Analysis Of Dynamic Characteristics Of Tube Structure Based On ODE Solver

The tube structure is playing an important role in the modern architecture. It has good intensity and rigidity. It is beautiful in appearance and flexible in usage. Moreover, it receives strength with ration and has strong integrity. So it is adopted extensively in high building. In this paper, tube structure of high building is divided into a piece of elements by finite element technology and corresponding vibration differential equations about tube structure are founded based on energy variation principle and boundary conditions. Then the equations by a series of mapping technique are changed into a standard eigenvalue problem of ordinary differential equations, in order to solve directly by a solver of Ordinary Differential Equation (ODE in short). COLSYS, a general purpose program, has a feature of self-adaptability to satisfy the error tolerance given by users. Among the mapping technique, inverse iteration has an effect of the lowest-order eigenfunction and filtering out the higher-order ones, the application of eigenvalue shift can greatly improve the convergence rate of inverse iteration, and orthogonalization can help user to remove components of the first i-1 eigenfunctions from the user provided trial function and the odd are regarded as inverse iteration initial solution. It was carried on in the process of inverse iteration. As to tube structure, its section is other constant or sectional by stage in high direction. The method in this article applies to this kind of structure even more. Following research mainly is carried on while dynamic analysis of tube structure is gone on in the article. 1) Through mechanics and numerical analysis method, translation is realized from actual structure to mechanical model. 2) Through finite element technology and minimum potential energy principle, transformation from mechanics model to mathematics model is get. 3) Applied mathematics skills, ordinary differential equations are changed into standard non-linear ODE questions. 4) Through computer language, mechanics model is translated computer model and the research of the subject is finished. In the analysis of this article, the method of strip element about distributed mass is applied. It is different from one of lumped mass model. By looking the calculated result, the method in the paper is of these features, such as few input quantity, high calculating precision and fast computing speed. The advantages of the present methodology, compared to that of conventional finite element method, were approved by two examples, that the higher degree of solving accurate by using the numerical analysis method, ODE, would be gotten only with fewer and directive line elements.