The effect of the longitudinal to transverse moduli ratio on the natural frequencies of symmetric cross-ply laminated cylindrical helical springs

The first six free vibration frequencies of symmetric cross-ply laminated c ylindrical helical springs with fired-fixed ends are theoretically computed based on the transfer matrix method. The rotary inertia, shear and axial d eformation effects are taken into account in the solution. Considering diff erent values for the helix pitch angles and the number of active turns, a p arametric study is performed to analyze the effects of the ratio of the lon gitudinal Young's modulus to the transverse Young's modulus on the natural frequencies of such springs with square section. The results are given in d imensionless graphical forms.