Visco-elastic systems under narrow-band excitation

The study of the response of nonlinear systems to narrow-band random excitation is importance. For example, the excitation of secondary system would be a narrow-band random process if the primary system could be modeled as a single-degree-of-freedom system with light damping subject to borad-band excitation. In the theory nonlinear random vibration, most results obtained so far are attributed to the response of nonlinear oscillators to borad-band random excitation. In comparison, results on the effect of narrow-band excitation on non-linear oscillators are quite limited. Furthermore, some results in this area are disputable. For linear viscoelastic systems under both additive and multiplicative borad-band excitation excitations, Ariaratnam studied the stochastic stability of the system by using the method of stochastic averaging. Cai, Lin and Xu determined the condition for asymptotic sample stability of the system by using an improved stochastic averaging procedure. In this paper, the response of visco-elastic systems to combined deterministic harmonic and random excitation is investigated. The method of harmonic balance and the method of stochastic averaging are used to determine the response of the system. Theoretical analyses and numerical simulations show that when the intensity of the random excitation increase, the steady state solution may change form a limit cycle to a diffused limit cycle. Under some conditions the system may have two steady state solutions and jumps may exist.