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Half-plane Green`s function for anti-plane elastic 1D hexagonal QCs

Tsviatko V. Rangelov, George D. Manolis, Petia S. Dineva

Abstract

This paper presents an analytical derivation of a frequency-dependent fundamental solution plus a Green's function for the uni-dimensional, hexagonal quasicrystal sheet subjected to elastic waves under anti-plane strain conditions. Furthermore, closed-form solutions for the free-fields developing in this sheet for propagating shear waves are also obtained. The analysis presented here provides a foundation for understanding quasicrystal dynamic behavior and for advancing relevant computational methods.

Half-plane Green`s function for anti-plane elastic 1D hexagonal QCs

Abstract

This paper presents an analytical derivation of a frequency-dependent fundamental solution plus a Green's function for the uni-dimensional, hexagonal quasicrystal sheet subjected to elastic waves under anti-plane strain conditions. Furthermore, closed-form solutions for the free-fields developing in this sheet for propagating shear waves are also obtained. The analysis presented here provides a foundation for understanding quasicrystal dynamic behavior and for advancing relevant computational methods.

Paper Structure

This paper contains 9 sections, 32 equations.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Fundamental Solution and Green's Function for Quasicristals
  4. Fundamental solution derivation
  5. Green's function derivation
  6. Free-field Waves in Quasicrystals
  7. Full-plane wave solutions
  8. Half-plane wave solutions
  9. Conclusions

Theorems & Definitions (1)

  • Remark 3.1