Response and stability of SDOF viscoelastic system under wideband noise excitations

The response and stability of a single degree-of-freedom (SDOF) viscoelastic system with strongly nonlinear stiffness under the excitations of wideband noise are studied in this paper. Firstly, terms associated with the viscoelasticity are approximately equivalent to damping and stiffness forces; the viscoelastic system is approximately transformed to SDOF system without viscoelasticity. Then, with application of the method of stochastic averaging, the averaged Itô differential equation is obtained. The stationary response and the largest Lyapunov exponent can be analytically expressed. The effects of different system parameters on the response and stability of the system are discussed as well.