单向复合材料矩形截面圆柱弹簧的自由振动

Free Vibration of Unidirectional Composite Cylindrical Helical Springs with Rectangular Cross section

摘要:

把自然弯扭梁理论推广到材料为各向异性的情况，并得到了单向复合材料矩形截面杆件的圣维南扭转翘曲函数的解析公式.在此基础上，进一步导出了单向复合材料非圆截面圆柱螺旋弹簧的运动微分方程，它们由14个1阶偏微分方程组成.方程中不仅考虑了转动惯量、轴向和剪切变形的影响，而且首次考虑了簧丝横截面的翘曲变形对弹簧固有频率和振动模态的影响.由于方程呈现出很强的刚性，这里采用改进的Riccati传递矩阵法对弹簧的自由振动微分方程进行求解.计算表明，对于单向复合材料矩形截面圆柱螺旋弹簧，翘曲变形对其自由振动特性具有重大的影响，是必须考虑的重要因素.最后，研究了各种设计参数对此类弹簧固有频率的影响.

Abstract:

The naturally curved and twisted beam theory was applied to the beams for anisotropic materials, and an analytical expression for the warping function of Saint Venant’s torsion of unidirectional composite bars with rectangular cross section was obtained. Then, the differential equations of motion for unidirectional composite cylindrical helical springs with noncircular cross sections, which consist of 14 first order partial differential equations, were further derived. In the formulation, the warping effect upon natural frequencies and vibration mode shapes was first studied in addition to considering the rotary inertia, the shear and axial deformation effects. Improved Riccati transfer matrix method was introduced to solve the free vibration differential equations of the springs which presented a strong rigidity. Calculation results show that, for unidirectional composite cylindrical helical springs with rectangular cross section, the warping deformation has a significant influence on the free vibration characteristics of such springs, which should be considered in the free vibration analysis. Finally, the effects of various parameters on the natural frequencies of the springs were investigated.