An Uncertain Vibration Analysis Method for Nonlinear Systems Under Interval Process Excitations

This paper proposes an interval vibration analysis method for nonlinear systems subjected to uncertain excitations, through which its dynamic displacement response bounds can be calculated effectively. In the proposed method, the uncertain excitations are described using the interval process model developed by the authors in recent years. Firstly, the displacement response of a certain degree of freedom for a nonlinear system at an arbitrary time point is expressed as a function of several standard uncorrelated interval variables by using the interval K–L expansion. Secondly, two constrained optimization models are established for the lower and upper bounds of the displacement response of the nonlinear system at the time point. Thirdly, the efficient global optimization (EGO) method is used to solve the above optimization models, and the dynamic displacement response bounds of the nonlinear system can be further obtained. Finally, the effectiveness of the proposed method is verified by investigating two numerical examples.