Fundamental Frequencies of Uniaxial Composite Barrel and Hyperboloidal Springs

The fundamental natural frequencies of uniaxial composite non-cylindrical helical springs (barrel and hyperboloidal types) 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 twelve scalar ordinary differential equations with variable coefficients governing the free vibration behavior of non-cylindrical helical springs made of an anisotropic material. Numerical results are verified with the reported values for isotropic non-cylindrical helices. A parametric study is performed to investigate the effects of the number of active coils (n = 5–0), the helix pitch angle (α = 5° and 25°), the ratio of the minimum to maximum cylinder radii (R_min/R_max), and the ratio of the maximum cylinder diameter to the wire diameter (D_max/d) on the fundamental free vibration frequencies of constant-pitch composite barrel and hyperboloidal helical springs with circular section and fixed-fixed ends.