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Pseudo-damping in undamped plates and shells
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10.1121/1.2747093
/content/asa/journal/jasa/122/2/10.1121/1.2747093
http://aip.metastore.ingenta.com/content/asa/journal/jasa/122/2/10.1121/1.2747093
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Schematic description of a simply supported beam on an elastic foundation with an axial compressive force applied at each end.

Image of FIG. 2.
FIG. 2.

(Color online) A typical impulse response of a beam with no internal dissipation shows a decay when its natural frequency distribution has a condensation point provided by the spring on which it rests and the axial compressive force.

Image of FIG. 3.
FIG. 3.

(Color online) Schematic of a plate that rests on an elastic foundation with in-plane compressive forces applied at each edge.

Image of FIG. 4.
FIG. 4.

For a plate resting on an elastic foundation, without the compressive in-plane forces: (a) dispersion relation, (b) modal distribution, and (c) modal density. Elastic foundation introduces a condensation region where the change in natural frequency with respect to wave number nearly vanishes.

Image of FIG. 5.
FIG. 5.

(Color online) Impulse response of the simply supported plate depicted in Fig. 2 (a) with (horizontal line is initial displacement) and (b) without the elastic foundation. Presence of elastic foundation leads to pseudo-damping of the plate response.

Image of FIG. 6.
FIG. 6.

For a plate resting on an elastic foundation and under compressive in-plane forces: (a) dispersion relation, (b) modal distribution, and (c) modal density. Compressive forces move the frequency at which condensation develops.

Image of FIG. 7.
FIG. 7.

(Color online) Impulse response of the plate under compressive in-plane forces (horizontal line is initial displacement).

Image of FIG. 8.
FIG. 8.

Coordinate system for a spherical shell element. , , , , thickness , and radius .

Image of FIG. 9.
FIG. 9.

For the spherical shell element in Fig. 7: (a) dispersion, (b) modal distribution, and (c) modal density.

Image of FIG. 10.
FIG. 10.

(Color online) Impulse response of the spherical shell element, which includes modes in the simulations (horizontal line is initial displacement). Position of excitation and response at , .

Image of FIG. 11.
FIG. 11.

Cylindrical shell element and the coordinate system that describes it. , , with dimensions , thickness , and radius .

Image of FIG. 12.
FIG. 12.

Dispersion (a) and modal density (b) of the cylindrical shell element.

Image of FIG. 13.
FIG. 13.

(Color online) Impulse response of a cylindrical shell (horizontal line is initial displacement). Simulations considered include modes. Position of excitation and response , .

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/content/asa/journal/jasa/122/2/10.1121/1.2747093
2007-08-01
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Pseudo-damping in undamped plates and shells
http://aip.metastore.ingenta.com/content/asa/journal/jasa/122/2/10.1121/1.2747093
10.1121/1.2747093
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