Free Vibration and Hysteretic Damping

I would like to add yet another note to those already published on the notions of viscous and hysteretic damping in a simple oscillator. In particular, I would like to hammer a nail into the coffin of the so-called “complex stiffness.“ One of the features which hysteretic damping may be defined to possess is the property that the energy loss per cycle (in sinusoidal motion) is independent of the frequency of oscillation, ω. This property is derived from some experimental evidence. It is shown in Reference 1 that this behaviour is reproduced by the particular integral of the equation