Hybrid DSC-T/β-newmark method for dynamic response analysis of isotropic thin plates on elastic foundations

The static/dynamic analysis of the thin plate is of great importance in engineering problems. Based on the complexity of the problem, only for some important cases of boundary conditions, analytical solutions were derived. While in general case, numerical approaches should be implemented to solve the problem. The discrete singular convolution (DSC) technique is one of the most accurate methods. Until now, this method is difficult to be used for the determination of the static and dynamic responses for plates with semi-rigid boundary conditions. Based on the fact that DSC method using the Taylor approach (DSC-T) is recently used for the analysis of the free vibration of free and semi-rigid edges rectangular plate, this study aims to extend the application of the DSC-T methods to the static and dynamic analysis of the thin rectangular plate restrained with the dowels and resting on elastic foundation. The DSC-T approach is extended to the resolution of the static case of a dowelled plate, and with the combination of the Newmark scheme, to the case of the dynamic load. The results showed the applicability of the studied method for the determination of static and dynamic responses of the plates. Besides, it is shown that there is a linear relationship between the value of the depth and the decrement of the modified Vlasov soil. The value of the logarithmic decrement of the soil is highly influenced by the thickness of the plate namely for membranes and very thin plates. The DSC-T method could be recommended for the engineering design of a variety of civil structures.