The first six resonance frequencies of unidirectional composite noncylindrical helical springs (barrel and hyperboloidal types) made of carbon-epoxy (T300/N5208) material are determined theoretically based on the transfer matrix method. The rotary inertia, shear, and axial deformation effects are considered with the first-order shear deformation theory. The overall transfer matrix is obtained by integrating the 12 scalar ordinary differential equations with variable coefficients governing the free-vibration behavior of noncylindrical helical springs made of an anisotropic material. Numerical results are verified with the reported values for isotropic noncylindrical helices. A parametric study is performed to investigate the effects of the number of active coils (n = 5-10), the helix pitch angle (α = 5° and 25°), the ratio of the minimum to maximum cylinder radii (R{sub}(min)/R{sub}(max) = 0.1 and 0.9), and the ratio of the maximum cylinder diameter to the wire diameter (D{sub}(max)/d = 5 and 15) on the free-vibration frequencies of constant-pitch composite barrel and hyperboloidal helical springs with circular sections and fixed-fixed ends.
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机译：理论上，基于传递矩阵法确定了碳-环氧（T300 / N5208）材料制成的单向复合非圆柱螺旋弹簧（筒形和双曲面型）的前六个共振频率。一阶剪切变形理论考虑了旋转惯性，剪切和轴向变形的影响。整体传递矩阵是通过将12个标量常微分方程与可变系数相集成而得到的，该系数控制由各向异性材料制成的非圆柱螺旋弹簧的自由振动行为。用各向同性非圆柱螺旋的报告值验证了数值结果。进行参数研究以研究有源线圈数量（n = 5-10），螺旋螺距角（α= 5°和25°），最小与最大圆柱半径之比（R {sub }（min）/ R {sub}（max）= 0.1和0.9），以及自由振动时最大圆柱直径与线径的比率（D {sub}（max）/ d = 5和15）固定截面的固定节距复合圆筒和双曲面螺旋弹簧的频率。
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