Optimum design of stochastically excited non-linear dynamic systems without geometric constraints

This paper presents an e9cient procedure for min–max dynamic response optimization of stochastically excited non-linear systems with multiple time-delayed inputs. This procedure employs a stochastic linearization technique to overcome system non-linearity and an auto-covariance analysis technique to represent the original stochastic mechanical model in a suitable form for optimization. Special attention is given to the sensitivity analysis, due to the complex nature of the problem. Therefore, exact expressions are obtained in a simple form for the evaluation of the required gradients, which greatly improve the stability and e9ciency of the optimization algorithm. The numerical results and performance are presented by means of solving two min–max dynamic response optimization problems