层状复合材料矩形截面圆柱螺旋弹簧自由振动特性研究

Free vibration behavior of laminated composite cylindrical helical springs with rectangular cross-section

对层状复合材料矩形截面圆柱螺旋弹簧自由振动特性进行研究,首次考虑簧丝截面翘曲变形对固有频率和振动模态的影响。在各向异性自然弯扭梁理论基础上,导出该弹簧运动微分方程,为由14个一阶偏微分方程组成。弹簧固有频率可用改进的Riccati传递矩阵法确定,单元传递矩阵则采用Scaling-Squaring方法及Pad'e逼近表达式计算。结果表明:对对称层压复合材料矩形截面的圆柱螺旋弹簧,翘曲变形对其固有频率有一定影响,在自由振动分析中应考虑。研究各种设计参数对该弹簧固有频率影响,并发现一些与各向同性材料矩形截面圆柱螺旋弹簧不同的性质。

Free vibration behavior of laminated composite cylindrical helical springs with rectangular cross-section was studied. The effect of warping deformation of wire cross-section on natural frequencies and vibration modal shapes was considered in the formulation at first time. The differential equations of motion for the springs consisting of 14 first-order partial differential equations were derived using the naturally curved and twisted anisotropic beam theory. The natural frequencies of the springs were determined by use of improved Riccati transfer matrix method. The element transfer matrix used in the solution was calculated using the scaling and squaring method and Pad＇e approximations. Results showed that the warping deformation has a certain influence on the natural frequencies, it should be considered in free vibration analysis of the springs. Finally, the effects of various parameters on the natural frequencies were investigated, and some properties different from those of isotropic cylindrical helical springs with rectangular cross-section were found.