THE VIBRATION OF PLATES ON TWO-DIMENSIONALLY PERIODIC POINT SUPPORTS

✍ Scribed by B.R. Mace

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 512 KB
• Volume: 192
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1996.0211

✦ Synopsis

The vibration of a thin plate lying on point supports is considered. The supports form an orthogonal, two-dimensionally periodic array, and can exert both translational and rotational constraints. The response to a convected harmonic pressure is determined by using Fourier transforms and the structural periodicity. The motion consists of a series of harmonics whose amplitudes are found explicitly. A condition for the propagation of free waves is found, and propagation surfaces are seen to define the frequency-wavenumber relation for such propagating waves. The case of point supports which exert no rotational constraint is considered in more detail. The structure of the propagation surfaces is examined. There is seen to be an interlacing of the propagation surfaces and so-called critical surfaces, which represent the frequency-wavenumber relation for wave propagation in the absence of the supports. Conclusions are drawn regarding the density of propagation surfaces and the modal density of a finite structure. Fluid loading and acoustic radiation are considered.