Title of Paper:结构动力微分方程的一种高精度摄动解

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Date of Publication:2013-01-01

Journal:工程力学

Volume:30

Issue:5

Page Number:8-12

ISSN No.:1000-4750

Abstract:The structural dynamics equations were converted to the state equations
   in which the displacement and velocity response were taken as the state
   variables. In order to solve the state equations, the perturbation
   method was used, and a new series form of analytical solutions was
   presented. At the same time, the corresponding iterated computation
   formats and steps for the dynamics equations were established. The
   algorithm needs only repetitious matrix-vector multiplication and vector
   summation without inversion of H matrix and calculation of exponential
   matrix e~H Thusly, the computation stability and efficiency are very
   high. The items of the series solution and the accuracy of the algorithm
   can be directly controlled by the tolerance parameter, and
   theoretically, the algorithm can easily achieve arbitrary-order
   accuracy, and be suitable for parallel computing and compression
   storage. Generally, the algorithm combines the high-efficiency of the
   linear acceleration methods and the high-precision of precise
   integration methods. This method can be used for calculating the large
   sparse linear dynamic equations of engineering structures. At last, a
   model numerical example was given to demonstrate the validity and
   efficiency of the method.

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