The ensemble statistics of the response of structural components with uncertain properties

• Main Author: Brown, A. W.
• Published: University of Cambridge 2003
• Subjects: 519
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.596977

Statistical Energy Analysis is a method commonly used in the engineering analysis of complex dynamic systems at medium or high frequencies. This research is particularly motivated by the lack of a successful general method for the prediction of response variance when using this technique. For a structure with sufficient parameter randomness, a method based on certain universal properties of the eigensolutions of a structure is proposed, which does not rely on knowledge of the statistics of the structural parameters. The physics literature on random matrix theory contains evidence that the eigensolutions of elastodynamic structures may be described by results from a specific ensemble of matrices, called the ‘Gaussian Orthogonal Ensemble’. The random matrix theory results are shown to match numerical results generated by consideration of rectangular mass or stiffness loaded plates, given enough structural irregularity. The energy density response variance of a generic elastodynamic structure is analysed using point process theory. It is found that a prediction which assumes full Gaussian Orthogonal Ensemble statistics corresponds well to the frequency response statistics of an ensemble of rectangular mass and stiffness loaded plate, if there is sufficient randomly placed point mass and stiffness. In some cases discrepancies are found between theory and simulation, and possible reasons for these are identified. A numerical investigation of the form of the energy PDF for the plate simulation is carried out. The statistics of a point-to-point transfer function are also investigated using point process theory.