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Quasi-static and dynamical analysis for viscoelastic Timoshenko beam with fractional derivative constitutive relation

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Abstract

The equations of motion governing the quasi-static and dynamical behavior of a viscoelastic Timoshenko beam are derived. The viscoelastic material is assumed to obey a three-dimensional fractional derivative constitutive relation. The quasi-static behavior of the viscoelastic Timoshenko beam under step loading is analyzed and the analytical solution is obtained. The influence of material parameters on the deflection is investigated. The dynamical response of the viscoelastic Timoshenko beam subjected to a periodic excitation is studied by means of mode shape functions. And the effect of both transverse shear and rotational inertia on the vibration of the beam is discussed.

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, 200072, Shanghai, P R China

    Zhu Zheng-you Professor & Cheng Chang-jun

  2. Department of Mathematics, Shanghai University, 200436, Shanghai, P R China

    Zhu Zheng-you Professor

  3. Shanghai Supercomputer Center, 201203, Shanghai, P R China

    Li Gen-guo

  4. Department of Mechanics, Shanghai University, 200436, Shanghai, P R China

    Cheng Chang-jun

Authors
  1. Zhu Zheng-you Professor
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  2. Li Gen-guo
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  3. Cheng Chang-jun
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Contributed CHENG Chang-jun

Foundation item: the National Natural Science Foundation of China (19772027); the Science Foundation of Shanghai Municipal Commission of Sciences and Technology (98JC14032); the Science Foundation of Shanghai Municipal Commission of Education (99A01)

Biography: ZHU Zheng-you (1937−)

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Zheng-you, Z., Gen-guo, L. & Chang-jun, C. Quasi-static and dynamical analysis for viscoelastic Timoshenko beam with fractional derivative constitutive relation. Appl Math Mech 23, 1–12 (2002). https://doi.org/10.1007/BF02437724

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  • DOI: https://doi.org/10.1007/BF02437724

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