Vibration approximate analytical solutions of circular plate consideration of complex pre-stress distribution
The influence of the complex pre-stress on the circular plate is investigated herein, with which to solve the non-uniform pre-stress distribution problem. According to the strain–stress equation, the motion differential equations of the circular thin plate with complex pre-stress distribution are de...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SAGE Publishing
2020-12-01
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| Series: | Journal of Low Frequency Noise, Vibration and Active Control |
| Online Access: | https://doi.org/10.1177/1461348419852456 |
| _version_ | 1819175614086643712 |
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| author | Chen Luyun Yi Hong |
| author_facet | Chen Luyun Yi Hong |
| author_sort | Chen Luyun |
| collection | DOAJ |
| description | The influence of the complex pre-stress on the circular plate is investigated herein, with which to solve the non-uniform pre-stress distribution problem. According to the strain–stress equation, the motion differential equations of the circular thin plate with complex pre-stress distribution are derived. Based on the Rayleigh–Ritz theory of energy method, the complex pre-stress distribution function and vibration-displacement function are expanded into the cosine trigonometric series, and the approximate analytical solutions of structural free vibration for circular plate are proposed. A circular plate with simply supported boundary condition, for example, the effectiveness of the proposed method is confirmed through numerical calculations and the finite element method verification. The influence of different type’s distribution of welding residual stress on the natural frequency and mode shape for circular plate structure are compared. The proposed approach in present article can be used in arbitrary pre-stress distribution problem. |
| first_indexed | 2024-12-22T20:57:40Z |
| format | Article |
| id | doaj.art-b023d37404ba4444a1c8c0d7a08a1f04 |
| institution | Directory Open Access Journal |
| issn | 1461-3484 2048-4046 |
| language | English |
| last_indexed | 2024-12-22T20:57:40Z |
| publishDate | 2020-12-01 |
| publisher | SAGE Publishing |
| record_format | Article |
| series | Journal of Low Frequency Noise, Vibration and Active Control |
| spelling | doaj.art-b023d37404ba4444a1c8c0d7a08a1f042022-12-21T18:12:54ZengSAGE PublishingJournal of Low Frequency Noise, Vibration and Active Control1461-34842048-40462020-12-013910.1177/1461348419852456Vibration approximate analytical solutions of circular plate consideration of complex pre-stress distributionChen LuyunYi HongThe influence of the complex pre-stress on the circular plate is investigated herein, with which to solve the non-uniform pre-stress distribution problem. According to the strain–stress equation, the motion differential equations of the circular thin plate with complex pre-stress distribution are derived. Based on the Rayleigh–Ritz theory of energy method, the complex pre-stress distribution function and vibration-displacement function are expanded into the cosine trigonometric series, and the approximate analytical solutions of structural free vibration for circular plate are proposed. A circular plate with simply supported boundary condition, for example, the effectiveness of the proposed method is confirmed through numerical calculations and the finite element method verification. The influence of different type’s distribution of welding residual stress on the natural frequency and mode shape for circular plate structure are compared. The proposed approach in present article can be used in arbitrary pre-stress distribution problem.https://doi.org/10.1177/1461348419852456 |
| spellingShingle | Chen Luyun Yi Hong Vibration approximate analytical solutions of circular plate consideration of complex pre-stress distribution Journal of Low Frequency Noise, Vibration and Active Control |
| title | Vibration approximate analytical solutions of circular plate consideration of complex pre-stress distribution |
| title_full | Vibration approximate analytical solutions of circular plate consideration of complex pre-stress distribution |
| title_fullStr | Vibration approximate analytical solutions of circular plate consideration of complex pre-stress distribution |
| title_full_unstemmed | Vibration approximate analytical solutions of circular plate consideration of complex pre-stress distribution |
| title_short | Vibration approximate analytical solutions of circular plate consideration of complex pre-stress distribution |
| title_sort | vibration approximate analytical solutions of circular plate consideration of complex pre stress distribution |
| url | https://doi.org/10.1177/1461348419852456 |
| work_keys_str_mv | AT chenluyun vibrationapproximateanalyticalsolutionsofcircularplateconsiderationofcomplexprestressdistribution AT yihong vibrationapproximateanalyticalsolutionsofcircularplateconsiderationofcomplexprestressdistribution |