On the accuracy of lumped mass models for free vibration of beams

Abstract eng:
The accuracy of natural frequencies and mode shapes of beams, calculated using lumpedmass models, was investigated for various support configurations. With practical computations in mind, the aim of this research was to determine the level of discretisation required in order to achieve a given level of accuracy, thus providing guidance to structural practitioners in the course of vibration serviceability checks. Natural frequencies and mode shapes calculated using the lumped mass model were compared with the practically exact values determined using either the Euler-Bernoulli beam model, or a refined finite-element analysis. It was found that the natural frequencies for all beams (except those with a free end) rapidly converge to the exact values as the number of adopted masses is increased. As a rough guide, at least twice the number of masses as the mode number in question need to be adopted, to give results with an error of less than 2%. For two-span beams of unequal span lengths, computed natural frequencies based on a given number of masses per span become less accurate as the difference in length between the two spans increases. It is concluded that the lumped-mass model generally provides a quick and accurate approximation of natural frequencies and mode shapes for simply supported beams with spans that are equal or nearly equal to each other, but caution is required when modelling beams with free ends or with spans that differ significantly in length.

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