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Acoustics: Sound Fields, Transducers and Vibration, 2nd Edition
book

Acoustics: Sound Fields, Transducers and Vibration, 2nd Edition

by Leo Beranek, Tim Mellow
May 2019
Intermediate to advanced content levelIntermediate to advanced
900 pages
29h 35m
English
Academic Press
Content preview from Acoustics: Sound Fields, Transducers and Vibration, 2nd Edition

Part XXXX: Shells

14.16. Shell wave equation in polar coordinates

Like a plate, a shell has bending stiffness, but it has additional stiffness because of its curvature. If you hold a sheet of paper by the edge, it will hang down because it has no stiffness. However, if you curve it even slightly, it will support small objects such as a pencil. The dynamic shell wave equations [9] are obtained by adding an axial inertia term to the static shell equations [8]. We shall simplify our analysis by assuming that the shell is shallow, or the radius of curvature R is large, so that we can ignore radial and tangential components of the displacement η ˜ . This is a reasonable assumption for height/radius ratios up to around 0.25. The following ...
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Publisher Resources

ISBN: 9780128152287