. Astron. 55, 2114–2121 (2012). https://doi.org/10.1007/s11433-012-4704-y

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  • DOI: https://doi.org/10.1007/s11433-012-4704-y

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