Elastodynamics of a multilayered transversely isotropic half-space due to the rigid motion of foundation

P. Karimi, A. Amiri-Hezaveh, H. Moghaddasi, F. A. Sabet, Martin Ostoja Starzewski

Research output: Contribution to journalArticle

Abstract

A transversely isotropic multilayered half-space is considered as a support of a massless circular rigid foundation undergoing forced vibrations. The problem formulation adopts the axes of material symmetry of layers with the half-space aligned depth-wise. The problem solution involves two coupled wave equations accompanied by mixed boundary conditions. Employing the influence functions, which contain the effects of the entire domain, i.e. reflecting and refracting phenomena as a consequence of the inhomogeneity of media, the governing equations reduce to a set of Fredholm integral equations of the second kind, which are then solved numerically. To illustrate the method's accuracy, a comparison between the result of this study and the existing solutions for the vibration of a foundation on a layered isotropic half-space is given. Also, the result of the vibration of the disc on a transversely isotropic half-space is determined and compared to the available solution in the literature To explore the effect of stratification as well as material anisotropy on wave motion, dispersion curves corresponding to surface waves are shown. These curves indicate the existence of limiting values for both small and large values of wavenumbers as compared to layers’ thicknesses. Also, exploring the effect of various material properties (e.g., the negative Poisson ratio) and different layers’ arrangements, it is found that the impedance functions of the multilayered medium are closely related to the frequency of excitation while showing almost no sensitivity to properties of the half-space and, in particular, for rocking motion.

Original languageEnglish (US)
Pages (from-to)106-128
Number of pages23
JournalWave Motion
Volume88
DOIs
StatePublished - May 2019

Fingerprint

elastodynamics
half spaces
vibration
forced vibration
Poisson ratio
curves
stratification
surface waves
wave equations
integral equations
inhomogeneity
impedance
boundary conditions
formulations
anisotropy
sensitivity
symmetry
excitation

Keywords

  • Dispersion curves
  • Impedance functions
  • Multilayered medium
  • Poisson ratio
  • Rigid disc
  • Transmission–reflection matrix
  • Transversely isotropic

ASJC Scopus subject areas

  • Modeling and Simulation
  • Physics and Astronomy(all)
  • Computational Mathematics
  • Applied Mathematics

Cite this

Elastodynamics of a multilayered transversely isotropic half-space due to the rigid motion of foundation. / Karimi, P.; Amiri-Hezaveh, A.; Moghaddasi, H.; Sabet, F. A.; Starzewski, Martin Ostoja.

In: Wave Motion, Vol. 88, 05.2019, p. 106-128.

Research output: Contribution to journalArticle

Karimi, P. ; Amiri-Hezaveh, A. ; Moghaddasi, H. ; Sabet, F. A. ; Starzewski, Martin Ostoja. / Elastodynamics of a multilayered transversely isotropic half-space due to the rigid motion of foundation. In: Wave Motion. 2019 ; Vol. 88. pp. 106-128.
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