Abstract
The propagation of elastic waves in thick-walled pipe with an embedded inhomogeneity is considered. The pipe is excited by a point force applied on its surface and the time harmonic problem is solved using the null field approach, a method whose main characteristics are surface integral representations and expansions in spherical and cylindrical vector wave functions. Entering in the expression for the scattered field are the transition matrix for the cavity, the reflection matrices for the inner and outer surfaces of the pipe, the transformation functions between the spherical and cylindrical vector wave functions and also the translation for the cylindrical waves. Numerical examples, both in the frequency and time domain, are presented for a spherical cavity and an open circular crack.
Similar content being viewed by others
References
P. C. Waterman, Matrix theory of elastic wave scattering.J. Acoust. Soc. Am. 60 (1976) 567–580.
P. W. Waterman, Matrix theory of elastic wave scattering. II. A new conservation law.J. Acoust. Soc. Am. 63 (1978) 1320–1325.
Y.-H. Pao and V. Varatharajulu, Scattering matrix for elastic waves. I. Theory.J. Acoust. Soc. Am. 60 (1976) 556–566.
V.V. Varadan, Scattering matrix for elastic waves. II. Application to elliptic cylinders.J. Acoust. Soc. Am. 63 (1978) 1014–1024.
S. Ström, Introduction to integral representations and integral equations for time-harmonic acoustic, electromagnetic and elastodynamic wave fields. In V.V. Varadan, A. Lakhtakia and V.K. Varada (eds.),Acoustic, Electromagnetic and Elastic Wave Scattering. North-Holland, Amsterdam (1991) Vol. 1.
A. Boström and G. Kristensson, Elastic wave scattering by a three-dimensional inhomogeneity in an elastic half space.Wave Motion 2 (1980) 335–353.
A. Boström and A. Karlsson, Broad-band synthetic seismograms for a spherical inhomogeniety in a many-layered half space.Geogphys. J. R. Astr. soc. 89 (1987) 257–547.
A. Karlsson, Scattering of Rayleigh Lamb waves from a 2d-cavity in an elastic plate.Wave Motion 6 (1984) 205–222.
A. Boström and A. Karlsson, Point-force excitation of an elastic plate with an embedded cavity.J. Appl. Mech. 52 (1985) 937–942.
A. Boström, Transmission and reflection of acoustic waves by an obstacle in a waveguide.Wave Motion 2 (1980) 167–184.
S. Olsson, Scattering of Acoustic waves by a sphere outside an infinite circular cylinder.J. Acoust. Soc. Am. 88 (1990) 515–524.
S. Olsson, Transmission and reflection of elastic waves by a spherical obstacle in an infinite circular cylindrical rod.Comm. Div. Mech. Division of Mechanics, CTH, Götenborg (1992).
S. Olsson, Point force excitation of an infinite circular with an embedded spherical cavity.J. Acoust. Soc. Am. 93 (1993) 2479–2488.
A. Boström, G. Kristensson and S. Ström, Transformation properties of plane, spherical and cylindrical scalar and vector wave functions. In: V.V. Varadan, A. Lakhtakia and V.K. Varadan (eds),Acoustic, Electromagnetic and Elastic Wave Scattering. North-Holland, Amsterdam (1991) Vol. 1.
A. Boström and A. Eriksson, Scattering by two penny-shaped cracks with spring boundary conditions.Comm. Div. Mech. 1992: 4, Division of Mechanics, CTH, Götenborg (1992; accepted for publication inProc. R. Soc. Lond. A.).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Olsson, S. Point force excitation of a thick-walled elastic infinite pipe with an embedded inhomogeneity. J Eng Math 28, 311–325 (1994). https://doi.org/10.1007/BF00128750
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00128750