Dispersion curves of elastic waveguides exhibit points where the group velocity vanishes while the wavenumber remains finite. These are the so-called zero-group-velocity (ZGV) points. As the elastodynamic energy at these points remains confined close to the source, they are of practical interest for nondestructive testing and quantitative characterization of structures. These applications rely on the correct prediction of the ZGV points. In this contribution, we first model the ZGV resonances in anisotropic plates based on the appearance of an additional modal solution. The resulting governing equation is interpreted as a two-parameter eigenvalue problem. Subsequently, we present three complementary numerical procedures capable of computing ZGV points in arbitrary nondissipative elastic waveguides in the conventional sense that their axial power flux vanishes. The first method is globally convergent and guarantees to find all ZGV points but can only be used for small problems. The second procedure is a very fast, generally-applicable, Newton-type iteration that is locally convergent and requires initial guesses. The third method combines both kinds of approaches and yields a procedure that is applicable to large problems, does not require initial guesses and is likely to find all ZGV points. The algorithms are implemented in GEW ZGV computation (doi: 10.5281/zenodo.7537442).
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February 2023
February 24 2023
Computing zero-group-velocity points in anisotropic elastic waveguides: Globally and locally convergent methods
Daniel A. Kiefer
;
Daniel A. Kiefer
a)
1
Institut Langevin, ESPCI Paris, Université PSL, CNRS
, 75005 Paris, France
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Bor Plestenjak
;
Bor Plestenjak
2
Faculty of Mathematics and Physics, University of Ljubljana
, SI-1000 Ljubljana, Slovenia
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Hauke Gravenkamp
;
Hauke Gravenkamp
3
International Centre for Numerical Methods in Engineering (CIMNE)
, 08034 Barcelona, Spain
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Claire Prada
Claire Prada
1
Institut Langevin, ESPCI Paris, Université PSL, CNRS
, 75005 Paris, France
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Daniel A. Kiefer
1,a)
Bor Plestenjak
2
Hauke Gravenkamp
3
Claire Prada
1
1
Institut Langevin, ESPCI Paris, Université PSL, CNRS
, 75005 Paris, France
2
Faculty of Mathematics and Physics, University of Ljubljana
, SI-1000 Ljubljana, Slovenia
3
International Centre for Numerical Methods in Engineering (CIMNE)
, 08034 Barcelona, Spain
a)
Electronic mail: [email protected]
J. Acoust. Soc. Am. 153, 1386–1398 (2023)
Article history
Received:
October 29 2022
Accepted:
January 30 2023
Citation
Daniel A. Kiefer, Bor Plestenjak, Hauke Gravenkamp, Claire Prada; Computing zero-group-velocity points in anisotropic elastic waveguides: Globally and locally convergent methods. J. Acoust. Soc. Am. 1 February 2023; 153 (2): 1386–1398. https://doi.org/10.1121/10.0017252
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