KEYNOTE: Robin Langley - Efficient methods of computing the steady state and transient response of random dynamic systems at high frequencies

Across a range of industries, there is a requirement to predict the vibration and vibro-acoustic performance of an engineering system at high frequencies, meaning frequencies at which the wavelength of the vibration is much smaller than the length scale of the system. Computational difficulties arise due to the fact that very many vibration modes of the system can be excited, and moreover, the response is sensitive to small changes in the system that arise from manufacturing uncertainties. A direct computational approach is to perform Monte Carlo simulations using fine mesh finite element (FE) models, but this requires a significant amount of computer time and often the required statistical distributions of the properties of the random system are not available. This presentation will review the results arising from an alternative approach which is based on a combination of random matrix theory, random point process theory, and energy flow analysis. The fundamental methodology will be described and then a number of applications will be presented including variance and confidence level prediction in Statistical Energy Analysis (SEA) and hybrid FE/SEA models; the statistical properties of frequency response functions, including level crossing rates and maximum values, and the special properties of causal functions; impact analysis, including power inputs due to impact and the prediction of the mean and variance of the transient response. The talk will focus on the underpinning theoretical approach but a number of industrial applications will also be presented.