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 引用本文: 富明慧 刘祚秋 林敬华. 一种广义精细积分法[J]. 力学学报, 2007, 23(5): 672-677.
Minghui Fu, Zuoqiu Liu, Jinghua Lin. A Generalized Precise Time Step Integration Method[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(5): 672-677.
 Citation: Minghui Fu, Zuoqiu Liu, Jinghua Lin. A Generalized Precise Time Step Integration Method[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(5): 672-677.

## A Generalized Precise Time Step Integration Method

• 摘要: 提出了求解非齐次动力方程特解的一种精细数值积分法，该方法与通解精细积分法具有相同精度. 首先选取一个积分形式的非齐次方程特解，将积分区域划分为2^N份，并对之进行精细的数值积分；然后针对载荷为多项式、指数函数及三角函数的情况，将积分求和转化为一个递推过程，按此只需n次矩阵乘法就能计算出积分和，从而得到非齐次方程的特解. 该方法的优点是能与通解的精细积分过程有机地结合起来，具有极高的精度和效率，同时还具有较广泛的适用范围. 算例结果证明了该方法的有效性.

Abstract: A precise time step integration method (PTSIM) applied for linear time-invariant dynamic system with non-homogeneous vectors is presented, which is of the same accuracy of the precise time step integration method of general solution. Firstly, the domain of integration is separated into sections. And then a particular solution in the form of integration is chosen and is solved by precise numerical algorithm. Secondly, when the non-homogeneous vector is kind of polynomial, exponential function or trigonometric function, the integration can be converted to a recursion. So the particular solution in the form of integration is precisely obtained by only matrix multiplications. The merit of the new PTSIM is that the process of calculating the general solution and the one of calculating the particular solution are organically combined together. And it is of high precision, efficiency and widely applicability. Numerical examples are given to demonstrate the validity and efficiency of the new PTSIM.

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