Energy Transport in Complex Systems:  Ultrasonic and Structural Vibration Examples

Dr. Joseph Turner
Fraunhofer Institute for Nondestructive Testing
Saarbrucken, Germany

Sponsored by the Dept. of Engineering Mechanics

Date:  Tuesday, February 18, 1997
Time:  3:30 p.m.
Place:  306 Bancroft Hall


The response of complex systems, such as materials with fine microstructure or multicomponent vibrating structures, cannot always be described in a deterministic fashion.  The wave propagation description is complicated by the heterogeneities and discontinuities in these systems which scatter the propagating energy in many directions.  For this reason, statistical methods are often used to describe the system response.  One such method is discussed here.  The mean field and field covariance of these systems are first written in terms of Dyson and Bethe-Salpeter equations, respectively.  The latter equation is then reduced to an equation of radiative transfer in the limit that the heterogeneities are weak, i.e. when the attenuations per wave number are small.  This radiative transfer equation describes the propagation of diffuse energy as a function of space, time, and propagation direction.  Two examples are presented - ultrasonic backscatter from a polycrystalline metal for materials characterization and the response of a vibrating plate with many attachments.  Solutions of the derived radiative transfer equations are presented and compared with commonly observed phenomena.