Dynamic analysis of systems with hysteretic damping

Experimental observations have shown that the dissipation per cycle in many materials does not depend on the deformation frequency over a wide frequency range. A linear model used frequently to represent this type of mechanical behavior is the concept of hysteretic damping. Herein, time and frequency domain models of hysteretic damping are investigated. The validity of time domain and random vibration analyses of systems with hysteretic damping that is described by a constant complex valued stiffness coefficient was examined. It was shown that, although, this model, can be efficient for frequency domain analysis of harmonic vibration of engineering systems, it does not represent a causal system and thus, is not appropriate for time domain analysis involving transient processes. Using a viscoelastic model, proposed by Biot, a study of dynamic systems with linear hysteretic damping is conducted. These systems results in integro-differential equations in the time domain. A time domain technique for the numerical solution of the integro-differential equation of motion is proposed. The response of a mass supported by Biot's hysteretic element is examined under harmonic excitation and ground motion