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Quasi-static and dynamical analyses of a thermoviscoelastic Timoshenko beam using the differential quadrature method

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Abstract

The quasi-static and dynamic responses of a thermoviscoelastic Timoshenko beam subject to thermal loads are analyzed. First, based on the small geometric deformation assumption and Boltzmann constitutive relation, the governing equations for the beam are presented. Second, an extended differential quadrature method (DQM) in the spatial domain and a differential method in the temporal domain are combined to transform the integro-partial-differential governing equations into the ordinary differential equations. Third, the accuracy of the present discrete method is verified by elastic/viscoelastic examples, and the effects of thermal load parameters, material and geometrical parameters on the quasi-static and dynamic responses of the beam are discussed. Numerical results show that the thermal function parameter has a great effect on quasi-static and dynamic responses of the beam. Compared with the thermal relaxation time, the initial vibrational responses of the beam are more sensitive to the mechanical relaxation time of the thermoviscoelastic material.

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Authors and Affiliations

  1. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, 200072, China

    Qiang Lyu, Jingjing Li & Nenghui Zhang

  2. Department of Mechanics, College of Sciences, Shanghai University, Shanghai, 200444, China

    Jingjing Li & Nenghui Zhang

Authors
  1. Qiang Lyu
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  2. Jingjing Li
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  3. Nenghui Zhang
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Correspondence to Nenghui Zhang.

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Citation: LYU, Q., LI, J. J., and ZHANG, N. H. Quasi-static and dynamical analyses of a thermoviscoelastic Timoshenko beam using the differential quadrature method. Applied Mathematics and Mechanics (English Edition), 40(4), 549–562 (2019) https://doi.org/10.1007/s10483-019-2470-8

Project supported by the National Natural Science Foundation of China (Nos. 11772182 and 90816001)

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Lyu, Q., Li, J. & Zhang, N. Quasi-static and dynamical analyses of a thermoviscoelastic Timoshenko beam using the differential quadrature method. Appl. Math. Mech.-Engl. Ed. 40, 549–562 (2019). https://doi.org/10.1007/s10483-019-2470-8

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  • DOI: https://doi.org/10.1007/s10483-019-2470-8

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2010 Mathematics Subject Classification

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