Application of a generalized continuum theory to the problem of spatial damping in complex mechanical systems

Abstract

The existence of a certain carrier medium is postulated. It is assumed that the medium is described by the equations of classical elasticity theory. It is further assumed that an infinite number of non-interacting oscillators is attached to each point of the carrier medium. Hence it appears that every material point consists of a single material point of the classical theory of elasticity and the attached oscillators. The analysis shows the main property of the vibratory field in the environment: the coefficient of spatial attenuation of vibration has a finite value even for negligibly small friction in the suspension of oscillators. This effect occurs only for the model that takes into account attached oscillators. From a physical point of view, this effect can be explained by the fact that the suspended oscillators act as dynamic vibration absorbers. This model allows determination of the global properties of the vibratory fields of complex engineering structures without accounting for the non-essential elements of these structures.