Risposta deterministica ed aleatoria dell'oscillatore elastoviscoso invecchiante

The dynamic response of a SDoF linear oscillator with both linear damping of Kelvin type and aging viscous damping is analyzed. The integro-differential equation of motion is recast as a third order linear differential equation with variable exponentially decaying coefficients. As regards the deterministic excitations, the free vibrations caused by an impressed displacement, the unit step excitation, and the sinusoidal resonant excitation are considered. The stochastic excitation is a zero mean stationary Gaussian process output of a second order linear filter. In both cases the presence of the Kelvin damping is fundamental: if this is absent, the response diverges as the damping goes to zero. Moreover, the response is viscoplastic, that is an impressed displacement is not recovered, differently from the hereditary damping in which it is wholly recovered at infinite time.