Dynamic stress analysis of a coil spring of arbitrary cross-section to general transient excitations

Abstract

Dynamic stresses in a coil spring of arbitrary cross-section subjected to general transient displacement with consideration of end effects are discussed. An analytical method is given for finding normal and shear stresses in the coil by use of the transfer matrix, the Laplace transform, Fourier expansion and the Fourier expansion collocation methods based on the three-dimensional theory for curved rods. For the circular cross-section coil, the stress differs along the boundary of the cross-section and has a maximum value at an interior point of the coil. The more effective coil spring having an oval cross-section is proposed. Both the principal normal and shear stresses along the surface of the proposed coil subjected to a transient excitation have been calculated. It is shown that the oval cross-section coil with an appropriate aspect ratio has various advantages as compared with the circular cross-section coil.