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

• Published in: Applied mathematics and mechanics Vol. 40; no. 4; pp. 549 - 562
• Main Authors: Lyu, Qiang, Li, Jingjing, Zhang, Nenghui
• Format: Journal Article
• Language: English
• Published: Shanghai Shanghai University 01.04.2019; Springer Nature B.V; Department of Mechanics, College of Sciences, Shanghai University,Shanghai 200444, China; Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China%Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
• Edition: English ed.
• Subjects: Applications of Mathematics; Classical Mechanics; Constitutive relationships; Deformation; Differential equations; Differential thermal analysis; Fluid- and Aerodynamics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Ordinary differential equations; Parameters; Partial Differential Equations; Relaxation time; Thermal relaxation; Timoshenko beams; Viscoelasticity; thermoviscoelasticity; differential quadrature method (DQM); 74H45; Timoshenko beam; thermal load; 74A15; dynamic response; O327
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-019-2470-8

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.