Analysis On The Vertical Collision Vibration Of Semi-infinite Elastic Medium And Single-layer Foundation

The paper has discussed the details that the displacements of surface points change as the time goes under the function of vertical impulsive load. Taking the theory of dynamic elasticity, it deduced the wave equation that contains the vibration criterion. Based on the theory of potential function, it made the comprehensive deduction with kinds of mathematic methods such as the Laplace transform, the Fourier-Bessel integral and so on, then the form solution of the displacements of surface points having been acquired, finally, the numerical integral method taking the MATLAB language has been employed for the purpose of getting the real values of displacement. In this paper, it is mainly focused on the study of two types of foundations, the first belonging to the semi-infinite elastic medium, with the second belonging to the single-layer foundation, which contains the upper layer of the linear elastomer and the lower layer of solid rock. It is also discussed that various problems affiliated with numerical methods influence the calculation process, aiming in achieving the most optional requirements of calculation accuracy and minimum calculation amount. For semi-infinite space, the extensive analysis was given on the influence of different factors on displacement of surface points. For single-layer foundation, the discussion was emphasized on the orienting relation between thickness of the soil layer and the reflection wave. From the points of theoretical creation and engineering application, the consideration of the semi-mathematic solution got perfect application.