Approximate Method for the Determination of Natural Frequencies of a Multi-Degree of Freedom Beam System

Abstract

In this paper, a simplified dynamic model is developed to predict the natural frequencies of a multi-Degree of freedom structural system using the concept of an elastic shear wave in a solid prismatic bar. The vibrating solid prismatic bar and the multi-degree of freedom beam system with distributed mass under self-excited vibration are assumed to be dynamically equivalent. Lumped mass idealization is used to discretize the original beam structure with distributed mass to a weightless beam with distributed masses substituted with lumped masses at different nodal points. A numerical example obtained from literature is given to illustrate the application of the present model. All the natural frequencies predicted using the present formulation compared favorably with those of other authors most especially in the first and second vibration mode. The correlation coefficient value was high showing high (0.991) showing high predictive ability of the present model.