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 wi de frequency range. A linear model used frequently to represent this t ype 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 ti me-domain representation for linear hysteretic damping is presented us ing the Hilbert transform. This time-domain representation is a mathem atically correct way to replace the complex-stiffness parameters or fr equency-dependent damping coefficients commonly used in differential e quations that model the dynamics of structures with linear hysteretic damping. A technique is proposed for the computation of the response o f structures containing linear hysteretic elements in the time domain; the convergence of the iterative technique is analyzed; and simple nu merical examples are developed to illustrate the application of the me thod.