用Adomian分解法求解分数阻尼梁的解析解  

Analytical Solution of a Fractionally Damped Beam by Using Adomian Decomposition Method

作　　者：梁祖峰[1] 唐晓艳[2] 

机构地区：[1]上海理工大学动力工程学院,上海200093 [2]上海交通大学物理系,上海200240

出　　处：《应用数学和力学》2007年第2期200-208,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10547124;10475055)

摘　　要：利用Adomian分解法,得到了由任意阶分数微分描述的具有阻尼特性的黏弹性连续梁的解析解.解中包含了任意的初始条件和零输入.为了更明确的分析,假定初始条件是奇次的,输入受力是针对某种特定梁的特殊过程.分别考虑了两种简单情况下梁的响应:阶跃激励和脉冲激励.然后在系统的不同组参数条件下绘制了梁的位移图,并且讨论了梁在不同微分阶数下响应情况.The analytical solution of a viscoelastic continuous beam whose damping characteristics are described in terms of a fractional derivative of arbitrary order was derived by means of the Adomian decoimposition method. The solution contains arbitrary initial conditions and zero input. For specific analysis, the initial conditions were assumed homogeneous, and the input force was treated as a special process with a particular beam. Two simple cases, step and impulse function responses, were considered respectively. Subsequently, some figures were plotted to show the displacement of the beam under different sets of parameters including different orders of the fractional detivatives.

关 键 词：黏弹性梁 分数微分 ADOMIAN分解法 振动 

分 类 号：O326[理学—一般力学与力学基础]