Simulation of fractionally damped mechanical systems by means of a Newmark-diffusive scheme
Simulation of fractionally damped mechanical systems by means of a Newmark-diffusive scheme
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DOI：
10.1016/j.camwa.2009.08.067
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发表时间：
2010-03
期刊：
影响因子：
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通讯作者：
J. Deü;D. Matignon
中科院分区：
文献类型：
--
作者：
J. Deü;D. Matignon
本文提出了一种求解含分数阶导数动力系统时域问题的Newmark扩散格式。该方案结合了用于求解二阶力学系统的经典Newmark时间积分方法（例如在有限元离散化后获得），以及基于将分数算子变换为线性微分方程对角系统的扩散表示，该线性微分方程可以被视为内部记忆变量。重点是给出的算法实现到一个有限元框架，选择扩散参数的策略，并与分数齐纳模型梁结构的应用。
A Newmark-diffusive scheme is presented for the time-domain solution of dynamic systems containing fractional derivatives. This scheme combines a classical Newmark time-integration method used to solve second-order mechanical systems (obtained for example after finite element discretization), with a diffusive representation based on the transformation of the fractional operator into a diagonal system of linear differential equations, which can be seen as internal memory variables. The focus is given on the algorithm implementation into a finite element framework, the strategies for choosing diffusive parameters, and applications to beam structures with a fractional Zener model.