精细积分法在非线性动力学问题中的应用

Precise Time Step Integration Method in Nonlinear Dynamics

针对非齐次结构动力方程Duhamel形式的特解,建立了一种高效的特解精细积分法,对于非齐次项为幂函数和指数函数的情况,该方法能给出计算机上最高精度的解答。上述特解精细积分过程能与通解精细积分过程有机地结合起来,并形成一种高效的广义精细积分法。在此基础上,建立了非线性动力学方程的一种迭代算法。该方法具有很高的精度和效率以及较大的适用范围。算例结果证明了该方法的有效性。

Based on the Duhamel form special solution of non-homogeneous structure dyanmic equation, this paper presents a high effective Precise Time Step Integration Method （PTSIM） for special solution. When the non-homo- geous term is power functions or exponential functions, the new algorithm gives the most accurate answer within the computer accuracy. Combining the process of PTSIM for general solution and the process of PTSIM for special solution together, a new high effective algorithm called General Precise Time Step Integration Method （GPTSIM） is constructed. Based on the GPTSIM, a new iterative algorithm is found to solve non-linear dynamic equations. The iterative algorithm presented in this paper has very high accuracy and efficiency, and a wide rage of application. Numerical examples are given to demonstrate the validity and efficiency of GPTI .