Surface Effects on the Scattering of SH-Wave Around an Arbitrary Shaped Nano-Cavity
By using the complex variable function theory and the conformal mapping method, the scattering of plane shear wave (SH-wave) around an arbitrary shaped nano-cavity is studied. Surface effects at the nanoscale are explained based on the surface elasticity theory. According to the generalized Yong–Lap...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2019/3084581 |
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| author | Hongmei Wu Zhiying Ou |
| author_facet | Hongmei Wu Zhiying Ou |
| author_sort | Hongmei Wu |
| collection | DOAJ |
| description | By using the complex variable function theory and the conformal mapping method, the scattering of plane shear wave (SH-wave) around an arbitrary shaped nano-cavity is studied. Surface effects at the nanoscale are explained based on the surface elasticity theory. According to the generalized Yong–Laplace equations, the boundary conditions are given, and the infinite algebraic equations for solving the unknown coefficients of the scattered wave solutions are established. The numerical solutions of the stress field can be obtained by using the orthogonality of trigonometric functions. Lastly, the numerical results of dynamic stress concentration factor around a circular hole, an elliptic hole and a square hole as the special cases are discussed. The numerical results show that the surface effect and wave number have a significant effect on the dynamic stress concentration, and prove that our results from theoretical derivation are correct. |
| format | Article |
| id | doaj-art-c845e31c8cca447991d69a99856629ec |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-c845e31c8cca447991d69a99856629ec2025-02-03T01:24:39ZengWileyAdvances in Mathematical Physics1687-91201687-91392019-01-01201910.1155/2019/30845813084581Surface Effects on the Scattering of SH-Wave Around an Arbitrary Shaped Nano-CavityHongmei Wu0Zhiying Ou1School of Mechanical and Electronical Engineering, Lanzhou University of Technology, Lanzhou, Gansu, ChinaSchool of Science, Lanzhou University of Technology, Lanzhou, Gansu, ChinaBy using the complex variable function theory and the conformal mapping method, the scattering of plane shear wave (SH-wave) around an arbitrary shaped nano-cavity is studied. Surface effects at the nanoscale are explained based on the surface elasticity theory. According to the generalized Yong–Laplace equations, the boundary conditions are given, and the infinite algebraic equations for solving the unknown coefficients of the scattered wave solutions are established. The numerical solutions of the stress field can be obtained by using the orthogonality of trigonometric functions. Lastly, the numerical results of dynamic stress concentration factor around a circular hole, an elliptic hole and a square hole as the special cases are discussed. The numerical results show that the surface effect and wave number have a significant effect on the dynamic stress concentration, and prove that our results from theoretical derivation are correct.http://dx.doi.org/10.1155/2019/3084581 |
| spellingShingle | Hongmei Wu Zhiying Ou Surface Effects on the Scattering of SH-Wave Around an Arbitrary Shaped Nano-Cavity Advances in Mathematical Physics |
| title | Surface Effects on the Scattering of SH-Wave Around an Arbitrary Shaped Nano-Cavity |
| title_full | Surface Effects on the Scattering of SH-Wave Around an Arbitrary Shaped Nano-Cavity |
| title_fullStr | Surface Effects on the Scattering of SH-Wave Around an Arbitrary Shaped Nano-Cavity |
| title_full_unstemmed | Surface Effects on the Scattering of SH-Wave Around an Arbitrary Shaped Nano-Cavity |
| title_short | Surface Effects on the Scattering of SH-Wave Around an Arbitrary Shaped Nano-Cavity |
| title_sort | surface effects on the scattering of sh wave around an arbitrary shaped nano cavity |
| url | http://dx.doi.org/10.1155/2019/3084581 |
| work_keys_str_mv | AT hongmeiwu surfaceeffectsonthescatteringofshwavearoundanarbitraryshapednanocavity AT zhiyingou surfaceeffectsonthescatteringofshwavearoundanarbitraryshapednanocavity |