Integral Theories of Random Vibration of Complex Structures

Abstract This article is aimed at the analysis of various theories enabling determination of fields of high-frequency vibration of complex dynamic structures. The considered theories are characterized by different degrees of information and ease of application. Chapter I deals with the classical theory of random vibration of complex structures. It gives full information on the vibration field of the structures, but it can hardly be practically applied in the case of the broad band random load. Further suggested integral methods do not require accurate detailing of the structure but only its integral characteristics. The simpliest of these integral methods (the Bolotin method) is discussed in Chapter 2. It enables the determination of mean values of stationary vibration of the structure. The theory of vibrational conductivity (Chapter 4) enables the determination of the spectral densities of acceleration of the structure points on the basis of the differential equation of thermal conductivity. More complete information on space distribution of vibration can be obtained with the theory of medium with complex structure (Chapter 3). In this case a boundary problem is discussed which has much in common with the problem of dynamical viscoelasticity.