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Nov 1982

Volume 72, Issue S1, pp. S1-S108

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back to top Session X. Memorial Session for John C. Johnson
Invited Papers
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Natural modes, coupled modes, and transients of vibratory systems (A)

Eugen J. Skudrzyk

J. Acoust. Soc. Am. Volume 72, Issue S1, pp. S43-S44 (1982); (2 pages)

Online Publication Date: 12 Aug 2005

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Resonances of a point driven vibrator occur when the reflected waves reach the driver in phase with the outgoing wave, antiresonances occur when these two waves are in antiphase. The frequency response for the outgoing wave field determines the geometric mean line through the frequency response curve of the vibrator. Reflections at the boundaries of the vibrator, at ribs and appendages, or at material variations, have no effect on the “mean‐line response.” Plate modes are scalar functions of the position. In contrast, shell modes are represented by three‐dimensional functions. But they are also described by uncoupled and orthogonal mode functions. Isolated vibrating systems always have orthogonal modes. It may sometimes be convenient to describe a vibrator by mode functions of some simpler vibrator. Every mode then is represented by a sum of mode functions which are coupled (e.g., plate with a mass load). The transients of a complex vibrator can be built up from the transients of its modes. An understanding of the theory of transients is important, for instance, when frequency modulated pulses are generated; increasing the damping may lead to long duration transients; the aim here is to cancel the switching‐on transient with the switching‐off transient which can only be done if damping is small. The theory of natural modes and transients will be illustrated by practical examples. [This work was sponsored by the Office of Naval Research, Code 474.]
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