Free-Form Optimization of Thin-Walled Structure for Frequency Response Problem
We present a node-based free-form optimization method for designing forms of thin-walled structures in order to control vibration displacements or mode at a prescribed frequency. A squared displacement error norm is introduced at the prescribed surface as the objective functional to control the vibr...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2015/471646 |
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| _version_ | 1832562075260420096 |
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| author | Masatoshi Shimoda Yang Liu |
| author_facet | Masatoshi Shimoda Yang Liu |
| author_sort | Masatoshi Shimoda |
| collection | DOAJ |
| description | We present a node-based free-form optimization method for designing forms of thin-walled structures in order to control vibration displacements or mode at a prescribed frequency. A squared displacement error norm is introduced at the prescribed surface as the objective functional to control the vibration displacements to target values in a frequency response problem. It is assumed that the thin-walled structure is varied in the normal direction to the surface and the thickness is constant. A nonparametric shape optimization problem is formulated, and the shape gradient function is theoretically derived using the material derivative method and the adjoint variable method. The shape gradient function obtained is applied to the surface of the thin-walled structure as a fictitious traction force to vary the form. With this free-form optimization method, an optimum thin-walled structure with a smooth free-form surface can be obtained without any shape parameterization. The calculated results show the effectiveness of the proposed method for the optimal free-form design of thin-walled structures with vibration mode control. |
| format | Article |
| id | doaj-art-bec049e0be9340659a888bf268d85897 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-bec049e0be9340659a888bf268d858972025-02-03T01:23:31ZengWileyShock and Vibration1070-96221875-92032015-01-01201510.1155/2015/471646471646Free-Form Optimization of Thin-Walled Structure for Frequency Response ProblemMasatoshi Shimoda0Yang Liu1Department of Advanced Science and Technology, Toyota Technological Institute, 2-12-1 Hisakata, Tenpaku-ku, Nagoya 468-8511, JapanDepartment of Mechanical Engineering, Sojo University, 4-22-1 Ikeda, Nishi-ku, Kumamoto 860-0082, JapanWe present a node-based free-form optimization method for designing forms of thin-walled structures in order to control vibration displacements or mode at a prescribed frequency. A squared displacement error norm is introduced at the prescribed surface as the objective functional to control the vibration displacements to target values in a frequency response problem. It is assumed that the thin-walled structure is varied in the normal direction to the surface and the thickness is constant. A nonparametric shape optimization problem is formulated, and the shape gradient function is theoretically derived using the material derivative method and the adjoint variable method. The shape gradient function obtained is applied to the surface of the thin-walled structure as a fictitious traction force to vary the form. With this free-form optimization method, an optimum thin-walled structure with a smooth free-form surface can be obtained without any shape parameterization. The calculated results show the effectiveness of the proposed method for the optimal free-form design of thin-walled structures with vibration mode control.http://dx.doi.org/10.1155/2015/471646 |
| spellingShingle | Masatoshi Shimoda Yang Liu Free-Form Optimization of Thin-Walled Structure for Frequency Response Problem Shock and Vibration |
| title | Free-Form Optimization of Thin-Walled Structure for Frequency Response Problem |
| title_full | Free-Form Optimization of Thin-Walled Structure for Frequency Response Problem |
| title_fullStr | Free-Form Optimization of Thin-Walled Structure for Frequency Response Problem |
| title_full_unstemmed | Free-Form Optimization of Thin-Walled Structure for Frequency Response Problem |
| title_short | Free-Form Optimization of Thin-Walled Structure for Frequency Response Problem |
| title_sort | free form optimization of thin walled structure for frequency response problem |
| url | http://dx.doi.org/10.1155/2015/471646 |
| work_keys_str_mv | AT masatoshishimoda freeformoptimizationofthinwalledstructureforfrequencyresponseproblem AT yangliu freeformoptimizationofthinwalledstructureforfrequencyresponseproblem |