基于精细积分方法,提出了具有分数阶导数型本构关系的粘弹性结构动力响应的一种新的数值计算方法。该方法首先将系统的动力学微积分方程转化为含分数阶导数项的一阶常微积分方程组,然后采用精细积分法对方程进行积分计算得到系统响应。数值计算结果与解析法及ZhangShimizu算法的结果相吻合，并显示随计算步长减小其计算的收敛性更好。
Abstract
According to the precise integral method, a new numerical algorithm is proposed for dynamical responses of viscoelasticity structure with the fractional derivative constitutive relation. In this approach, the fractional differential equation for the dynamic of a system is transformed into a set of first order ordinary differential equations which contain fractional derivative terms. The precise integral method is used to integrate these terms and obtain the response of the system. Numerical results obtained using this scheme agree well with those obtained using an analytical method and an numerical scheme proposed by ZhangShimizu. Results also show that the solution converges as the step length is decreased.
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基金
收稿日期：2009-01-18修回日期：2009-11-12基金项目：江苏省高校自然科学基金项目(08KJD130002)作者简介：银花(1978—)，博士生。*陈宁(通信作者),副教授，博士。Emial: chenning@njfu.com.cn。引文格式：银花,陈宁,赵尘,等. 分数阶导数型粘弹性结构动力学方程的数值算法[J]. 南京林业大学学报:自然科学版,2010,34(2):115-118.
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