Finite Element Solution of Dynamic Response of Helical Springs

Abstract A numerical solution is presented to describe wave propagations in axially impacted helical springs. The governing equations for such problem are two coupled hyperbolic, partial differential equations of second order. The axial and rotational strains and velocities are considered as principal dependent variables. Since the governing equations are non-linear, the solution of the system of equations can be obtained only by some approximate numerical simulation. The finite element method, based on the Galerkin formulation, is applied to discretize the mathematical equations leading to a non-linear system of equations solved by an iterative Gauss substitution method. The computed results describe the evolution of axial and rotational strains and velocities, in different sections of the spring and show the interaction between axial and rotational waves. To validate the reliability of the model presented herein, the numerical results are compared with those of other workers obtained by the method of characteristics. (Received in May 2007, accepted in September 2007. This paper was with the authors 2 months for 2 revisions.)