层状复合材料矩形截面圆柱螺旋弹簧自由振动特性的研究

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振动与冲击 ›› 2012, Vol. 31 ›› Issue (22) : 105-111.

论文

层状复合材料矩形截面圆柱螺旋弹簧自由振动特性的研究

郝颖，虞爱民

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Study on the free vibration behavior of laminated composite cylindrical helical springs with rectangular cross-section

Hao Ying Yu Aimin

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摘要

对层状复合材料矩形截面圆柱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和振动模态的影响。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。计算结果表明：对于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的影响，在自由振动分析中应该加以考虑。最后研究了各种设计参数对该弹簧固有频率的影响，并发现了一些与各向同性材料矩形截面圆柱螺旋弹簧不同的性质。

Abstract

Free vibration behavior of laminated composite cylindrical helical springs with rectangular cross-section is studied. The effect of the warping deformation of wire cross-section on natural frequencies and vibration mode shapes is first considered in the formulation. The differential equations of motion for the springs including warping, which consist of 14 first-order partial differential equations, are derived using naturally curved and twisted anisotropic beam theory. The natural frequencies of the springs are determined by the use of improved Riccati transfer matrix method. The element transfer matrix used in the solution is calculated using the Scaling and Squaring method and Pad´e approximations. Calculations show that the warping deformation has a certain 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 have been investigated, and some properties, different from those of isotropic cylindrical helical springs with rectangular cross-section, have been found.

导出引用

郝颖;虞爱民 . 层状复合材料矩形截面圆柱螺旋弹簧自由振动特性的研究[J]. 振动与冲击, 2012, 31(22): 105-111

Hao Ying Yu Aimin . Study on the free vibration behavior of laminated composite cylindrical helical springs with rectangular cross-section[J]. Journal of Vibration and Shock, 2012, 31(22): 105-111