| Free vibration of space-mega-frame, frame-shear wall and bundled-tube structures was analyzed and researched by semi-analytical method of ODE (Ordinary Differential Equation) Solver in this paper. Utilizing the free vibration semi-analytical method, the above-mentioned three kinds of structure were analyzed in elastic extent, based on three-dimensional model of generalized Timoshenko cantilever beam regarded as to be built on a semi infinite elastic subgrade, by means of ODE Solver. The principal work performed by the thesis can be summarized as follows:(1) Introduced the background and significance of the topics.(2) Discussed the the analysis model about free vibration analysis of tall building structure.(3) Discussed how to solve various equivalent stiffness more precisely according to the simplification comments of the various tall building structures.(4) Introduced the principal and means of the vibration analysis of tall building structure adopted ODE method. Analysed the free vibration issueses of several typical structures.The results of analysis and calculation examples with tall building structure show that the simplified analytical model is rational and applicable. Furthermore, the calculation results obtained from the above-mentioned analytical model were very close to those of resulted from their corresponding precise models. Therefore a sort of quick and simplified analytical method suited the preliminary design and global behavior evaluation of tall building structure was presented.
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