The Study Of A Precise Method For Dynamic Flexibility Of Layer Foundation In Hamilton System

It is generally feel that the study about dynamic characteristics of layered foundation is more complex and more difficult than that of uniform soil, so the study about dynamic flexibility of layered elastic foundation is the problem which is often encountered in the research of the seismic response analysis of engineering structures. Among the numerous study methods, the propagation matrix method is the most typical method for dynamic flexibility of layered elastic foundation. But if the layer of foundation is large, it will emerge index overflow in the numerical simulation, and the inverse Fourier transform about wavenumber in infinite domain is very time consuming. The paper attempts to apply the precise integration method to deduce the calculation process of the dynamic flexibility in the frequency-wavenumber domain, and then convert to the spatial domain to get the dynamic flexibility in it.The precise integration method used here can produce numerical results up to the precision of the computer used and preserve the symplectic structure of the Hamilton systern.It is a precise numerical method for solving sets of first order linear ordinary differential equations with specified initial value conditions for time domain problems, or with specilied two-point boundary value conditions for space domain problems. In this paper, the derivation of fundamental governing equations of layered elastic foundation is made in the duality system, and governing equations are represented as Hamilton canonical equations in the frequency-wavenumber domain. Based on this point, a new method is proposed to solve dynamic flexibility of layered elastic foundation. The segment matrix of micro layer is obtained by using the precise integration method, and then, through merging segment matrix of micro layer, we evaluate the segment matrix of the whole foundation. Finally, the dynamic flexibility of layered elastic foundation is calculated by incorporating the radiation condition of boundary into the segment matrix of the whole foundation. In the end, accuracy of this method is verified by numerical examples.Having got the dynamic flexibility of layer foundation in the frequency-wavenumber domain, thus the formula which is about the uniformly distributed harmonic force and the concentrated harmonic force at the foundation surface is derived and simplified in the spatial domain. However, there is a singularity in the process of integral transformation from the frequency-wavenumber domain to the spatial domain about displacement. And if the layer foundation parameters are constant, the singular value is proportional to the frequency. The paper tries to divide singularity from the integral interval, and use the variable step five points Legendre-Gauss integration to solve respectively. Eventually, we obtain the dynamic flexibility about the uniformly distributed harmonic force and the concentrated harmonic force in the spatial domain. The numerical examples suggest that the method used to solve the dynamic flexibility is effective, and testify that the method proposed to solve dynamic flexibility of layered elastic foundation is easy to simulate the layer characteristic of natural foundation and gives high precision.