Elastodynamic response of a wedge to surface pressures

J. D. Achenbach; R. P. Khetan

doi:10.1016/0020-7683(77)90084-1

Elastodynamic response of a wedge to surface pressures

J. D. Achenbach^*, R. P. Khetan

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

An elastic wedge of interior angle κπ, where 1 < κ ≤ 2, is subjected to the impact of spatially uniform pressures on its faces. The application of the pressures produces a system of longitudinal waves, transverse waves and head waves. In this paper the elastodynamic stress singularity in the circumferential stress at the vertex of the wedge is analyzed. The analysis is based on self-similarity of first-order time derivatives of the displacement potentials. By means of appropriate transformations the statement of the problem is reduced to two Laplace's equations, whose solutions in half-planes are coupled along the real axes. The solutions to this system are obtained by using elements of analytic function theory, together with summations over Chebychev polynomials along the real axes.

Original language	English (US)
Pages (from-to)	1157-1171
Number of pages	15
Journal	International Journal of Solids and Structures
Volume	13
Issue number	11
DOIs	https://doi.org/10.1016/0020-7683(77)90084-1
State	Published - 1977
Externally published	Yes

Funding

Acknowledgement-The work reported here was carried out in the course of research sponsored by the National Science Foundation under Grant No. ENG 70-01465 A02 to Northwestern University.

ASJC Scopus subject areas

Modeling and Simulation
General Materials Science
Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering
Applied Mathematics

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10.1016/0020-7683(77)90084-1

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title = "Elastodynamic response of a wedge to surface pressures",

abstract = "An elastic wedge of interior angle κπ, where 1 < κ ≤ 2, is subjected to the impact of spatially uniform pressures on its faces. The application of the pressures produces a system of longitudinal waves, transverse waves and head waves. In this paper the elastodynamic stress singularity in the circumferential stress at the vertex of the wedge is analyzed. The analysis is based on self-similarity of first-order time derivatives of the displacement potentials. By means of appropriate transformations the statement of the problem is reduced to two Laplace's equations, whose solutions in half-planes are coupled along the real axes. The solutions to this system are obtained by using elements of analytic function theory, together with summations over Chebychev polynomials along the real axes.",

author = "Achenbach, {J. D.} and Khetan, {R. P.}",

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year = "1977",

doi = "10.1016/0020-7683(77)90084-1",

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T1 - Elastodynamic response of a wedge to surface pressures

AU - Achenbach, J. D.

AU - Khetan, R. P.

N1 - Funding Information: Acknowledgement-The work reported here was carried out in the course of research sponsored by the National Science Foundation under Grant No. ENG 70-01465 A02 to Northwestern University.

PY - 1977

Y1 - 1977

N2 - An elastic wedge of interior angle κπ, where 1 < κ ≤ 2, is subjected to the impact of spatially uniform pressures on its faces. The application of the pressures produces a system of longitudinal waves, transverse waves and head waves. In this paper the elastodynamic stress singularity in the circumferential stress at the vertex of the wedge is analyzed. The analysis is based on self-similarity of first-order time derivatives of the displacement potentials. By means of appropriate transformations the statement of the problem is reduced to two Laplace's equations, whose solutions in half-planes are coupled along the real axes. The solutions to this system are obtained by using elements of analytic function theory, together with summations over Chebychev polynomials along the real axes.

AB - An elastic wedge of interior angle κπ, where 1 < κ ≤ 2, is subjected to the impact of spatially uniform pressures on its faces. The application of the pressures produces a system of longitudinal waves, transverse waves and head waves. In this paper the elastodynamic stress singularity in the circumferential stress at the vertex of the wedge is analyzed. The analysis is based on self-similarity of first-order time derivatives of the displacement potentials. By means of appropriate transformations the statement of the problem is reduced to two Laplace's equations, whose solutions in half-planes are coupled along the real axes. The solutions to this system are obtained by using elements of analytic function theory, together with summations over Chebychev polynomials along the real axes.

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Elastodynamic response of a wedge to surface pressures

Abstract

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