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Modes Coupling Seismic Waves and Vibrating Buildings: Existence

In: Integral Methods in Science and Engineering, Volume 1

Author

Listed:
  • D. Volkov

    (Worcester Polytechnic Institute)

  • S. Zheltukhin

    (Worcester Polytechnic Institute)

Abstract

We prove an existence result for frequency modes coupling seismic waves and vibrating tall buildings. The derivation from physical principles of a set of equations modeling this phenomenon was done in previous studies. In this model all vibrations are assumed to be anti-plane and time harmonic so the two dimensional Helmholtz equation can be used. A coupling frequency mode is obtained once we can determine a wavenumber such that the solution of the corresponding Helmholtz equation in the lower half plane with relevant Neumann and Dirichlet at the interface satisfies a specific integral equation at the base of an idealized tall building.

Suggested Citation

  • D. Volkov & S. Zheltukhin, 2017. "Modes Coupling Seismic Waves and Vibrating Buildings: Existence," Springer Books, in: Christian Constanda & Matteo Dalla Riva & Pier Domenico Lamberti & Paolo Musolino (ed.), Integral Methods in Science and Engineering, Volume 1, chapter 0, pages 325-334, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-59384-5_29
    DOI: 10.1007/978-3-319-59384-5_29
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