The Methods for Efficient Transverse Vibration of Structural Dynamics: a Historical Point of View

Abstract

The different assumptions and corresponding theories of transverse vibrations of beams are presented. Eight mathematical models, namely Euler-Bernoulli, Rayleigh, Euler-Bernoulli modified, Bress, Volterra, Ambartsumyan, Timoshenko and Love theory are firstly discussed. Then, different theories of dynamic behaviours of beams can be obtained from the equations of the theory of elasticity, which are presented with respect to average values. Nowadays, beam elements are usually based on two theories, i.e Euler-Bernoulli and Timoshenko beam theory. One of the recent developments pointed out is the computer program ABAQUS, a finite element based crosssectional and non-linear analysis for beam. Finally, several examples are presented as numerical validations in which FE results are compared with those from the theories in the literature where available and appropriate.