Finite Difference Method for Simulatting Transverse Vibrations of an Axially Moving Viscoelatic String
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摘要: 给出了微分本构粘弹性轴向运动弦线横向振动数值仿真的一种差分法．文中建立了具有微分本构的粘弹性运动弦线的横向振动模型；通过对系统的控制方程和本构方程在不同的分数节点离散，得到一种新的差分方法．利用这一方法，弦线振动方程的数值计算过程可以交替地显式进行，且有较小的截断误差和好的数值稳定性．与通用的方法比较，新的方法计算简单、方便．文中利用方程的不变量检验了数值结果的可靠性，并利用这一方法给出了一类弦线模型的参数振动分析．Abstract: Finite difference method is presented to simulate transverse vibrations of an axially moving string.The equation of motion is derived first.By discretizing the governing equation and the equation of stress_strain relation at different frictional knots,two linear sparse finite difference equation systems are obtained.The two resulting difference schemes can be calculated alternatively,which make the computation much more efficient.The numerical method makes the nonlinear model easier to deal with and of truncation errors.It also shows stability for small initial values,so it can be used in analyzing the nonlinear vibration of viscoelastic moving string effectively.Numerical examples are presented to demonstrate the efficiency and the stability of the algorithm,and dynamic analysis of a viscoelastic string is given by using the numerical results.
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