The theory of multiple scattering of waves in random media is applied to determine mean and mean-square responses of prototypical examples of simple master structures coupled to distributions of uncertain substructures. The results are compared with earlier simple speculations and with numerical simulations.

We seek to determine the correct time-domain description of diffuse energy transport in quasi-one-dimensional irregular structures. Previous numerical work on diffuse energy transport in Anderson localizing statistically ho mogeneous and statistically isotropic two-dimentional systems, with and without damping, is being extended to quasi-one-dimensional systems, with special attention paid to power variances and applications in disordered truss systems.

Recent theory has predicted that a reverberant acoustic field will ``remember'' the location of its source by having an enhanced diffuse energy density there. It is predicted that the enhancement will be by a factor of two at early times, after a few side-wall reflections, and a factor of three at much later times comparable to the modal density. This prediction is now being investigated at ultrasonic frequencies in laboratory-sized elastic bodies.

Methods used successfully to derive energy transport relations for waves in random media are being applied to the problem of linear vibrations of complex structures. Finite-element models for complex structures are used as a starting point for the rational derivation of a simplified set of equations describing mean energy transport. The simple equations are derived using a concept of incoherence between substructures. They are further simplified by neglecting couplings between pseudomodes at very different frequencies. The validity of this problematic assumption is explored and justified.