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On the limitations of linear beams for the problems of moving mass-beam interaction using a meshfree method

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Abstract

This paper deals with the capabilities of linear and nonlinear beam theories in predicting the dynamic response of an elastically supported thin beam traversed by a moving mass. To this end, the discrete equations of motion are developed based on Lagrange’s equations via reproducing kernel particle method (RKPM). For a particular case of a simply supported beam, Galerkin method is also employed to verify the results obtained by RKPM, and a reasonably good agreement is achieved. Variations of the maximum dynamic deflection and bending moment associated with the linear and nonlinear beam theories are investigated in terms of moving mass weight and velocity for various beam boundary conditions. It is demonstrated that for majority of the moving mass velocities, the differences between the results of linear and nonlinear analyses become remarkable as the moving mass weight increases, particularly for high levels of moving mass velocity. Except for the cantilever beam, the nonlinear beam theory predicts higher possibility of moving mass separation from the base beam compared to the linear one. Furthermore, the accuracy levels of the linear beam theory are determined for thin beams under large deflections and small rotations as a function of moving mass weight and velocity in various boundary conditions.

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Authors and Affiliations

  1. Department of Civil Engineering, Islamic Azad University, Chalous Branch, Chalous, Iran

    Keivan Kiani

  2. Department of Civil Engineering, University of Science and Culture, P.O. Box 13145-871, Tehran, Iran

    Ali Nikkhoo

Authors
  1. Keivan Kiani
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  2. Ali Nikkhoo
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Correspondence to Ali Nikkhoo.

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Kiani, K., Nikkhoo, A. On the limitations of linear beams for the problems of moving mass-beam interaction using a meshfree method. Acta Mech Sin 28, 164–179 (2012). https://doi.org/10.1007/s10409-012-0021-y

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  • DOI: https://doi.org/10.1007/s10409-012-0021-y

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