| In order to prevent and abate the loss caused by natural or man-made disasters such as earthquake, typhoon and war, dynamic analyses of engineering structures are gaining more and more attention. The dynamic analysis of a structure involves the cooperation of the up-structure and the foundation. Because of the infinity of the half space foundation and the diversity of the soil property, dynamic problems in the geotechnical engineering are very complex. As the calculating capacity of the computer has rapidly developed, it is now feasible to solve dynamic proplems by using 3D numerical analysis method. In this thesis, the static and dynamic proplems of plates resting on Winkler foundation, two-parameter foundation, elastic half-space foundation and layered foundation are analyzed by coupling FEM, BEM and radiate infinite elements. The main works are as following:(1) The free vibration of the elastic plate is analyzed. According to the Mindlin plate theory, the parametric FEM model of the plate is established. Then the problem of free vibration of the elastic plate is converted to the problem of solving the general eigenvalues. The program for analyzing free vibration of the elastic plate is coded, which is then used to analyze the free vibration of circular and square plates. The results are compared with those by p-Ritz method, and good agreement has been achieved.(2) The free vibration of the elastic plate resting on Winkler foundation is analyzed. The FEM format for plate-foundation cooperation is deduced, and the program for analyzing free vibration of the elastic plate resting on Winkler foundation is coded, which is then used to analyze the free vibration of circular and square plates resting on Winkler foundation. The effects of plate thickness and foundation modulus are studied, and some regular results have been obtained.(3) The dynamic response of the plate resting on Winkler foundation subjected to moving load is analyzed. The dynamic equilibrium equation is solved by Newmark method, and the responding computer program is coded. The thin and thick plates are analyzed respectively. The effects of load moving velocity, foundation modulus and damping ratio are studied, and the influences of the related parameters are analyzed.(4) The free vibration and forced vibration of the elastic plate resting on two-parameter foundation is analyzed by coupling FEM and BEM. Based on Pasternak theory of two-parameter foundation, the FEM format for plate-foundation cooperration within the plate zone is proposed. The effect of foundation outside the plate zone is considered by BEM method. The responding computer program is coded. The calculated results of the inherent frequencies agree with the tested values. When the variable frequent load is subjected, the dynamic responses of the foundation plate reach the maximum while resonance occurs. Meanwhile, the damping can significantly reduce the resonant response.(5) The model of three-dimensional point-radiate 8-node infinite element is established. Its stiffness and mass matrices are deduced. Its mapping function and displacement function are very concise. It can be easily coupled with the 3D 20-node isoparametric element. The responding program coupling finite and infinite elements for the static analysis is coded, and is applied to analyze the static cooperation of the half space foundation and the plate. Results show that it is accurate to simulate the half space foundation by coupling finite elements and point-radiate infinite elements. The static analysis not only can be as a base of the dynamic analysis, but also has the practic significance in engineering.(6) According to Lysmer's equations for the viscous boundary, a new kind of radiate damping matrix is deduced. In the usual dynamic analysis of geotechnical engineering, an artificial viscous boundary is often made to simulate the radiate damping effect of the foundation. The conventional viscous boundary is limited for the plane surface boundary. On the other side, the presented damping matrix can be applied to simulate the radiate damping effect of the 3D curved surface boundary. Therefore, it can be used to enlarge the applicability of the viscous boundary.(7) The program for 3D dynamic analysis by coupling point-radiate infinite elements and finite elements is coded. At first, the free vibration of a square plate resting on the half space foundation is analyzed. Then the dynamic responses of the plate subjected to suddenly applied load and harmonious load are analyzed. Results show that when the exciting frequency is far from the inherent frequencies, the dynamic response coefficient is insignificant,and the damping effect is neglectable. When the exciting frequency is close to the inherent frequencies, the dynamic response coefficient is significant,and the damping effect is obvious.(8) The model of three-dimensional axis-radiate 8-node infinite element is established. It can be easily coupled with the 3D 20-node isoparametric element to simulate the layered foundation. The responding infinite-finite element program for static analysis is coded, and then used to solve the static problems of the plate resting on the layered foundation. Results show the efficiency and accuracy of the method of coupling the axis-radiate elements with the finite elements.(9) The program for dynamic analysis by coupling axis-radiate infinite elements and finite elements is coded, and then used to analyze the dynamic response of a square plate resting on the layered foundation. The effects of load increasement speed and damping raito are studied.
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