多自由度非线性动力学方程的能量校准算法

AN ENERGY ADJUSTING ALGORITHM FOR THE NONLINEAR DYNAMIC EQUATION WITH MULTI-DEGREES OF FREEDOM

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．

An energy adjusting numerical algorithm for the nonlinear dynamic equation with multi-degree of freedom is proposed. First, by the Taylor＇s expansion and Duhamel integration, an integral iteration formula with an undetermined parameter is obtained. Second, the original dynamical equation is transsormed into an energy adjusting equation to determine the undetermined parameter. Finally, substituting the parameter into the integral iteration formula, an accurate numerical value is obtained. Some examples show that the method can eliminate the algorithm damping and enjoys better stability than the Runge-Kutta method under a large integral step.