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Shock and Vibration
Volume 2015 (2015), Article ID 376854, 11 pages
Research Article

Topology Optimization for Minimizing the Resonant Response of Plates with Constrained Layer Damping Treatment

State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China

Received 26 November 2014; Revised 1 March 2015; Accepted 6 March 2015

Academic Editor: Miguel Neves

Copyright © 2015 Zhanpeng Fang and Ling Zheng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A topology optimization method is proposed to minimize the resonant response of plates with constrained layer damping (CLD) treatment under specified broadband harmonic excitations. The topology optimization problem is formulated and the square of displacement resonant response in frequency domain at the specified point is considered as the objective function. Two sensitivity analysis methods are investigated and discussed. The derivative of modal damp ratio is not considered in the conventional sensitivity analysis method. An improved sensitivity analysis method considering the derivative of modal damp ratio is developed to improve the computational accuracy of the sensitivity. The evolutionary structural optimization (ESO) method is used to search the optimal layout of CLD material on plates. Numerical examples and experimental results show that the optimal layout of CLD treatment on the plate from the proposed topology optimization using the conventional sensitivity analysis or the improved sensitivity analysis can reduce the displacement resonant response. However, the optimization method using the improved sensitivity analysis can produce a higher modal damping ratio than that using the conventional sensitivity analysis and develop a smaller displacement resonant response.