Abstract
This paper investigates topology optimization of the electrode coverage over piezoelectric patches attached to a thin-shell structure to reduce the energy consumption of active vibration control under harmonic excitations. The constant gain velocity feedback control method is employed, and the structural frequency response under control is analyzed with the finite element method. In the mathematical formulation of the proposed topology optimization model, the total energy consumption of the control system is taken as the objective function, and a constraint of the maximum allowable dynamic compliance is considered. The pseudo-densities indicating the distribution of surface electrode coverage over the piezoelectric layers are chosen as the design variables, and a penalized model is employed to relate the active dam** effect and these design variables. The sensitivity analysis scheme of the control energy consumption with respect to the design variables is derived with the adjoint-variable method. Numerical examples demonstrate that the proposed optimization model is able to generate optimal topologies of electrode coverage over the piezoelectric layers, which can effectively reduce the energy consumption of the control system. Also, numerical comparisons with a minimum-volume optimization model show the advantage of the proposed method with respect to energy consumption. The proposed method may provide useful guidance to the layout optimization of piezoelectric smart structures where the energy supply is limited, such as miniature vibration control systems.
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Acknowledgements
The authors would like to thank Prof. Krister Svanberg for providing the source code of the GCMMA algorithm. The authors also acknowledge the support of the Natural Science Foundation of China (11602049, 11425207, and U1608256), China Postdoctoral Science Foundation (2015 M581328), and Research Project of State Key Laboratory of Mechanical System and Vibration (MSV201603).
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Zhang, X., Takezawa, A. & Kang, Z. Topology optimization of piezoelectric smart structures for minimum energy consumption under active control. Struct Multidisc Optim 58, 185–199 (2018). https://doi.org/10.1007/s00158-017-1886-y
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DOI: https://doi.org/10.1007/s00158-017-1886-y