The Effect of the Longitudinal to Transverse Moduli Ratio on the Natural Frequencies of Symmetric Cross-Ply Laminated Cylindrical Helical Springs

Abstract

The first six free vibration frequencies of symmetric cross-ply laminated cylindrical helical springs with fixed-fixed ends are theoretically computed based on the transfer matrix method. The rotary inertia, shear and axial deformation effects are taken into account in the solution. Considering different values for the helix pitch angles and the number of active turns, a parametric study is performed to analyze the effects of the ratio of the longitudinal Young’s modulus to the transverse Young’s modulus on the natural frequencies of such springs with square section. The results are given in dimensionless graphical forms.