In-Plane and Out-of-Plane Free Vibration Analysis of Archimedes-Type Spiral Springs

Abstract

The in-plane and out-of-plane free vibration frequencies of Archimedes-type spiral springs are computed by the transfer matrix method. Taking into account the effects of the axial and the shear deformations and the rotary inertia, the overall dynamic transfer matrix is computed up to any desired numerical accuracy by the complementary functions method. Since there are no restrictions for the number of coils and for the form of the spring (close-coiled or open-coiled), the presented method is general. After having verified the soundness of the computer program devised, the effects of the number of coils, of the axial and shear deformations, of rotary inertia and of the boundary conditions on the frequencies are also investigated.