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3. Conclusion

Author

Andrianov, Igor V., Awrejcewicz, Jan, Danishevskyy, Vladyslav V., Öchsner, Andreas, Series editor, da Silva, Lucas F. M., Series editor, Altenbach, Holm, Series editor, Andrianov, Igor V., Awrejcewicz, Jan, and Danishevskyy, Vladyslav V.

Published
2018
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7. Nonlinear Elastic Problems

Author

Andrianov, Igor V., Awrejcewicz, Jan, Danishevskyy, Vladyslav V., Öchsner, Andreas, Series editor, da Silva, Lucas F. M., Series editor, Altenbach, Holm, Series editor, Andrianov, Igor V., Awrejcewicz, Jan, and Danishevskyy, Vladyslav V.

Published
2018
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8. Local Stresses in Elastic Fibrous Composites

Author

Andrianov, Igor V., Awrejcewicz, Jan, Danishevskyy, Vladyslav V., Öchsner, Andreas, Series editor, da Silva, Lucas F. M., Series editor, Altenbach, Holm, Series editor, Andrianov, Igor V., Awrejcewicz, Jan, and Danishevskyy, Vladyslav V.

Published
2018
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11. Introduction

Author

Andrianov, Igor V., Awrejcewicz, Jan, Danishevskyy, Vladyslav V., Öchsner, Andreas, Series editor, da Silva, Lucas F. M., Series editor, Altenbach, Holm, Series editor, Andrianov, Igor V., Awrejcewicz, Jan, and Danishevskyy, Vladyslav V.

Published
2018
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27. Conclusion

Author

Andrianov, Igor V., primary, Awrejcewicz, Jan, additional, and Danishevskyy, Vladyslav V., additional

Published
2017
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30. Introduction

Author

Andrianov, Igor V., primary, Awrejcewicz, Jan, additional, and Danishevskyy, Vladyslav V., additional

Published
2017
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32. Elastic waves in heterogeneous media. Supplementary material. from Elastic waves in periodically heterogeneous two-dimensional media: locally periodic and anti-periodic modes

Author

Andrianov, Igor V., Danishevskyy, Vladyslav V., and Rogerson, Graham

Subjects
Quantitative Biology::Quantitative Methods, High Energy Physics::Lattice, Physics::Medical Physics
Abstract

Dispersion surfaces of the lattice models; Waves in the viscoelastic lattice; Continuous approximations; Dispersion diagrams of the fibrous medium

Published
2018
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34. Composite dynamic models for periodically heterogeneous media.

Author

Colquitt, Daniel J, Danishevskyy, Vladyslav V, and Kaplunov, Julius

Subjects
*ELASTIC waves, *DYNAMIC models, *THEORY of wave motion, *ELASTIC wave propagation, *UNIT cell, *MEDIA studies
Abstract

Propagation of elastic waves through discrete and continuous periodically heterogeneous media is studied. A two-scale asymptotic procedure allows us to derive macroscopic dynamic equations applicable at frequencies close to the resonant frequencies of the unit cells. Matching the asymptotic solutions by two-point Padé approximants, we obtain new higher-order equations that describe the dynamic behaviour of the medium both in the low and in the high frequency limits. An advantage of the proposed approach is that all the macroscopic parameters can be determined explicitly in terms of the microscopic properties of the medium. Dispersion diagrams are evaluated and the propagation of transient waves induced by pulse and harmonic loads is considered. The developed analytical models are verified by comparison with data of numerical simulations. For high-contrast media, we can observe an analogy between the propagation of waves in heterogeneous solids and in thin-walled waveguides. It is also shown that different combinations of cell resonances may result in some additional types of waves that do not appear in the classical continuous theory. [ABSTRACT FROM AUTHOR]

Published
2019
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