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.

System-of-system Approaches and Challenges for Multi-Site Manufacturing

In the multi-site manufacturing domain, systems-of-systems (SoS) are rarely called so. However, there exist a number of collaborative manufacturing paradigms which closely relate to system-of-system principles. These include distributed manufacturing, dispersed network manufacturing, virtual enterprises and cloud manufacturing/manufacturing-as-a-service. This paper provides an overview of these terms and paradigms, exploring their characteristics, overlaps and differences. These manufacturing paradigms are then considered in relation to five key system-of-systems characteristics: autonomy, belonging, connectivity, diversity and emergence. Data collected from two surveys of academic and industry experts is presented and discussed, with key challenges and barriers to multi-site manufacturing SoS identified.