Abstract:
The variational method for determining localized waves (trapped modes) is modified for periodic elastic waveguides with partially clamped surfaces. Two sufficient conditions for the existence of localized fields in waveguides with defects (cavities with positive volume and cracks) are established. In the presence of elastic and geometrical symmetries, localized fields were also found in periodic elastic waveguides with surfaces free of external loads.
Keywords:
periodic waveguide with defects, localized elastic fields, variational method.
This publication is cited in the following 9 articles:
Marco Moscatelli, Claudia Comi, Jean-Jacques Marigo, “Wave transmission in quasi-periodic lattices”, Phil. Trans. R. Soc. A., 382:2279 (2024)
S. A. Nazarov, “Threshold resonances and virtual levels in the spectrum of cylindrical and periodic waveguides”, Izv. Math., 84:6 (2020), 1105–1160
S. A. Nazarov, “Various manifestations of Wood anomalies in locally distorted quantum waveguides”, Comput. Math. Math. Phys., 58:11 (2018), 1838–1855
S. A. Nazarov, “The asymptotic behaviour of the scattering matrix in a neighbourhood of the endpoints of a spectral gap”, Sb. Math., 208:1 (2017), 103–156
S. A. Nazarov, K. M. Ruotsalainen, M. Silvol, “Trapped modes under interaction of elastic and electric fields in a piezoelectric waveguide”, Dokl. Phys., 60:10 (2015), 451
S.A. Nazarov, “The eigenfrequencies of a slightly curved isotropic strip clamped between absolutely rigid profiles”, Journal of Applied Mathematics and Mechanics, 78:4 (2014), 374
S. A. Nazarov, “The Mandelstam Energy Radiation Conditions and the Umov–Poynting Vector in Elastic Waveguides”, J Math Sci, 195:5 (2013), 676
S. A. Nazarov, “Elastic waves trapped by a homogeneous anisotropic semicylinder”, Sb. Math., 204:11 (2013), 1639–1670
Sonia Fliss, “A Dirichlet-to-Neumann Approach for The Exact Computation of Guided Modes in Photonic Crystal Waveguides”, SIAM J. Sci. Comput., 35:2 (2013), B438
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