ANALYSIS OF HYSTERETIC DAMPING USING ANALYTIC SIGNALS

The purpose of this technical note is to present a time-domain formula tion for linear hysteretic damping. The integro-differential equations that govern the dynamics of structures with linear hysteretic damping are transformed into ordinary differential equations in analytic sign als-that is, complex-valued signals in which the real and imaginary pa rts are a Hilbert transform pair. The poles of this type of system sho w radial symmetry in the complex plane, determining that for each stab le pole in the left-hand half of the complex plane, there is an ''unst able'' pole in the right-hand half The impulse response functions of t hese unstable poles are bounded but noncausal. To illustrate the formu lation, the analytic impulse response of a single-degree-of-freedom os cillator with linear hysteretic damping is obtained. The response of t he structure to any loading signal can be obtained using time convolut ion of this impulse response function and the corresponding analytic e xcitation signal.