粘弹性旋转梁的分数阶模型及其数值算法

Fractional order model of viscoelastic rotating beam and its numerical algorithm

为了探究载荷、转速和材料对粘弹性旋转梁位移数值解的影响,采用数学建模的方法,根据粘弹性材料的本构关系、应变位移关系和哈密尔顿原理,推导出了粘弹性旋转梁的分数阶模型,以Legendre小波为基函数进行数值模拟,给出在均布载荷和线性载荷下的位移数值解。研究结果表明:载荷、转速和材料的不同均会对粘弹性旋转梁位移数值解产生影响。研究结论初步突破在时域内建立并求解分数阶粘弹性旋转梁的分数阶模型,有助于对旋转梁振动的研究。

In order to investigate the effect of load,speed and material on the numerical solution of viscoelastic rotating beam displacement,a mathematical modeling method was used to derive a fractional-order model of the viscoelastic rotating beam based on the constitutive relationship,strain displacement relationship,and Hamilton principle of viscoelastic materials.Numerical simulation was performed using Legendre wavelet as the basis function.The displacement solutions are given under uniform and linear loads.The results show that the difference in load,speed and material will affect the numerical solution of the viscoelastic rotating beam displacement.The preliminary conclusion of the research is to establish and solve the fractional-order model of fractional-order viscoelastic rotating beam in the time domain,which is helpful for the research on the vibration of rotating beam.