Dynamic response of an infinite Timoshenko beam on a nonlinear viscoelastic foundation to a moving load

The present paper investigates the dynamic response of infinite Timoshenko beams supported by nonlinear viscoelastic foundations subjected to a moving concentrated force. Nonlinear foundation is assumed to be cubic. The nonlinear governing equations of motion are developed by considering the effects...

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Bibliographic Details
Published in:Nonlinear dynamics 2013-07, Vol.73 (1-2), p.285-298
Main Authors: Ding, Hu, Shi, Kang-Li, Chen, Li-Qun, Yang, Shao-Pu
Format: Article
Language:English
Subjects:
Automotive Engineering
Beams (structural)
Classical Mechanics
Closed form solutions
Control
Cybernetics
Deformation effects
Differential equations
Dynamic response
Dynamical Systems
Engineering
Equations of motion
Exact solutions
Formability
Foundations
Fourier transforms
Green's functions
Integrals
Mathematical analysis
Mathematical models
Mechanical Engineering
Moving loads
Nonlinear dynamics
Nonlinear equations
Nonlinearity
Original Paper
Perturbation methods
Product design
Shear modulus
Timoshenko beams
Vibration
Viscoelasticity
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Summary:The present paper investigates the dynamic response of infinite Timoshenko beams supported by nonlinear viscoelastic foundations subjected to a moving concentrated force. Nonlinear foundation is assumed to be cubic. The nonlinear governing equations of motion are developed by considering the effects of the shear deformable beams and the shear modulus of foundations at the same time. The differential equations are, respectively, solved using the Adomian decomposition method and a perturbation method in conjunction with complex Fourier transformation. An approximate closed form solution is derived in an integral form based on the presented Green function and the theorem of residues, which is used for the calculation of the integral. The dynamic response distribution along the length of the beam is obtained from the closed form solution. The derivation process demonstrates that two methods for the dynamic response of infinite beams on nonlinear foundations with a moving force give the consistent result. The numerical results investigate the influences of the shear deformable beam and the shear modulus of foundations on dynamic responses. Moreover, the influences on the dynamic response are numerically studied for nonlinearity, viscoelasticity and other system parameters.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-013-0784-0