层状复合材料矩形截面非圆柱螺旋弹簧的自由振动  

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

作　　者：郝颖[1] 虞爱民[1] 

机构地区：[1]同济大学航空航天与力学学院,上海200092

出　　处：《振动工程学报》2013年第3期335-342,共8页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(10572105);上海市重点学科建设项目资助(B302)

摘　　要：对层状复合材料矩形截面非圆柱(锥形、桶形和双曲形)螺旋弹簧的自由振动特性进行了研究,方程中首次考虑了簧丝截面的翘曲变形对固有频率的影响。在各向异性自然弯扭梁理论的基础上,导出了该弹簧在考虑翘曲效应时的运动微分方程,它们由14个变系数的一阶偏微分方程组成。弹簧的固有频率可以使用改进的Riccati传递矩阵法确定,单元传递矩阵则采用Scaling-Squaring方法以及Pad′e逼近表达式进行计算。数值结果表明,翘曲变形对该弹簧的固有频率有着重大的影响,是自由振动分析中必须考虑的重要因素。最后研究了各种设计参数对对称层合复合材料矩形截面双曲形弹簧固有频率的影响。Free vibration behavior of laminated composite non-cylindrical （conical, barrel, and hyperboloidal types） helical springs with rectangular cross-section is investigated. The effect of the warping deformation of wire cross-section on natural frequencies is first considered in the formulations. The differential equations of motion for the springs including warping, which consist of 14 first-order partial differential equations with variable coefficients, are derived using naturally curved and twisted anisotropic beam theory. The natural frequencies of the springs are determined using improved Riccati transfer matrix method. The element transfer matrix is calculated by using the Scaling and Squaring method and Padels approximations. Calculated re- sults show that the warping deformation has a significant influence on the natural frequencies, which should be considered in the free vibration analysis of the springs. Finally, the effects of various parameters on the natural frequencies for symmetrically laminated composite hyperholoidal springs with rectangular cross-section have been studied.

关 键 词：层状复合材料 自由振动 非圆柱螺旋弹簧 翘曲效应 固有频率 

分 类 号：O326[理学—一般力学与力学基础] TU332[理学—力学]