Free Vibration Behavior of Unidirectional Composite Cylindrical Helical Springs With Circular Section

Abstract

The free vibration problem of unidirectional composite cylindrical helical springs is modeled theoretically as a continuous system considering the rotary inertia, shear and axial deformation effects. The first order shear deformation theory is employed in the mathematical model. The twelve scalar ordinary differential equations governing the free vibration behavior of cylindrical helical springs made of an anisotropic material are solved simultaneously by the transfer matrix method. The overall transfer matrix of the helix is computed up to any desired accuracy by using the effective numerical algorithm available in the literature. The theoretical results are verified with the reported values, which were obtained theoretically and experimentally for straight beams. A parametric study is performed to investigate the effects of the number of active coils, the helix pitch angle and material types on the fundamental natural frequencies of helical springs with circular section and fixed-fixed ends.