Dynamic Stress and Displacement in an Elastic Half-Space with a Cylindrical Cavity
The dynamic response of an elastic half-space with a cylindrical cavity in a circular cross-section is analyzed. The cavity is assumed to be infinitely long, lying parallel to the plane-free surface of the medium at a finite depth and subjected to a uniformly distributed harmonic pressure at the inn...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.3233/SAV-2010-0602 |
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| author | İ. Coşkun H. Engin A. Özmutlu |
| author_facet | İ. Coşkun H. Engin A. Özmutlu |
| author_sort | İ. Coşkun |
| collection | DOAJ |
| description | The dynamic response of an elastic half-space with a cylindrical cavity in a circular cross-section is analyzed. The cavity is assumed to be infinitely long, lying parallel to the plane-free surface of the medium at a finite depth and subjected to a uniformly distributed harmonic pressure at the inner surface. The problem considered is one of plain strain, in which it is assumed that the geometry and material properties of the medium and the forcing function are constant along the axis of the cavity. The equations of motion are reduced to two wave equations in polar coordinates with the use of Helmholtz potentials. The method of wave function expansion is used to construct the displacement fields in terms of the potentials. The boundary conditions at the surface of the cavity are satisfied exactly, and they are satisfied approximately at the free surface of the half-space. Thus, the unknown coefficients in the expansions are obtained from the treatment of boundary conditions using a collocation least-square scheme. Numerical results, which are presented in the figures, show that the wave number (i.e., the frequency) and depth of the cavity significantly affect the displacement and stress. |
| format | Article |
| id | doaj-art-f90e182728b54d0ab16e06ac16805c92 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-f90e182728b54d0ab16e06ac16805c922025-02-03T01:10:30ZengWileyShock and Vibration1070-96221875-92032011-01-0118682783810.3233/SAV-2010-0602Dynamic Stress and Displacement in an Elastic Half-Space with a Cylindrical Cavityİ. Coşkun0H. Engin1A. Özmutlu2Faculty of Civil Engineering, Yıldız Technical University, Davutpaşa Campus, 34210 Esenler, Istanbul, TurkeyFaculty of Civil Engineering, Istanbul Technical University, 34469 Maslak, Istanbul, TurkeyDepartment of Civil Engineering, Trakya University, 2250 Karaağaç, Edirne, TurkeyThe dynamic response of an elastic half-space with a cylindrical cavity in a circular cross-section is analyzed. The cavity is assumed to be infinitely long, lying parallel to the plane-free surface of the medium at a finite depth and subjected to a uniformly distributed harmonic pressure at the inner surface. The problem considered is one of plain strain, in which it is assumed that the geometry and material properties of the medium and the forcing function are constant along the axis of the cavity. The equations of motion are reduced to two wave equations in polar coordinates with the use of Helmholtz potentials. The method of wave function expansion is used to construct the displacement fields in terms of the potentials. The boundary conditions at the surface of the cavity are satisfied exactly, and they are satisfied approximately at the free surface of the half-space. Thus, the unknown coefficients in the expansions are obtained from the treatment of boundary conditions using a collocation least-square scheme. Numerical results, which are presented in the figures, show that the wave number (i.e., the frequency) and depth of the cavity significantly affect the displacement and stress.http://dx.doi.org/10.3233/SAV-2010-0602 |
| spellingShingle | İ. Coşkun H. Engin A. Özmutlu Dynamic Stress and Displacement in an Elastic Half-Space with a Cylindrical Cavity Shock and Vibration |
| title | Dynamic Stress and Displacement in an Elastic Half-Space with a Cylindrical Cavity |
| title_full | Dynamic Stress and Displacement in an Elastic Half-Space with a Cylindrical Cavity |
| title_fullStr | Dynamic Stress and Displacement in an Elastic Half-Space with a Cylindrical Cavity |
| title_full_unstemmed | Dynamic Stress and Displacement in an Elastic Half-Space with a Cylindrical Cavity |
| title_short | Dynamic Stress and Displacement in an Elastic Half-Space with a Cylindrical Cavity |
| title_sort | dynamic stress and displacement in an elastic half space with a cylindrical cavity |
| url | http://dx.doi.org/10.3233/SAV-2010-0602 |
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