Forced Oscillation of a Spring-Mass System Having Combined Coulomb and Viscous Damping

Abstract

The solution for the response of a mass-excited spring-mass system influenced by both Coulomb and viscous damping has been presented by J. P. Den Hartog and by L. S. Jacobsen. However, there appears to be available no practical compilation of the results for the support-excited system, interest in which has been heightened by the demands of military installations of delicate electronic equipment. In the present paper, an analytic solution for the response of the support-excited system is presented. The solution to the equation of motion is developed through the application of a Fourier series to represent the frictional force opposing the relative motion between mass and supporting structure. It is assumed that no stops occur during any portion of the steady-state oscillation. The results are presented in a form convenient for observing the influence of system parameters.