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Quasi-static and dynamical analysis for viscoelastic Timoshenko beam with fractional derivative constitutive relation |
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| Authors: | Zhu Zheng-you Li Gen-guo Cheng Chang-jun |
| Affiliation: | 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China;2. Department of Mathematics, Shanghai University, Shanghai 200436, P. R. China;3. Shanghai Supercomputer Center, Shanghai 201203, P. R. China;4. Department of Mechanics, Shanghai University, Shanghai 200436, P. R. China |
| 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. |
| Keywords: | viscoelastic Timoshenko beam fractional derivative constitutive relation weakly singular Volterra integro_differential equation dynamical response |
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