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.
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Contributed CHENG Chang-jun
Foundation item: the National Natural Science Foundation of China (19772027); the Science Foundation of Shanghai Municipal Commission of Sciences and Technology (98JC14032); the Science Foundation of Shanghai Municipal Commission of Education (99A01)
Biography: ZHU Zheng-you (1937−)
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Zheng-you, Z., Gen-guo, L. & Chang-jun, C. Quasi-static and dynamical analysis for viscoelastic Timoshenko beam with fractional derivative constitutive relation. Appl Math Mech 23, 1–12 (2002). https://doi.org/10.1007/BF02437724
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DOI: https://doi.org/10.1007/BF02437724
Key words
- viscoelastic Timoshenko beam
- fractional derivative constitutive relation
- weakly singular Volterra integro-differential equation
- dynamical response