Free vibration analysis of beams resting on elastic foundation using modified Vlasov model

Free Vibration Analysis of Beams Resting on Elastic Foundation Using Modified Vlasov Model Beams resting on elastic foundation are very common in structural systems. For this reason in the technical literature numerous works have been concerned with such problems. In these kinds of problems, the structural system should be analysed by using a realistic model for soil-structure interaction. It is well known that dynamic analysis is an important part of engineering investigations in these problems, so that the free vibration analysis should be done to do this, because a knowledge of natural frequencies of vibration and associated mode shapes are guide for researchers in the dynamic analysis. Therefore free vibration analysis is an important part of the researches made on structural dynamics. The purpose of this study is to analyse the effects of various parameters such as subsoil depth, beam length, their ratio and the value of the vertical deformation parameter within the soil on the natural frequency parameters of beams on elastic foundation using modified Vlasov model. This analysis has been carried out by the aid of a computer program coded by using finite element method. The first ten natural frequencies and mode shapes corresponding to the first six of them are presented. For this purpose, in the first chapter, after brief information about soil-structures interaction is given, a brief review of previous studies of beams on elastic foundation are presented. Then finite element formulation of the problem is presented after some basic information about this method is given. In the second chapter, the first ten natural frequency parameters of beams considered and mode shapes corresponding to the first six of them for several subsoil depth, beam length, their ratio and value of the vertical deformation parameter within the soil are presented in tabular and graphical forms. In the third chapter, the conclusions drawn from the results are given and some recommendations for future studies are made. This chapter is followed by a list of references. It is concluded that generally, the effect of the subsoil depth on the frequency parameters of the beam on elastic foundation is larger than that of the other parameters considered in this study. Keywords : Parametric analysis, Beams on elastic foundation, Modified Vlasov model, Free vibration, Finite element method VI