Abstract:Free vibration behavior of laminated composite non-cylindrical (conical, barrel, and hyperboloidal types) helical springs with rectangular cross-section is investigated. The effect of the warping deformation of wire cross-section on natural frequencies and vibration mode shapes is first considered in the formulations. The differential equations of motion for the springs including warping, which consist of 14 first-order partial differential equations with variable coefficients, are derived using naturally curved and twisted anisotropic beam theory. The natural frequencies of the springs are determined using improved Riccati transfer matrix method. The element transfer matrix is calculated by the use of the Scaling and Squaring method and Pad′e approximations. Calculated results show that the warping deformation has a significant influence on the natural frequencies, which should be considered in the free vibration analysis of the springs. Finally, the effects of various parameters on the natural frequencies for symmetrically laminated composite barrel springs with rectangular cross-section have been studied.