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 homogeneous 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.

A radiative transfer equation is being developed for the description of the evolution and equilibration of diffuse acoustic intensity on complex submerged shells. The diffuse intensity has, as its source, a coherent field generated by deterministic loads or by waves incident from the fluid. It is scattered by structural heterogeneities on the shell. The net disturbance on the structure, and consequently also the net radiation to the fluid, is then composable as a coherent part, described by ray launching and tracing, and a diffuse part described by the radiative transfer equation.

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 substantially simplified by some of the couplings between modes at very different frequencies. The validity of this problematic assumption is explored and justified.

It is well known that structural damage affects linear vibrational responses. However, in practical cases, the effects are merely small perturbations upon undamaged system responses. Detection of small cracks in structures by means of linear vibration response is therefore difficult. The bi-linear stiffness of an opening and closing crack, however, may substantially and qualitatively change the small amplitude response. This project, which is analytical, numerical, and experimental, is intended to elucidate the potential for practical nonlinear vibrational nondestructive evaluation.