Frequency Analysis for a Timoshenko Beam Located on an Elastic Foundation

It is quite usual to encounter a beam with different types of cross section or even structuraldiscontinuities such as a crack along its length. Furthermore, in many occasions such a beam mayhappen to be exposed to the oscillatory fluctuations. Therefore, any information about its naturalfrequencies may be worthwhile. Amongst the problems of discontinues beam analysis, in this paper aspecial kind of frequency analysis for a cracked and stepped beam located on an elastic foundation isconsidered. Accordingly, following a look out at the definition of Timoshenko beams, a specialmodeling trend known as the wave method is introduced. Based on the d'Alembert’s approach for thesolution of wave differential equations, the technique of wave method is mainly depended on the studyof transmission and reflection of waves colliding to a barrier. The method results in a global frequencymatrix, which its determinant gives out the natural frequencies. The wave method is employed for thefrequency analysis in some kinds of cracked and stepped beams with different types of boundaryconditions. In some typical cases, the results are compared to other similar works and confirmed to beconvincing.

Keywords:

Timoshenko beam , Elastic Foundation , Wave approach , Cracked stepped beam , Frequency analysis