The ability to predict the effect of dimension and thickness variability on the dynamic response of realistically uncertain engineering structures is examined in this thesis. Initially, available methods for predicting key response statistics and probabilities, for both low and high frequencies are examined to establish their strengths and limitations for specified levels of random dimension variability. For low frequency applications, the ability of Direct Integration (DI) and the First-Order Reliability Method (FORM) to predict exceedance probability is examined. For high frequency applications, the ability of the methods of Statistical Energy Analysis (SEA) and DI to predict the mean and standard deviation of the energy response is examined. The use of Extreme Value (EV) theory is included as a way to bound responses using simulated or measured responses. The strengths and limitations of Monte Carlo simulation methods are explored for both low and high frequency responses of randomly uncertain structures using both simple mode superposition plate-structure solutions and (commercially available) finite element solutions for coupled plate structures. To address, without the need to undertake expensive Monte Carlo simulation, the problem of predicting response bounds for structures with varying levels of uncertainty, a novel DI-EV method is developed and examined. It is tested first on a simple plate structure, then on a coupled plate structure, with low-level and high-level random dimension and thickness uncertainty. In addition, the method is compared with the SEA-EV method. The thesis shows that the results from the existing SEA-EV bounding approach gives good bounds only at particular frequencies and mainly for low levels of dimension variability. In contrast, the proposed DI-EV bounding approach compare extremely well with Monte Carlo simulations, which is not only at all frequencies but also with both low-level and high-level uncertainties, for simple and coupled plate structures with dimension and thickness variation.

This thesis is concerned with efficient uncertainty identification (UI) – namely the nonlinear inverse problem of establishing specific statistical properties of an uncertain structure from a practically-limited supply of low-frequency dynamic response information. An established UI approach (published in 2005) which uses Maximum Likelihood Estimation (MLE) and the Perturbation Method of uncertainty propagation is adopted for the study using (for the first time) mode shape information rather than just natural or resonant frequencies. The thesis develops a method based on the use of selected coefficients in a generalized displacement model i.e. a weighted series of spatially-continuous multiply-differentiable base functions to approximate the structural free-vibration response of an uncertain structure. The focus is placed on the estimation (from relatively small data sets) of the statistical properties of the location of an attached point-mass with normally-distributed position. Simulated data for uncertain point-mass-loaded linear beam and plate structures is initially used to test the method making use of as much exact or closed-form differentiable information as possible to obtain frequencies and mode shapes. In the case of plate structures, extensive use is made of the Rayleigh Ritz method to generate the required response coefficients. This is shown to have significant advantages over alternatives such as the Finite Element method. The approach developed for use with free vibration information is then tested on measured experimental data obtained from an acoustically-forced clamped plate. Structural displacement measurements are taken from the plate using Vibromap 1000, a commercially-available ESPI-based holomodal measurement system capable of wide-field vibration response observation in real-time, or quantitative displacement response measurement. The thesis shows that the developed uncertainty identification method works well for beams and plates using simulated free-vibration data