针对线性动力状态方程 ，结合泰勒级数展开式和广义精细积分法，提出了一种避免状态矩阵求逆的线性动力分析的通用积分格式。首先，将非齐次项在 时刻利用泰勒公式将其展开成幂级数形式，然后结合广义精细积分法中的递推公式即可求解出非齐次项的动力响应。该方法计算格式统一，易于编程，通过选取幂级数的项数，可得到不同的计算精度。与传统的数值积分法相比，本文方法具有很高的精度、稳定性及适当的效率，可用于求解任意激励下结构的动力响应。
Abstract
For the state equation v?=H?v+r(t) used in describing linear dynamics systems, a general integration scheme was proposed with the combination of the Taylor series expansion and generalized precise time step integration method.The non-homogenous term at the moment of ti+1(i=0, 1, 2, …, n) was developed into a power series by the Taylor formula,and then the dynamic response due to the non-homogenous term was solved by introducing the recursive formula in the generalized precise time step integration method.The algorithm has an uniform computing scheme,which makes the programming simpler.Moreover, the different calculation accuracy can be obtained by selecting the term number of power series.Compared with the traditional numerical integration method, the proposed algorithm has higher precision, better stability and proper efficiency.Therefore ,it can be used to solve the dynamic response of a structure under arbitrary excitation.
关键词
线性动力分析 /
精细积分法 /
泰勒级数 /
递推算法 /
通用格式
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Key words
linear dynamic analysis /
precise integration method /
Taylor's series /
recursive algorithm /
general scheme
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参考文献
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