Study On Dynamic Response Of A Thin Plate On Elastic Foundation

The dynamic response of beam and plate on elastic foundation is becoming more and more attractive in geotechnical engineering and transportation engineering. There were a lot of researcher studying this problem, and they achieved many valuable conclusions. But the dynamic response theory concerned with this is still in research stage. It has not good method to consider the influence of the velocity and frequency of the dynamic loads, and much study based on the dynamic response of a plate of infinite extent on elastic foundation. At the same time, the different researcher had achieved different conclusions because of using the various mechanic models. In this paper, the dynamic response of a Kirchhoff plate on elastic foundation is investigated, close-form deflection response of a plate subjected to semi-sine load and moving load, and the influence of the moving velocity, frequency and the physical parameters of foundation were studied systemically.Based on a thin plate and Winkler foundation model, transient dynamic response of a viscoelastic foundation supported infinite strip due to semi-sine load of FWD was studied. Analytical solution for displacements and stresses were obtained, with the help of triangular series method in combination with the Laplace-Fourier transform method. The dynamic displacement response of a thin plate, which has horizontal resistance at its bottom, resting on elastic foundation has also been investigated when the system is subjected to a semi-sine load of FWD. Finally, the influence of transient load period, physical parameters of foundation and plate, and the horizontal resistance were discussed.The dynamic response of a thin slab on elastic foundation, subjected to moving area load and moving area harmonic load, is investigated by triangular series and integral transformation method. Analytical solutions for displacement and tensile stress were obtained, and the effects of the moving speed, physical parameters of slab and sub-grade were investigated. It is shown that the velocity and frequency of load have some affects on dynamic response of plate.The viscous damping is considered, the problem of steady state response of a plate on viscoelastic Kelvin foundation subjected to moving load. The theorem of residue was employed to evaluate the generalized integral such that a close-form solution could be achieved. The influence of viscous damping was discussed; it was shown that the influence of frequency and moving velocity depended on the size of viscous damping.The harmonic response of a thin plate subjected to in-plane tensile resting on a Winkler -type viscoelastic foundation was investigated when the system was subjected to a moving harmonic load. Analyses were performed to investigate the effects of axial force, and examine how the axial force affects the critical velocity and critical frequency.The analytical solutions of a rectangular plate having arbitrary and supports on viscoelastic foundation subjected to moving harmonic loads were obtained with the help of the modal superposition principle and the triangular series method. The response to a single moving harmonic concentrated load is first investigated, and then the effects of velocity, frequency, elastic foundation stiffness and viscous damping were studied. Finally, the variation of maximum dynamic displacement was affected by the displacement and the differences in phase between multiple moving loads.The dynamic response of the infinite plate rested on a elastic layer-sub-grade subjected to a moving line load was investigated. A higher-order continuum model derived from the modified Vlazov model presents the sub-grade. By the present method, the subsoil lso could be assumed to have uniform depth with linearly varying elastic modulus resting on a stiff soil layer or bedrock. The effects of the soil stiffness and the inhomogeneity, velocity and sub-grade depth were analyzed. The method presented can be adopted to calculate the dynamic response of pavement resting on layer-sub-grade.In comparison with the other theories, the...