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Applied Mathematics and Mechanics

, Volume 40, Issue 4, pp 549–562 | Cite as

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

  • Qiang Lyu
  • Jingjing Li
  • Nenghui ZhangEmail author
Article
  • 63 Downloads

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.

Key words

Timoshenko beam thermoviscoelasticity thermal load dynamic response differential quadrature method (DQM) 

Chinese Library Classification

O327 

2010 Mathematics Subject Classification

74A15 74H45 

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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and MechanicsShanghai UniversityShanghaiChina
  2. 2.Department of Mechanics, College of SciencesShanghai UniversityShanghaiChina

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