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.

Nonautonomous elementary net systems and their application to programmable logic control

In this paper, a novel approach to Petri net modeling of programmable logic controller (PLC) programs is presented. The modeling approach is a simple extension of elementary net systems, and a graphical design tool that supports the use of this modeling approach is provided. A key characteristic of the model is that the binary sensory inputs and binary actuation outputs of the PLC are explicitly represented. This leads to the following two improvements: outputs are unambiguous, and interaction patterns are more clearly represented in the graphical form. The use of this modeling approach produces programs that are simple, lightweight, and portable. The approach is demonstrated by applying it to the development of a control module for a MonTech Positioning Station. © 2008 IEEE.