Vertical vibrations of a rigid edge inclusion under a harmonic load

Попов, В. Г.

doi:10.1007/bf00846787

Int Appl Mech

1995

DOI: 10.1007/bf00846787

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Vertical vibrations of a rigid edge inclusion under a harmonic load

В. Г. Попов¹

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Cited by 3 publications

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“…In [15] the solutions of elasticity static problems were constructed for linear, circular, spherical and cylindrical defects. The method of discontinuous solutions was extended to the problem of wave diffraction in papers [16][17][18]. In [19] the method of discontinuous solutions is extended to the defect of an arbitrary form.…”

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The discontinuous solutions of Lame’s equations for a conical defect

Vaysfeld

Reut

2018

Frattura Ed Integrità Strutturale

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ABSTRACT. In this article the discontinuous solutions of Lame's equations are constructed for the case of a conical defect. Under a defect one considers a part of a surface (mathematical cut on the surface) when passing through which function and its normal derivative have discontinuities of continuity of the first kind. A discontinuous solution of a certain differential equation in the partial derivatives is a solution that satisfies this equation throughout the region of determining an unknown function, with the exception of the defect points. To construct such a solution the method of integral transformations is used with a generalized scheme. Here this approach is applied to construct the discontinuous solution of Helmholtz's equation for a conical defect. On the base of it the discontinuous solutions of Lame's equations are derived for a case of steady state loading of a medium.

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confidence: 99%

“…The inverse integral Kantorovich-Lebedev transformation is applied to the obtained expression (16), and final solution is derived in the form 2 …”

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confidence: 99%

The discontinuous solutions of Lame’s equations for a conical defect

Vaysfeld

Reut

2018

Frattura Ed Integrità Strutturale

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“…Conditions (1.2) incorporate the displacement of the inclusion due to a rotation of its cross-section [15]. The displacements u x 0 ( )and v x 0 ( )are determined from the equations of the theory of elastic plates [12], which have the following form in the case of plane strain:…”

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confidence: 99%

Interaction of plane elastic harmonic waves with a perfectly bonded elastic inclusion

Litvin

Попов

2010

Int Appl Mech

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The interaction of plane harmonic waves with a thin elastic inclusion in the form of a strip in an infinite body (matrix) under plane strain conditions is studied. It is assumed that the bending and shear displacements of the inclusion coincide with the displacements of its midplane. The displacements in the midplane are found from the theory of plates. The priblem-solving method represents the displacements as discontinuous solutions of the Lamé equations and finds the unknown discontinuities solving singular integral equations by the numerical collocation method. Approximate formulas for the stress intensity factors at the ends of the inclusion are derived

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Harmonic Vibrations Under the Conditions of Antiplane Deformation of a Half Space Containing a Thin Rigid Striplike Inclusion Crossing the Boundary

Попов

2014

J Math Sci

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Vertical vibrations of a rigid edge inclusion under a harmonic load

Cited by 3 publications

References 2 publications

The discontinuous solutions of Lame’s equations for a conical defect

The discontinuous solutions of Lame’s equations for a conical defect

Interaction of plane elastic harmonic waves with a perfectly bonded elastic inclusion

Harmonic Vibrations Under the Conditions of Antiplane Deformation of a Half Space Containing a Thin Rigid Striplike Inclusion Crossing the Boundary

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