Free vibration analysis of dowelled rectangular isotropic thin plate on a Modified Vlasov soil type by using discrete singular convolution method

The behaviour of plates resting on elastic foundations has wide interest because it is an important model for many engineering applications. Natural frequencies and corresponding mode shapes are guides to investigating the behaviour of a soil-structure system with time. Therefore, free vibration analysis constitutes a considerable part of research done on this topic. In this study, the effects of the stiffness of a surrounding Modified Vlasov soil type, the soil depth, and the aspect ratio on the free vibration of a thin rectangular dowelled plate on the Modified Vlasov soil type are investigated. We used a discrete singular convolution (DSC) with a Taylor series expansion method to apply the boundary conditions. The two formulas of the Taylor series expansion are used in the DSC to eliminate the fictitious points outside the physical domain. It is noticed that beyond a certain depth, neither the effective depth of the soil nor the, frequency varies consistently. Furthermore, the dynamically activated depth influences the frequency values for plates more than for beams. In addition, the effect of the elastic rotational stiffness of the surrounding soil is found to be negligible compared to that of the elastic vertical translational one. The results obtained can serve as a basis for the dynamic analysis of rigid pavements.