Free vibration characteristics of composite barrel and hyperboloidal coil springs

The first six resonance frequencies of unidirectional composite noncylindri cal helical springs (barrel and hyperboloidal types) made of carbon-epoxy ( T300/N5208) material are determined theoretically based on the transfer mat rix method The rotary inertia, shear, and axial deformation effects are con sidered with the first-order shear deformation theory. The overall transfer matrix is obtained by integrating the 12 scalar ordinary differential equa tions with variable coefficients governing the free-vibration behavior of n oncylindrical helical springs made of an anisotropic material. Numerical re sults are verified with the reported values for isotropic noncylindrical he lices. A parametric study is performed to investigate the effects of the nu mber of active coils (n = 5-10), the helix pitch angle (alpha = 5 degrees a nd 25 degrees), the ratio of the minimum to maximum cylinder radii (Rmin/Rm ax = 0.1 and 0.9), and the ratio of the maximum cylinder diameter to the wi re diameter (D-max/d = 5 and 15) on the free-vibration frequencies of const ant-pitch composite barrel and hyperboloidal helical springs with circular sections and fixed-fixed ends.