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

doi:10.1007/s10483-019-2470-8

Applied Mathematics and Mechanics (English Edition) ›› 2019, Vol. 40 ›› Issue (4): 549-562.doi: https://doi.org/10.1007/s10483-019-2470-8

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

Qiang LYU¹, Jingjing LI^1,2, Nenghui ZHANG^1,2

1. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
2. Department of Mechanics, College of Sciences, Shanghai University, Shanghai 200444, China

收稿日期:2018-05-05 修回日期:2018-08-17 出版日期:2019-04-01 发布日期:2019-04-01
通讯作者: Nenghui ZHANG E-mail:nhzhang@shu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11772182 and 90816001)

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

Qiang LYU¹, Jingjing LI^1,2, Nenghui ZHANG^1,2

1. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
2. Department of Mechanics, College of Sciences, Shanghai University, Shanghai 200444, China

Received:2018-05-05 Revised:2018-08-17 Online:2019-04-01 Published:2019-04-01
Contact: Nenghui ZHANG E-mail:nhzhang@shu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11772182 and 90816001)

摘要/Abstract

摘要：

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.

关键词: reservoir filtration, new model, exact analytical solutions, Timoshenko beam, dynamic response, thermoviscoelasticity, thermal load, differential quadrature method (DQM)

Abstract:

Key words: Timoshenko beam, thermal load, reservoir filtration, new model, exact analytical solutions, differential quadrature method (DQM), dynamic response, thermoviscoelasticity

中图分类号:

74A15
74H45

Qiang LYU, Jingjing LI, Nenghui ZHANG. Quasi-static and dynamical analyses of a thermoviscoelastic Timoshenko beam using the differential quadrature method[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(4): 549-562.

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

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

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