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李伟东 吕和祥. 多自由度非线性动力学方程的能量校准算法[J]. 力学学报, 2007, 23(3): 356-364. DOI: 10.6052/0459-1879-2007-3-2006-280
引用本文: 李伟东 吕和祥. 多自由度非线性动力学方程的能量校准算法[J]. 力学学报, 2007, 23(3): 356-364. DOI: 10.6052/0459-1879-2007-3-2006-280
Weidong Li, Hexiang Lv. The energy equation adjusting algorithm for the nonlinear dynamic equation with multi-degree of freedom[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(3): 356-364. DOI: 10.6052/0459-1879-2007-3-2006-280
Citation: Weidong Li, Hexiang Lv. The energy equation adjusting algorithm for the nonlinear dynamic equation with multi-degree of freedom[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(3): 356-364. DOI: 10.6052/0459-1879-2007-3-2006-280

多自由度非线性动力学方程的能量校准算法

The energy equation adjusting algorithm for the nonlinear dynamic equation with multi-degree of freedom

  • 摘要: 针对非线性动力学方程,通过Taylor展开和Duhamel积分,得到一个具有待定参数的逐步积分求解公式;通过数学变换,将原动力学方程转换为一个能确定待定参数的能量校准方程;最后将该参数回代入逐步积分公式,得到数值解. 数值算例的结果说明了该方法的有效性,可以消除算法阻尼和抑制数值解发散,同时,在大步长的条件下也得到了非常准确而且稳定的结果,可以对系统长期性态进行仿真.

     

    Abstract: The energy adjust numerical algorithm for the nonlineardynamic equation with multi-degree of freedom has been proposed. First, bythe Taylor expanded formula and Duhamel integration, an integral iterationformula which has an undetermined parameter has been achieved. Second,through some mathematic approach, the original dynamical equation has beenconverted to an energy adjusting equation which can determine theundetermined parameter. Finally, substituting the parameter into theintegral iteration formula, an accurate numerical value has been achieved.All examples show that the method can eliminate the algorithm damping andhas better stability than the Runge-Kutta method under bigger integral step.

     

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