NONLINEAR VIBRATIONS OF FRACTIONALLY DAMPED SYSTEMS

This paper deals with the harmonic oscillations of periodically excite d nonlinear systems where hysteresis is simulated via fractional opera tor representations. Employing a diophantine version of the fractional operational powers, the energy constrained Lindstedt-Poincare perturb ation procedure is utilized to establish the harmonic solution. The co nstrained perturbation procedure was employed since it allows for the handling of strong damping and exciting forces over the full span of t he driving frequency range. Based on the approach taken, the long time behavior of the fractionally damped Duffing's equation is studied in detail. Of special interest is the determination of the influence of f ractional order on the frequency amplitude response behavior.