- Letter
- Open Access
Extreme wave skewing and dispersion spectra of anisotropic elastic plates
Phys. Rev. Research 7, L012043 – Published 26 February, 2025
DOI: https://doi.org/10.1103/PhysRevResearch.7.L012043
Abstract
Guided wave dispersion is commonly assessed by Fourier analysis of the field along a line, resulting in frequency-wave-number dispersion curves. In anisotropic plates, a point source can generate multiple dispersion branches pertaining to the same modal surface, which arise due to the angle between the power flux and the wave vector. We show that this phenomenon is very particular near zero-group-velocity points and occurs in all directions independent of the degree of anisotropy. Stationary phase points accurately describe measurements on a monocrystalline silicon plate.
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References (28)
- B. A. Auld, Acoustic Fields and Waves in Solids, 2nd ed. (Krieger, Malabar, FL, 1990), Vol. 1.
- K.-J. Langenberg, R. Marklein, and K. Mayer, Ultrasonic Nondestructive Testing of Materials: Theoretical Foundations (CRC Press, Boca Raton, FL, 2012).
- A. G. Every, W. Sachse, K. Y. Kim, and M. O. Thompson, Phonon focusing and mode-conversion effects in silicon at ultrasonic frequencies, Phys. Rev. Lett. 65, 1446 (1990).
- M. R. Hauser, R. L. Weaver, and J. P. Wolfe, Internal diffraction of ultrasound in crystals: Phonon focusing at long wavelengths, Phys. Rev. Lett. 68, 2604 (1992).
- A. G. Every, Formation of phonon-focusing caustics in crystals, Phys. Rev. B 34, 2852 (1986).
- R. E. Vines, S.-I. Tamura, and J. P. Wolfe, Surface acoustic wave focusing and induced Rayleigh waves, Phys. Rev. Lett. 74, 2729 (1995).
- A. A. Maznev, A. M. Lomonosov, P. Hess, and A. A. Kolomenskii, Anisotropic effects in surface acoustic wave propagation from a point source in a crystal, Eur. Phys. J. B 35, 429 (2003).
- A. G. Every, A. A. Maznev, W. Grill, M. Pluta, J. D. Comins, O. B. Wright, O. Matsuda, W. Sachse, and J. P. Wolfe, Bulk and surface acoustic wave phenomena in crystals: Observation and interpretation, Wave Motion 50, 1197 (2013).
- D. A. Kiefer, S. Mezil, and C. Prada, Beating resonance patterns and extreme power flux skewing in anisotropic elastic plates, Sci. Adv. 9, eadk6846 (2023).
- W. Duan and T.-H. Gan, Investigation of guided wave properties of anisotropic composite laminates using a semi-analytical finite element method, Compos. B Eng. 173, 106898 (2019).
- S. I. Ranganathan and M. Ostoja-Starzewski, Universal elastic anisotropy index, Phys. Rev. Lett. 101, 055504 (2008).
- A. Bossart and R. Fleury, Extreme spatial dispersion in nonlocally resonant elastic metamaterials, Phys. Rev. Lett. 130, 207201 (2023).
- K. Wang, Y. Chen, M. Kadic, C. Wang, and M. Wegener, Nonlocal interaction engineering of 2D roton-like dispersion relations in acoustic and mechanical metamaterials, Commun. Mater. 3, 35 (2022).
- J. H. Page, Focusing of ultrasonic waves by negative refraction in phononic crystals, AIP Adv. 6, 121606 (2016).
- M. Notomi, Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap, Phys. Rev. B 62, 10696 (2000).
- J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University Press, Princeton, 2008).
- E. Galiffi, G. Carini, X. Ni, G. Álvarez-Pérez, S. Yves, E. M. Renzi, R. Nolen, S. Wasserroth, M. Wolf, P. Alonso-Gonzalez, A. Paarmann, and A. Alù, Extreme light confinement and control in low-symmetry phonon-polaritonic crystals, Nat. Rev. Mater. 9, 9 (2024).
- X. Zhang, Q. Yan, W. Ma, T. Zhang, X. Yang, X. Zhang, and P. Li, Ultrafast anisotropic dynamics of hyperbolic nanolight pulse propagation, Sci. Adv. 9, eadi4407 (2023).
- B. A. Auld, Acoustic Fields and Waves in Solids, 2nd ed. (Krieger, Malabar, FL, 1990), Vol. 2.
- D. Royer and T. Valier-Brasier, Elastic Waves in Solids 1: Propagation (ISTE and John Wiley & Sons, New York, 2022).
- A. Velichko and P. D. Wilcox, Modeling the excitation of guided waves in generally anisotropic multilayered media, J. Acoust. Soc. Am. 121, 60 (2007).
- B. Chapuis, N. Terrien, and D. Royer, Excitation and focusing of Lamb waves in a multilayered anisotropic plate, J. Acoust. Soc. Am. 127, 198 (2010).
- A. Karmazin, E. Kirillova, W. Seemann, and P. Syromyatnikov, A study of time harmonic guided Lamb waves and their caustics in composite plates, Ultrasonics 53, 283 (2013).
- E. Glushkov, N. Glushkova, A. Eremin, and R. Lammering, Group velocity of cylindrical guided waves in anisotropic laminate composites, J. Acoust. Soc. Am. 135, 148 (2014).
- D. A. Kiefer, GEWtool (2025), doi:10.5281/zenodo.10114243, https://github.com/dakiefer/GEWtool.
- M. Thelen, N. Bochud, M. Brinker, C. Prada, and P. Huber, Laser-excited elastic guided waves reveal the complex mechanics of nanoporous silicon, Nat. Commun. 12, 3597 (2021).
- M. Ponschab, D. A. Kiefer, and S. J. Rupitsch, Simulation-based characterization of mechanical parameters and thickness of homogeneous plates using guided waves, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 66, 1898 (2019).
- V. Yantchev, L. Arapan, I. Katardjiev, and V. Plessky, Thin-film zero-group-velocity Lamb wave resonator, Appl. Phys. Lett. 99, 033505 (2011).