On the response distribution of nonparametric probabilistic models for mid- and high-frequency analysis

The local response of built-up structural and acoustic systems, consisting of stiff components with low modal density and flexible components with high modal density, may be very sensitive to uncertainty in spatial variations in the geometry, material properties, and boundary conditions of the flexible components. In this work, this uncertainty is considered by modeling the low modal density master system as deterministic and the high modal density subsystems in a nonparametric stochastic way, and by subsequently computing the response probability density function. The probability distribution of the master system's displacement degrees of freedom and the total subsystem energies is numerically computed by assuming that the distribution of the eigenvalues and eigenvectors of a decoupled subsystem correspond to those of a Gaussian Orthogonal Ensemble matrix. This approach is extensively validated by application to structures, consisting of thin plates attached to stiff structural components. Good agreement between the predicted probability distributions and the results of detailed Monte Carlo simulations is found. The validation examples also illustrate that the numerical procedure agrees better with the Monte Carlo simulations than a closed-form evaluation of the response probability density, which requires additional assumptions. © (2012) by the Katholieke Universiteit Leuven Department of Mechanical Engineering All rights reserved.