L-P摄动法在跌落冲击问题中的应用

本文先是试探性地将L-P摄动法对杜芬方程的一次渐近解应用于跌落冲击问题，结果很不理想。因此，提出一种新的解法：将L-P摄动法与包装动力学的能量法相结合，以一次渐近解为基础，用一个初始条件和两个峰值条件确定积分常数。本文取了一个振幅修正系数，其作用是根据具体问题的具体情况调节基频与高频成分的比例关系。算例表明，用本文这种一次渐近解绘制的产品加速度时间曲线与椭圆积分法非常接近，在峰值、波形与冲击持续时间三个方面的准确性都能达到令人满意的程度。

Application of L_P Perturbation Method in Dropping Shock Problem

The first_order approximate solution of Duffing Equation by using L_P perturbation method is tried to apply in analyzing dropping shock problem in the paper.Its regretful that the result is not satisfactory.So,a novel solution combining,L_P perturbation method with energy method is proposed.It is still based on first_order approximate solution,however the integral constant is determined by one initial condition and two peck value conditions.In order to fit the solution to the two peak value conditions simultaneously,a correction coefficient of amplitude is employed to adjust the proportion of basic frequency and higer frequencies for given event.The results show that the acceleration_time curve got by this method is very similar to the one got by elliptic integration method,and the accuracy of peak value,waveform and extended period of shock got by this method is satisfactory.