Abstract:
Of the methods currently available for predicting the propagation of structure- and air-borne sound in mechanical structures, most assume idealised mathematical models and an exact knowledge of structural properties. For complex structures such as buildings and vehicles, however, uncertainty and the sensitivity of vibrational response to small changes in structural detail are significant, and the apparent precision of 'exact' approaches is inappropriate and computationally expensive. This situation has lead to the development of a method known as Statistical Energy Analysis (SEA), which involves the notional division of the structure into a number of smaller subsystems, and a description of the response to forcing in terms of the temporal and spatial averages of subsystem energies. However, the difficulty of ensuring that certain assumptions implicit in SEA are satisfied for any given structure presents a significant barrier to its more widespread use. ·An alternative approach is presented in this thesis which avoids the assumptions of traditional SEA. The response of the structure to external forcing is described in terms of energy-bearing 'wave components' which propagate throughout the structure and undergo reflection and transmission at junctions and subsystems. The dynamic properties of the structure are represented by two global wave component scattering matrices, one for subsystems and one for junctions, and structural uncertainty is expressed in terms of statistical distributions of the eigenvalues and eigenvectors of the product of these global scattering matrices. A computationally inexpensive 'Scalar ensemble' method for estimating the average and variance of energy flows between subsystems is derived and its accuracy verified in comparisons with results obtained by Monte Carlo sampling. Features of ensemble variations in energy flow are investigated and quantitative measures of wave component and subsystem coupling strength in complex structures are developed. Consideration is also given to the reasons for failure of traditional SEA in a number of structures which satisfy widely accepted criteria for SEA applicability.