Probabilistic and Convex Modelling of Acoustically Excited Structures

This book summarises the analytical techniques for predicting the response of linear structures to noise excitations generated by large propulsion power plants. Emphasis is placed on beams and plates of both single-span and multi-span configurations, common in engineering structural systems. Since the natural frequencies and the associated normal modes play a central role in the random vibration analysis of a continuous dynamical system, rather detailed discussions are devoted to their determination. Material covered in the first chapter provides a useful reference for the subsequent discussion of multi-span structures. Also included in this volume is a hybrid probabilistic and convex-uncertainty modeling approach in which the upper and lower bounds of the cross-spectral densities of the acoustic excitation are obtained on the basis of measured data. The random vibration of a structure is treated, for the first time, as an "anti-optimization" problem of finding the least favourable value of the mean-square response.