A LOCAL MODAL/PERTURBATIONAL METHOD FOR ESTIMATING FREQUENCY RESPONSE STATISTICS OF BUILT-UP STRUCTURES WITH UNCERTAIN PROPERTIES

A local modal/perturbational method is described which enables estimates to be made of the statistics of frequency response functions of a system whose properties are uncertain. The method is computationally very efficient, providing these estimates at little cost above that required to perform a single deterministic frequency response prediction. Such an approach is typically required when there is significant uncertainty or variability in the properties of the system under consideration. This would often be at higher frequencies, where the dynamic behaviour becomes increasingly sensitive to small changes in system properties, but not at frequencies high enough such that broad-brush statistical methods, such as statistical energy analysis, are appropriate. approach the system is divided into subsystems. The frequency response of the baseline system is found using modal analysis. The global modes of the baseline system are found in terms of the subsystem modes using component mode synthesis. Uncertainty is then assumed to exist in the local modal properties of the subsystems. A perturbation is found which relates small changes in the local modal properties to those in the global modal properties, enabling the frequency response of the perturbed system to be estimated. Finally, a Monte Carlo simulation is used to estimate the frequency response function statistics. Numerical results are presented for a system comprising two spring-coupled rods.