层状复合材料矩形截面非圆柱螺旋弹簧的自由振动
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同济大学 航空航天与力学学院,同济大学 航空航天与力学学院

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国家自然科学基金项目(面上项目)各向异性闭口薄壁自然弯扭梁力学行为的理论研究


Free vibration of laminated composite non-cylindrical helical springs with rectangular cross-section
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School of Aerospace Engineering and Applied Mechanics,Tongji University

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The National Natural Science Foundation of China (General Program, Key Program, Major Research Plan)

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    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桶形弹簧固有频率的影响。

    Abstract:

    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 and vibration mode shapes 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 the use of the Scaling and Squaring method and Pad′e approximations. Calculated results 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 barrel springs with rectangular cross-section have been studied.

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引用本文

郝颖,虞爱民.层状复合材料矩形截面非圆柱螺旋弹簧的自由振动[J].振动工程学报,2013,26(3).[HAO Ying, YU Ai-min. Free vibration of laminated composite non-cylindrical helical springs with rectangular cross-section[J]. Journal of Vibration Engineering,2013,26(3).]

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  • 收稿日期:2012-01-08
  • 最后修改日期:2013-06-05
  • 录用日期:2013-04-24
  • 在线发布日期: 2013-07-05
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