随机激振位移作用下大位移单摆的非线性分析

本文应用非线性谱分析法对随机激振位移作用下大位移单摆的非线性随机响应进行了分析。结果表明，在小位移条件下，线性解可以得到较好的近似解，但线性解的误差随角位移的增大而显著增加。因此，对于大位移单摆，应当考虑其非线性效应。该方法勿需对非线性项线性化，从而消除了由于线性化所带来的人为误差，使计算结果趋于精确。

NONLINEAR ANALYSIS OF A SIMPLE PENDULUM WITH LARGE DISPLACEMENT UNDER THE ACTION OF RANDOM EXCITING DISPLACEMENT

Under the action of random exciting displacement, the response of a simple pendulum with large displacement was studied in this paper by means of nonlinear spectral analysis. It is not necessary to have the nonlinear term linearized in this method, so that the errors introduced by linearization can be eliminated. The study indicates that the linearized solution gives reasonable approximation when the displacement being small. When the displacement becomes large enough, the errors introduced by linearization increase significantly. Therefore, the nonlinear effect due to large displacement should be taken into consideration.