Topology Optimization of Constrained Layer Damping on Plates Using Method of Moving Asymptote (MMA) Approach
Damping treatments have been extensively used as a powerful means to damp out structural resonant vibrations. Usually, damping materials are fully covered on the surface of plates. The drawbacks of this conventional treatment are also obvious due to an added mass and excess material consumption. The...
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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-2010-0583 |
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| author | Zheng Ling Xie Ronglu Wang Yi Adel El-Sabbagh |
| author_facet | Zheng Ling Xie Ronglu Wang Yi Adel El-Sabbagh |
| author_sort | Zheng Ling |
| collection | DOAJ |
| description | Damping treatments have been extensively used as a powerful means to damp out structural resonant vibrations. Usually, damping materials are fully covered on the surface of plates. The drawbacks of this conventional treatment are also obvious due to an added mass and excess material consumption. Therefore, it is not always economical and effective from an optimization design view. In this paper, a topology optimization approach is presented to maximize the modal damping ratio of the plate with constrained layer damping treatment. The governing equation of motion of the plate is derived on the basis of energy approach. A finite element model to describe dynamic performances of the plate is developed and used along with an optimization algorithm in order to determine the optimal topologies of constrained layer damping layout on the plate. The damping of visco-elastic layer is modeled by the complex modulus formula. Considering the vibration and energy dissipation mode of the plate with constrained layer damping treatment, damping material density and volume factor are considered as design variable and constraint respectively. Meantime, the modal damping ratio of the plate is assigned as the objective function in the topology optimization approach. The sensitivity of modal damping ratio to design variable is further derived and Method of Moving Asymptote (MMA) is adopted to search the optimized topologies of constrained layer damping layout on the plate. Numerical examples are used to demonstrate the effectiveness of the proposed topology optimization approach. The results show that vibration energy dissipation of the plates can be enhanced by the optimal constrained layer damping layout. This optimal technology can be further extended to vibration attenuation of sandwich cylindrical shells which constitute the major building block of many critical structures such as cabins of aircrafts, hulls of submarines and bodies of rockets and missiles as an invaluable design tool. |
| format | Article |
| id | doaj-art-c8c4cbdb03634c3992a37f67921e6c86 |
| 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-c8c4cbdb03634c3992a37f67921e6c862025-08-20T03:24:08ZengWileyShock and Vibration1070-96221875-92032011-01-01181-222124410.3233/SAV-2010-0583Topology Optimization of Constrained Layer Damping on Plates Using Method of Moving Asymptote (MMA) ApproachZheng Ling0Xie Ronglu1Wang Yi2Adel El-Sabbagh3State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, ChinaState Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, ChinaState Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, ChinaDesign and Production Engineering Department, Faculty of Engineering, Ain Shams University, Cairo, EgyptDamping treatments have been extensively used as a powerful means to damp out structural resonant vibrations. Usually, damping materials are fully covered on the surface of plates. The drawbacks of this conventional treatment are also obvious due to an added mass and excess material consumption. Therefore, it is not always economical and effective from an optimization design view. In this paper, a topology optimization approach is presented to maximize the modal damping ratio of the plate with constrained layer damping treatment. The governing equation of motion of the plate is derived on the basis of energy approach. A finite element model to describe dynamic performances of the plate is developed and used along with an optimization algorithm in order to determine the optimal topologies of constrained layer damping layout on the plate. The damping of visco-elastic layer is modeled by the complex modulus formula. Considering the vibration and energy dissipation mode of the plate with constrained layer damping treatment, damping material density and volume factor are considered as design variable and constraint respectively. Meantime, the modal damping ratio of the plate is assigned as the objective function in the topology optimization approach. The sensitivity of modal damping ratio to design variable is further derived and Method of Moving Asymptote (MMA) is adopted to search the optimized topologies of constrained layer damping layout on the plate. Numerical examples are used to demonstrate the effectiveness of the proposed topology optimization approach. The results show that vibration energy dissipation of the plates can be enhanced by the optimal constrained layer damping layout. This optimal technology can be further extended to vibration attenuation of sandwich cylindrical shells which constitute the major building block of many critical structures such as cabins of aircrafts, hulls of submarines and bodies of rockets and missiles as an invaluable design tool.http://dx.doi.org/10.3233/SAV-2010-0583 |
| spellingShingle | Zheng Ling Xie Ronglu Wang Yi Adel El-Sabbagh Topology Optimization of Constrained Layer Damping on Plates Using Method of Moving Asymptote (MMA) Approach Shock and Vibration |
| title | Topology Optimization of Constrained Layer Damping on Plates Using Method of Moving Asymptote (MMA) Approach |
| title_full | Topology Optimization of Constrained Layer Damping on Plates Using Method of Moving Asymptote (MMA) Approach |
| title_fullStr | Topology Optimization of Constrained Layer Damping on Plates Using Method of Moving Asymptote (MMA) Approach |
| title_full_unstemmed | Topology Optimization of Constrained Layer Damping on Plates Using Method of Moving Asymptote (MMA) Approach |
| title_short | Topology Optimization of Constrained Layer Damping on Plates Using Method of Moving Asymptote (MMA) Approach |
| title_sort | topology optimization of constrained layer damping on plates using method of moving asymptote mma approach |
| url | http://dx.doi.org/10.3233/SAV-2010-0583 |
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