Application of the Ritz-Rayleigh method for Lamb waves in extremely anisotropic media

0525033 - ÚJF 2021 RIV NL eng J - Journal Article
Grabec, Tomáš - Sedlák, Petr - Seiner, H.
Application of the Ritz-Rayleigh method for Lamb waves in extremely anisotropic media.
Wave Motion. Roč. 96, č. 7 (2020), č. článku 102567. ISSN 0165-2125. E-ISSN 1878-433X
R&D Projects: GA MŠMT EF16_013/0001794
Institutional support: RVO:61389005
Keywords : Ritz-Rayleigh approach * Lamb waves * dispersion curves * anisotropic materials
OECD category: Nuclear related engineering
Impact factor: 2.020, year: 2020
Method of publishing: Limited access
https://doi.org/10.1016/j.wavemoti.2020.102567

We propose a numerical approach for the calculation of frequency-dispersion curves in a flat anisotropic waveguide based on the Ritz-Rayleigh method, offering several significant benefits over commonly used analytical and numerical models. The problem is linearized using a tailored functional basis based on Legendre polynomials, utilizing all symmetries provided by the problem to reduce the computational demands, which brings significant benefits for an inverse procedure, and thus for material characterization. The approach is completely general in terms of elastic properties and direction of propagation. As an exemplary calculation, frequency-dispersion curves of phase and group velocity are calculated for a (001)-oriented free-standing film of the Ni-Mn-Ga alloy exhibiting a strong cubic anisotropy. In the case of propagation along the [100] direction, the dispersion curves oscillate strongly, creating pairs of symmetric and antisymmetric modes. Taking advantage of the generality of the approach, the curves are also presented for the case of extreme anisotropy. Sets of curves for directions [110] and [1 0.9 0] (i.e., 3 degrees off [110]), where the pseudo-surface wave exists, are also calculated. High-frequency asymptotes are shown to correspond with surface and bulk modes propagating along the plate.
Permanent Link: http://hdl.handle.net/11104/0309230