 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| << Previous article | Volume 47, Issue 2 / 2012 | Next article >> |
| V.G. Popov, "Interaction of a Plane Harmonic Wave with a Thin Rigid Inclusion of the Shape of a Cylindrical Shell," Mech. Solids. 47 (2), 187-194 (2012) |
| Year |
2012 |
Volume |
47 |
Number |
2 |
Pages |
187-194 |
| DOI |
10.3103/S0025654412020057 |
| Title |
Interaction of a Plane Harmonic Wave with a Thin Rigid Inclusion of the Shape of a Cylindrical Shell |
| Author(s) |
V.G. Popov (Odessa National Maritime Academy, Didrikhsona 8, Odessa, 65029 Ukraine, dr.vg.popov@gmail.com) |
| Abstract |
The paper presents the solution of the problem of determining the stress state in an elastic matrix containing a rigid inclusion of the shape of a thin cylindrical shell. It is assumed that harmonic vibrations occur in the matrix under the conditions of axial symmetry (the symmetry axis is the inclusion axis) and the conditions of full adhesion between the inclusion and the matrix are satisfied. The vibrations are caused by the propagation of a plane wave whose front is perpendicular to the inclusion axis. The solution method is based on representing the displacements in the matrix as discontinuous solutions of the equations of axisymmetric oscillations of an elastic medium with unknown stress jumps on the inclusion surface. The realization of the boundary conditions for these jumps leads to a system of integral equations. Its solution is constructed numerically by the mechanical quadrature method with the use of special quadrature formulas for specific integrals. It is numerically investigated how the ratio of the inclusion geometric dimensions and the propagating wave frequency affect the stress concentration near the inclusion. |
| Keywords |
discontinuous solution, thin inclusion, stress intensity factor |
| References |
| 1. | M. I. Vinograd,
Inclusions in Steel and Its Properties
(Metallurgiya, Moscow, 1963)
[in Russian]. |
| 2. | G. I. Belchenko and S. I. Gubenko,
Nonmetallic Inclusions and Steel Quality
(Tekhnika, Kiev, 1980)
[in Russian]. |
| 3. | Rob Phillips,
Crystal Defects and Microstructure. Modeling across Scales
(Cambridge Univ. Press, Cambridge, 2001). |
| 4. | G. T. Sulim,
Foundations of Mathematical Theory of Thermoelastic Equilibrium of Deformable Solids with Thin Inclusions
(Naukova Dumka, Kiev, 1989)
[in Ukrainian]. |
| 5. | V. G. Popov, "Interaction of a Harmonic Torsional Wave with a Thin
Rigid Cylindrical Inclusion," Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 5, 75-81 (2004) [Mech. Solids (Engl. Transl.) 39 (5),
58-63 (2004)]. |
| 6. | V. G. Popov, "Determination of the Stress State in a Half-Space in
the Vicinity of Cylindrical Defects Appearing on the Surface under
Torsional Vibrations," Mat. Met. Fiz.-Mekh. Polya 51 (2),
105-111 (2008) [J. Math. Sci. (Engl. Transl.) 162 (1),
121-131 (2009)]. |
| 7. | V. Ya. Popov, Yu. A. Morozov, and N. D. Vaisfel'd, "On Solution of
Dynamic Problems of Elastic Stress Concentration near Defects on Cylindrical Surfaces," Prikl. Mekh. 35 (1), 28-36 (1999)
[Int. Appl. Mech. (Engl. Transl.) 35 (1), 24-32 (1999)]. |
| 8. | Z. T. Nazarchuk,
Numerical Investigation of Wave Diffraction on Cylindrical Structures
(Naukova Dumka, Kiev, 1989)
[in Russian]. |
|
| Received |
26 November 2009 |
| Link to Fulltext |
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