Monitoring of streambank stability and streamside vegetation in a livestock exclosure on the Warm Springs River, Oregon : comparison of ground-based surveys with aerial photographic analysis

The objective of this monitoring project was to determine the baseline condition for a 960-m long stream reach and its associated streamside zone, which terminates at the confluence with the Deschutes River. This stream reach had been damaged heavily in the February 1996 flood and had also received many years of overuse by livestock grazing. The monitoring project was conducted in July 1997 just after installation of riparian exclosure fencing. Future resurvey of the study area will allow determination of progress made in ecological recovery.

Analytical approximations for the modal acoustic impedances of simply supported, rectangular plates.

Coupling of the in vacuo modes of a fluid-loaded, vibrating structure by the resulting acoustic field, while known to be negligible for sufficiently light fluids, is still only partially understood. A particularly useful structural geometry for the study of this problem is the simply supported, rectangular flat plate, since it exhibits all the relevant physical features while still admitting an analytical description of the modes. Here the influence of the fluid can be expressed in terms of a set of doubly infinite integrals over wave number: the modal acoustic impedances. Closed-form solutions for these impedances do not exist and, while their numerical evaluation is possible, it greatly increases the computational cost of solving the coupled system of modal equations. There is thus a need for accurate analytical approximations. In this work, such approximations are sought in the limit where the modal wavelength is small in comparison with the acoustic wavelength and the plate dimensions. It is shown that contour integration techniques can be used to derive analytical formulas for this regime and that these formulas agree closely with the results of numerical evaluations. Previous approximations [Davies, J. Sound Vib. 15(1), 107-126 (1971)] are assessed in the light of the new results and are shown to give a satisfactory description of real impedance components, but (in general) erroneous expressions for imaginary parts.