一种分数阶导数阻尼下随机振动结构的数值模拟方法

摘要

提出了一种针对分数阶导数阻尼下随机振动结构的数值模拟方法.在对分数阶导数各种经典定义比较的基础上,首先指出了对分数阶导数进行数值计算的难点在于其对历史数据的全局依赖性.然后,对于受分数阶导数阻尼的随机振动结构,利用Riemann-Liouvill定义与Grunwald-Letnikov定义之间的关系,给出了一种对分数阶导数进行数值模拟的方法.通过合理地截断来缩短分数阶导数对历史数据的记忆,从而有效提高计算效率.最后,以分数阶导数阻尼下受高斯白噪声激励的线性随机振动结构为数值算例阐明了所提出方法的有效性.%A numerical simulation scheme for vibration structure with fractional order structural damping is proposed. The comparison of different representations of fractional derivatives reveals that the difficulties of the numerical computation lie in the global dependence of historical data. For a class of typical fractionally damped random vibration structures, employing the relationship between Riemann-Iiouvill and Grunwald-Letnikov definitions, a method of shortening the global memory of the fractional derivative is obtained. The method of choosing the truncation point is given and computational efficiency is improved significantly. The validity and effectiveness of the proposed scheme are verified by applying it to a fractionally damped linear structure subjected to Gaussian with noise.