【摘要】 本文对求解非线性振动的几种数值方法进行了比较,结果表明,在平均加速度法、线性加速度法、四阶龙格—库塔方法中,以四阶龙格—库塔法精度高,速度快。对周期性振动,可用线性插值的方法求得周期的准确值,并可用数值积分的方法求得各阶谐振动的大小,这有利于对数值结果进行深入分析。数值积分求得的各阶谐振动大小与摄动法相比较可以发现,二者的结果相当吻合。更多还原

【Abstract】 In this paper several numerical methods for calculating nonlinear vibrations are compared with each other.Results show that the fourth-order Runge-Kutta method is more accurate and effective than the constant-average-acceleration method and the linear acceleration method.Using linear interpolation can be calculated periods of periodic vibrations accurately, and with the aid of numerical integration the amplitudes of each harmonic vibrations can be calculated.The calculations help us analyse the numerical results more thoroughly.In calculating the amplitudes of each harmonic vibrations, the results of numerical integration method and those of perturbation method are very coincidental with one another.更多还原