Response of a non-linear system with restoring forces governed by fractional derivatives—Time domain simulation and statistical linearization solution
Response of a non-linear system with restoring forces governed by fractional derivatives—Time domain simulation and statistical linearization solution
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DOI：
10.1016/j.soildyn.2010.01.013
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发表时间：
2010-09
影响因子：
4
通讯作者：
P. Spanos;Georgios I. Evangelatos
中科院分区：
文献类型：
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作者：
P. Spanos;Georgios I. Evangelatos
本文研究了包含频率相关恢复力项的非线性系统的随机响应。这些术语在隔震和许多其他应用中使用分数导数精确建模。在此背景下，首次提出了一种确定系统在任意激励下时域响应的有效数值方法。该方法基于分数阶导数的Grunwald-Letnikov表示和著名的结构动力问题的Newmark数值积分格式。其次，对于随机激励的情况，除了时域解外，频域解可以很容易地用统计线性化的方法确定。在蒙特卡罗仿真环境下，利用本文所采用的时域解方案，验证了该解的可靠性。此外，还报道了几个相关参数的研究。
In this paper, the random response of a non-linear system comprising frequency dependent restoring force terms is examined. These terms are accurately modeled in seismic isolation and in many other applications using fractional derivatives. In this context, an efficient numerical approach for determining the time domain response of the system to an arbitrary excitation is first proposed. This approach is based on the Grunwald–Letnikov representation of a fractional derivative and on the well-known Newmark numerical integration scheme for structural dynamic problems. Next, it is shown that for the case of a stochastic excitation, in addition to the time domain solutions, a frequency domain solution can be readily determined by the method of statistical linearization. The reliability of this solution is established in a Monte Carlo simulation context using the herein adopted time domain solution scheme. Furthermore, several related parameter studies are reported.