On Free Vibrations With Combined Viscous and Coulomb Damping

A closed-form solution of the governing, nonlinear equation for free vibrations of a single-degree-of-freedom system, without stops, under combined viscous and Coulomb damping is first obtained. This is much less involved than forced-response considerations of the same system (with or without stops) the solution of which problem was first obtained by Den Hartog [1]. This note contains the first derivation, as far as the author is aware of, of the equation for the amplitude decay curve (or envelope) for such a system vibrating freely under no-stop conditions. This equation is presented in a form which enables the components of the damping force to be determined from the system’s experimental plot (or record) of displacement versus time.