Saturation and resonance of nonlinear system under bounded noise excitation

The principal resonance of a 2dof nonlinear oscillator due to bounded random excitations is investigated. Equations of modulation of response amplitude and phase are derived by the method of multiple scales. Steady-state moments for the response amplitude of the system are determined through the linearized Ito differential equation. The results of theoretical analyses are verified by numerical simulations. Saturation phenomena are found in the random counterpart. Some recommendations for potential applications of this random saturation phenomenon to vibration control problems are given at the end of the paper.