Elastic wave propagation and stop-band generation in strongly damaged solids
In this work, we study the propagation of elastic waves in elongated solids with an array of equallyspaced deep transverse cracks, focusing in particular on the determination of stop-bands. We consider solids with different types of boundary conditions and different lengths, and we show that the e...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Gruppo Italiano Frattura
2014-07-01
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| Series: | Fracture and Structural Integrity |
| Subjects: | |
| Online Access: | http://www.gruppofrattura.it/pdf/rivista/numero29/numero_29_art_4.pdf |
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| Summary: | In this work, we study the propagation of elastic waves in elongated solids with an array of equallyspaced
deep transverse cracks, focusing in particular on the determination of stop-bands. We consider solids
with different types of boundary conditions and different lengths, and we show that the eigenfrequencies
associated with non-localized modes lie within the pass-bands of the corresponding infinite periodic system,
provided that the solids are long enough. In the stop-bands, instead, eigenfrequencies relative to localized
modes may be found. Furthermore, we use an asymptotic reduced model, whereby the cracked solid is
approximated by a beam with elastic connections. This model allows to derive the dynamic properties of
damaged solids through analytical methods. By comparing the theoretical dispersion curves yielded by the
asymptotic reduced model with the numerical outcomes obtained from finite element computations, we observe
that the asymptotic reduced model provides a better fit to the numerical data as the slenderness ratio increases.
Finally, we illustrate how the limits of the stop-bands vary with the depth of the cracks. |
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| ISSN: | 1971-8993 1971-8993 |