Linear hysteretic damping and the Hilbert transform

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 linear hysteretic damping. Also referred to as structural damping and complex stiffness in the literature, this noncausal model is characterized by storage and loss moduli independent of frequency. In the present paper, a consistent time-domain representation for linear hysteretic damping is presented using the Hilbert transform. This time-domain representation is a mathematically correct way to replace the complex-stiffness parameters or frequency-dependent damping coefficients commonly used in differential equations that model the dynamics of structures with linear hysteretic damping. A technique is proposed for the computation of the response of structures containing linear hysteretic elements in the time domain; the convergence of the iterative technique is analyzed; and simple numerical examples are developed to illustrate the application of the method.