An exact solution for the vibration of helical springs using a Bernoulli-Euler model

Abstract A solution is obtained for the steady-state vibration behaviour of uniform helical springs in which the following effects are ignored; deformation due to shear and axial loads, the rotational inertias of the cross-section, and static loads applied to the spring. A theory is developed for the evaluation of the dynamic stiffness matrix. Natural frequencies are found using an adaption of the Wittrick-Williams algorithm. Details of the method of calculation are discussed. Results are presented for natural frequencies, and are compared with values obtained using other methods and assumptions. The method of this paper is shown to be particularly efficient.