The Full-Space Elastodynamic Green’s Functions for Time-Harmonic Radial and Axial Ring Sources in a Homogeneous Isotropic Medium

1999 ◽  
Vol 66 (3) ◽  
pp. 639-645
Author(s):  
Y. Lu
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Hankel Transform ◽  
Legendre Functions ◽  
Linear Elastic ◽  
Time Harmonic ◽  
Stress Components ◽  
Axial Ring ◽  
Logarithmic Singularities ◽  
Half Degree

The elastodynamic Green’s functions for time-harmonic radial and axial ring sources in a homogeneous, isotropic, linear elastic full-space medium are derived using the Fourier-Hankel transform. The Green’s functions are found to have the same logarithmic singularities as the Legendre functions of positive and negative half-degree of the second kind. As the frequency approaches zero, the Green’s functions approach the corresponding elastostatic Green’s functions. The far-field displacement and stress components are also derived.

Dynamic Green’s functions in anisotropic piezoelectric, thermoelastic and poroelastic solids

1994 ◽  
Vol 447 (1929) ◽  
pp. 175-188 ◽  
Keyword(s):  
Time Domain ◽  
Unit Sphere ◽  
Green's Functions ◽  
Green’S Functions ◽  
Fundamental Solutions ◽  
Anisotropic Elasticity ◽  
Field Equations ◽  
One Dimensional ◽  
Time Harmonic ◽  
Point Forces

A procedure is described to generate fundamental solutions or Green’s functions for time harmonic point forces and sources. The linearity of the field equations permits the Green’s function to be represented as an integral over the surface of a unit sphere, where the integrand is the solution of a one-dimensional impulse response problem. The method is demonstrated for the theories of piezoelectricity, thermoelasticity, and poroelasticity. Time domain analogues are discussed and compared with known expressions for anisotropic elasticity.

Anti-plane time-harmonic Green’s functions for a coated circular inhomogeneity in a piezoelectric medium with spring- or membrane-type imperfect interfaces

2016 ◽  
Vol 22 (9) ◽  
pp. 1813-1846 ◽  
Author(s):  
Yin Shi ◽  
Yongping Wan ◽  
Zheng Zhong
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Transversely Isotropic ◽  
Piezoelectric Medium ◽  
Two Phase ◽  
Imperfect Interfaces ◽  
Time Harmonic ◽  
Special Cases ◽  
Circular Inhomogeneity ◽  
Membrane Type

Two-dimensional anti-plane time-harmonic dynamic Green’s functions for a coated circular inhomogeneity in an infinitely extended matrix with spring- or membrane-type imperfect interfaces are presented. The inhomogeneity, coating and matrix are all assumed to be piezoelectric and transversely isotropic. By using the Bessel function expansions, explicit solutions for the electromechanical fields induced by a time-harmonic anti-plane line force and line charge located in the unbounded matrix, the annular coating and the circular inhomogeneity are derived. The present solutions can recover the anti-plane Green’s functions for some special cases, such as the dynamic or quasi-static Green’s functions of piezoelectricity with perfect interfaces, as well as the dynamic or quasi-static Green’s functions for a two-phase composite with perfect or imperfect interfaces. By means of detailed discussions, selected calculated results are graphically shown to demonstrate the dependence of the electromechanical fields on the circular frequency and the interface properties as well as the coating and size of the inclusion.

scholarly journals Time-harmonic Green’s functions for anisotropic magnetoelectroelasticity

2008 ◽  
Vol 45 (1) ◽  
pp. 144-158 ◽  
Author(s):  
R. Rojas-Díaz ◽  
A. Sáez ◽  
F. García-Sánchez ◽  
Ch. Zhang
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Time Harmonic
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