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Green's function for the viscoelastic and isotropic half-space

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

Abstract

A dynamic 3D Green's function for the homogeneous, isotropic and viscoelastic (of the Zener type) half-space is derived in a closed form. The results obtained here can be used as either stand-alone solutions for simple problems or in conjunction with a boundary integral equation formulations to account for complex boundary conditions. In the later case, mesh-reducing boundary element formulations can be constructed as an alternative method for numerical implementation purposes.

Green's function for the viscoelastic and isotropic half-space

Abstract

A dynamic 3D Green's function for the homogeneous, isotropic and viscoelastic (of the Zener type) half-space is derived in a closed form. The results obtained here can be used as either stand-alone solutions for simple problems or in conjunction with a boundary integral equation formulations to account for complex boundary conditions. In the later case, mesh-reducing boundary element formulations can be constructed as an alternative method for numerical implementation purposes.
Paper Structure (5 sections, 3 theorems, 40 equations)

This paper contains 5 sections, 3 theorems, 40 equations.

Table of Contents

  1. Introduction
  2. Mathematical statement of the problem
  3. Fundamental solution
  4. Correction term
  5. Conclusion

Key Result

Lemma 3.1

Let $\beta=\sqrt{\eta^2_1+\eta^2_2-k^2}$, then function is a solution of Eq. (eq3).

Theorems & Definitions (6)

  • Lemma 3.1
  • proof
  • Lemma 4.1
  • proof
  • Theorem 4.1
  • proof