分数阶导数型粘弹性结构动力学方程的数值算法  

A numerical algorithm for the dynamics equation of the fractional derivative viscoelasticity structure

作　　者：银花[1] 陈宁[2] 赵尘[1] 王大明[1] 

机构地区：[1]南京林业大学土木工程学院,江苏南京210037 [2]南京林业大学机械电子工程学院,江苏南京210037

出　　处：《南京林业大学学报（自然科学版）》2010年第2期115-118,共4页Journal of Nanjing Forestry University：Natural Sciences Edition

基　　金：江苏省高校自然科学基金项目(08KJD130002)

摘　　要：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Zhang-Shimizu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。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 Zhang-Shimizu. Results also show that the solution converges as the step length is decreased.

关 键 词：分数阶导数 粘弹性 动力学 状态方程 精细积分 

分 类 号：O322[理学—一般力学与力学基础]