{
  "id": "2308.12407",
  "version": "v1",
  "published": "2023-08-23T20:01:10.000Z",
  "updated": "2023-08-23T20:01:10.000Z",
  "title": "Existence of Rayleigh waves in the presence of impedance boundary conditions: A perpective from linear algebra",
  "authors": [
    "Fabio Andres Vallejo Narvaez"
  ],
  "comment": "In preparation for journal submission",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this work we present an alternative method to deal with the secular equation for surface Rayleigh waves occurring in an isotropic elastic half-space subjected to impedance boundary conditions of the type proposed by Godoy et al. [Wave Motion 49 (2012), 585-594]. The method is applied to a boundary condition that is defined by proportional relationships between both the stress and velocity components, with proportional constants being complex numbers with negative real part. Our analysis shows that a Rayleigh wave cannot exist in this scenario. Interestingly, the problem considered here contains the problems investigated recently by Vinh and Xuan [European Journal of Mechanics A/Solids 61 (2017) 180-185] and Giang and Vinh [J Eng Math (2021) 130:13] as particular cases, which allows us to demonstrate for the first time that the secular equation derived on those works has not complex roots outside the real axis for general impedance parameters. This is a crucial property that has only been verified for the stress-free secular equation by Achenbach in 1975. Our findings are primarily obtained through arguments from linear algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-23T20:01:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "impedance boundary conditions",
      "linear algebra",
      "complex roots outside",
      "surface rayleigh waves",
      "general impedance parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}