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Home  >  Transasctions of NAMP VOL2

9. On the Effect of Lumped Mass Matrices on the Dynamic Response of Non-Uniform Beams Under Moving Loads BY I.O. Abiala Transactions of NAMP Volume2,(November, 2016), pp 79 – 90
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Abstract

The effect of the Lumped Mass Matrices (LMM) on the dynamic response of non-uniform beams (NUB) under uniformly distributed moving loads is studied. The analysis was done by using the finite element numerical method. The material properties, such as the flexural rigidity and the cross-sectional area of the beams were assumed to be  functions of the spatial variable  . Also, the elements stiffness, mass and centripetal acceleration matrices as well as the load vectors were derived using the Galerkin’s Weighted Residual Method (GWRM). The Lumped Mass Matrices (LMM) for the problem was obtained using Archer’s principle. The dynamic responses of non-uniform beams under uniformly distributed moving loads were obtained using the Newmark’s numerical method. Furthermore, the dynamic responses of non-uniform beams (NUB) under moving loads using Consistent Mass Matrices (CMM) and Lumped Mass Matrices (LMM) were also compared. It was discovered that, the developed Lumped Mass matrix for the problem considered in this work, is unique and satisfies the general requirements of matrix lumping which does not require the inversion of the assembled mass matrix.

Keywords: Lumped Mass Matrices, dynamic response, non-uniform beams, Archer’s principle

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