Publisher : The Korean Society of Mechanical Engineers
DOI : 10.3795/KSME-A.2016.40.4.363
Title & Authors
Topology Optimization of a Vibrating System of Rigid and Flexible Bodies for Maximizing Repeated Eigenfrequencies Ahn, Byungseong; Kim, Suh In; Kim, Yoon Young;
When a system consisting of rigid and flexible bodies is optimized to improve its dynamic characteristics, its eigenfrequencies are typically maximized. While topology optimization formulations dealing with simultaneous design of a system of rigid and flexible bodies are available, studies on eigenvalue maximization of the system are rare. In particular, no work has solved for the case when the target frequency becomes one of the repeated eigenfrequencies. The problem involving repeated eigenfrequencies is solved in this study, and a topology optimization formulation and sensitivity analysis are presented. Further, several numerical case studies are considered to demonstrate the validity of the proposed formulation.
Topology Optimization;System of Rigid and Flexible Bodies;Repeated Eigenvalues;
Bendsoe, M. P. and Kikuchi, N., 1988, "Generating Optimal Topologies in Structural Design Using a Homogenization Method," Comput. Meth. Appl. Mech. Engng., Vol. 71, pp. 197-224.
Bendsoe, M. P. and Sigmund, O., 2003, Topology Optimization Theory, Methods and Applications. Springer-Verlag, New York.
Qian, Z. Y. and Ananthasuresh, G. K., 2004., "Optimal Embedding of Rigid Objects in the Topology Design of Structures," Mechanics Based Design of Structures and Machines, Vol. 32, pp. 165-193.
Zhu, J. H., Zhang, W. H. and Beckers P., 2009, "Integrated Layout Design of Multi-component System," Int. J. Numer Methods Eng, Vol. 78, No. 6, pp. 631-651.
Wei, P., Ma, H. and Wang, M. Y., 2014, "The Stiffness Spreading Method for Layout Optimization of Truss Structures," Struct. Multidisc. Optim., Vol. 49, pp. 667-682.
Wei, P., Shi, J. and Ma, H., 2012, "Integrated Layout Optimization Design of Multi-Component Systems Based on the Stiffness Spreading Method," In Proc. Of 7th China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems, Huangshan, China.
Seyranian, A. P., Lund, E. and Olhoff, N., 1994, "Multiple Eigenvalues in Structural Optimization Problems," Structural Optimization, Vol. 8, pp. 207-227.
Du, J. and Olhoff, N., 2007, "Topological Design of Freely Vibrating Continuum Structures for Maximum Values of Simple and Multiple Eigen Frequencies and Frequency Gaps," Struct Multidisc Optim, Vol. 34, pp. 91-110.
Pedersen, N. L., 2000, "Maximization of Eigenvalues Using Topology Optimization," Struct Multidisc Optim, Vol. 20, pp. 2-11.
Kim, T. S. and Kim, Y. Y., 2000, "Mac-based mode-tracking in Structural Topology Optimization," Computers & Structures, Vol. 74, pp. 375-383.