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Direct/InverseScattering of SH Wave in an Infinite Elastic Media with Micro/ Nano Inhomogeneity by Couple Stress Theory with Micro Inertia

Goodarzi, Azadeh | 2015

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 47952 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Mohammadi Shodja, Hossein; Fotouhi, Morteza; Hesaraki, Mahmoud
  7. Abstract:
  8. Direct/inverse scattering of high frequency SH-waves by a circular micro-/nano-fiberembedded in an infinite elastic isotropic medium is addressed in the framework of couple stresstheory with micro inertia. The inadequacy of classical theory of elasticity in the problems dealingwith propagation of high frequency waves as well as the problems concerning the elastic fields inthe vicinity of micro-/nano-size defects in which the wavelengths and the size of the defects arecomparable to intrinsic length of the material is well-known. These dilemmas can be remedied byemploying the more accurate higher order continuum theories. So, in the context of couple stresstheory with micro inertia, the far-field pattern of the scattered high frequency SH-waves by themicro-/nano-size scatterer as well as the dispersion relations are obtained. It is shown that, whenthe size of the scatterer is comparable to the characteristic lengths of the material, the classicaltheory lacks precision. Within this theory, the appearance of a new length scale, so-called ‘‘dynamic characteristic length’’ stems from consideration of the micro inertia, which gives rise to physicallyrealistic dispersion relations with characteristic resembling those observed in experiments. By using this theory, the corresponding analytical expressions of the elastodynamic fields, total and differential scattering cross-sections, and the dynamic stress concentration factor are presented and their dependence on the characteristic lengths and frequency are examined. In order to reconstruct the embedded micro-/nano-scatterer, linear samplingmethod and singular sources method are developed within the couple stress theory. For the casewhere the classical wavenumber is used, the errors in the reconstructed size, depending on the typeof the materials, are estimated. In the numerical examples, the effects of the characteristic lengthson the elastodynamic fields are examined. Also, several examples of the reconstruction of the sizeand the location of the micro-/nano-size elastic and rigid scatterer are presented
  9. Keywords:
  10. Singular Sources Method ; Couple Stress ; Linear Sampling ; Direct/Invers Scattering ; Couple Stress Theory with Microinertia ; Elastodynamic Field ; Micro/Nano Fiber

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