| 一种广义精细积分法 |
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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,2007,39(5):672-677. |
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| 作者姓名： | 富明慧 刘祚秋 林敬华 |
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| 作者单位： | 广州市中山大学应用力学与工程系 广州市中山大学应用力学与工程系 广州市中山大学应用力学与工程系 |
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| 基金项目： | 国家自然科学基金，广东省自然科学基金 |
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| 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.
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| 关 键 词： | 结构动力分析 精细积分 指数矩阵运算 数值积分 递推算法 |
| 文章编号： | 0459-1879（2007）05-0672-06 |
| 收稿时间： | 2007-01-18 |
| 修稿时间： | 2007-01-18 |
A GENERALIZED PRECISE TIME STEP INTEGRATION METHOD |
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| Fu Minghui,Liu Zuoqiu,Lin Jinghua.A GENERALIZED PRECISE TIME STEP INTEGRATION METHOD[J].chinese journal of theoretical and applied mechanics,2007,39(5):672-677. |
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| Authors: | Fu Minghui Liu Zuoqiu Lin Jinghua |
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| Affiliation: | Dept. of Applied Mechanics and Engineering,Guangdong Province Key Laboratory of Coastal Ocean Engineering,Guangzhou 510275,China |
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| 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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| Keywords: | structural dynamics precise time-step integration method the calculation technique of matrix exponential numerical integration recursive algorithm |
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