轴向变速运动粘弹性弦线横向振动的复模态Galerkin方法

在考虑初始张力和轴向速度简谐涨落的情况下,利用含预应力三维变形体的运动方程,建立了轴向变速运动弦线横向振动的非线性控制方程,材料的粘弹性行为由Kelvin模型描述.利用匀速运动线性弦线的模态函数构造了变速运动非线性弦线复模态Galerkin方法的基底函数,并借助构造出来的基底函数研究了复模态Galerkin方法在轴向变速运动粘弹性弦线非线性振动分析中的应用.数值结果表明,复模态Galerkin方法相比实模态Galerkin方法对变系数陀螺系统有较高的收敛速度.

Complex-Mode Galerkin Approach in Transverse Vibration of an Axially Accelerating Viscoelastic String

Under the consideration of harmonic fluctuations of initial tension and axially velocity,a nonlinear governing equation for transverse vibration of an axially accelerating string is set up by using the equation of motion for a 3-dimensional deformable body with initial stresses.The Kelvin model was used to describe viscoelastic behaviors of the material.The basis function of the complex-mode Galerkin method for axially accelerating nonlinear strings was constructed by using the modal function of linear moving strings with constant axially transport velocity. By the constructed basis functions,the application of the complex-mode Galerkin method in nonlinear vibration analysis of an axially accelerating viscoelastic string was investigated.Numerical results show that the convergence velocity of the complex-mode Galerkin method is higher than that of the real mode Galerkin method for a variable coefficient gyroscopic system.