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.

The design and construction of flat rectangular otter boards for bottom trawling: a review

The design and construction of the otter board is a subject of great importance for economy in trawling. This review incorporates a historical resume tracing the change and development• of otter boards. The size of the otter board and its relationship with the horse power of the engine and size of the net and the methods of rigging are dealt with. The factors influencing the horizontal spread are discussed. The effect of the angles of attack, heel and tilt and the ground reaction on the force coefficients have been reviewed and discussed with particular reference to flat rectangular otter boards used for bottom trawling. A short account of other designs of otter boards used for improved efficiency is given. Suggestion for improving the efficacy of otter boards based on the work hitherto done has been made. The contributions relating to the various aspects of design and performance of trawl boards carried out till 1969 have been considered.