Free Vibration Analysis of Pre-Loaded Cylindrical Helical Springs Made of Isotropic Materials

The free vibration equations developed of cylindrical isotropic helical springs loaded axially are solved numerically based on the transfer matrix method with an effective numerical algorithm formulated by the author. The axial and shear deformation effects together with the rotatory inertia effects are all considered based on the first order shear deformation theory. The natural frequencies of a helical spring under compression are compared with the results in the available literature. A good agreement is observed with related benchmark studies.