Fractional calculus for the solution of non-linear stochastic oscillators with viscous dampers devices

Fluid viscoelastic dampers are of great interest in different fields of engineering. Examples of their applications can be found in seismic mitigation design of structures or in vibration absorption in airplane suspension. Such devices introduce a non-linear dissipative term in the equation of motion and therefore, the solution of even a single degree of freedom system excited by a white noise process, becomes prohibitive. The solution is usually obtained by approximated methods, like the stochastic linearization technique. In this paper it is shown that, by means of fractional operators, it is possible to find the solution of oscillators provided with fluid viscoelastic devices, approaching the problem in its originally nonlinear form. Comparison with solutions obtained by Monte Carlo simulation are finally discussed.