Research On Natural-vibration Characteristics And Dynamic Response Of Three-Dimensional Embedded Frame Structure

The reverberation-ray matrix method proposed in 1998 by Pao, has been widely used in dynamic analysis of frame structure. At present, there are a lot of researches on two dimensional non-embedded structure. When considering the structure and the foundation medium, it may find a more outstanding problem. In this connection, we study the reverberation-ray matrix method for solving natural vibration characteristics and dynamic response of three dimensional embedded frame in this paper.This paper is based on Winkler foundation model, studied the basic principle of reverberation ray matrix method in pile-soil mutual effect founded on the Timoshenko beam theory. The wave equation of longitudinal wave, torsional wave and shear wave in the pile soil system is established. Based on the force balance and displacement compatibility condition, the scattering relation at the node is established, propagation matrix and permutation matrix is introduced, get the reverberation ray matrix of three dimensional embedded frame structure.Based on the basic formula of the reverberation-ray matrix method, The natural frequency and modal of the fully embedded single pile foundation, partial embedded single pile foundation and frame structure based on Timoshenko beam theory are obtained by using the method of gold searching in polar coordinates.Compared with the natural vibration characteristics of the non damping structure obtained by the finite element software. Result shows, Soil damping decreases natural frequency, Soil spring increases the natural frequency of the structure. For partially embedded structure, the damping of the soil can reduce the deformation of the embedded part. The influence of soil mass on the natural vibration characteristics of the structure decreases with the increase of the order number.Using the reverberation-ray matrix method of three dimensional embedded frame, the transient response of partially embeded pile foundation and frame structure under square wave pulse load is studied.On this basis, The propagation of elastic wave in the structure of partially embedded structure is discussed. The effects of material damping, spring coefficient of soil, damping coefficient of soil, embedment depth and the direction of pulse on the axial velocity and torsional velocity in the structure are discussed.The effects of different soil conditions[two layer soil(upper-soft lower-hard and upperhard lower-soft), three layer soil(soft interlayer and hard interbedded layers)] on the transient response of the receiving point are further studied. Research show, In the case of equal thickness, the distribution order of the soil layer has no effect on the transient response at the receiving point. In the case of the same total embedment depth, The thicker the hard soil layer, the weaker the signal received at the receiving point.