Engineering Transactions, 70, 4, pp. 355–371, 2022

Nonlinear Vibration of a Beam Resting on a Nonlinear Viscoelastic Foundation Traversed by a Moving Mass: A Homotopy Analysis

University of Imam Ali
Iran, Islamic Republic of

Mojtaba Mahmoudi MONFARED
Islamic Azad University
Iran, Islamic Republic of

In this study, the dynamic response of an Euler-Bernoulli beam resting on the nonlinear viscoelastic foundation under the action of a moving mass by considering the stretching effect of the beam’s neutral axis is investigated. A Dirac-delta function is applied to model the location of the moving mass along the beam as well as its inertial effects. The Galerkin decomposition method is used to transform a partial dimensionless nonlinear differential equation of dynamic motion into an ordinary nonlinear differential equation. Subsequently, the well-known homotopy analysis method (HAM) is employed to obtain an approximate analytical solution of this equation. The validity and accuracy of the solution are examined numerically using the fourth-order Runge-Kutta method. Finally, several examples are provided to show the effects of parameters such as linear and nonlinear stiffness coefficients of a viscoelastic foundation, velocity of the moving mass as well as Coriolis force, centrifugal force and inertia force of the moving mass on the dynamic deflection of the beam.

Keywords: Euler-Bernoulli beam; nonlinear viscoelastic foundation; moving mass; homotopy  analysis method
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DOI: 10.24423/EngTrans.2266.20221128