On topology optimization of damping layer in shell structures under harmonic excitations

This paper investigates the optimal distribution of damping material in vibrating structures subject to harmonic excitations by using topology optimization method. Therein, the design objective is to minimize the structural vibration level at specified positions by distributing a given amount of dam...

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Bibliographic Details
Published in:Structural and multidisciplinary optimization 2012-07, Vol.46 (1), p.51-67
Main Authors: Kang, Zhan, Zhang, Xiaopeng, Jiang, Shigang, Cheng, Gengdong
Format: Article
Language:English
Subjects:
Computational Mathematics and Numerical Analysis
Damping
Design optimization
Engineering
Engineering Design
Excitation
Mode superposition method
Research Paper
Sensitivity analysis
Structural vibration
Theoretical and Applied Mechanics
Topology optimization
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Summary:This paper investigates the optimal distribution of damping material in vibrating structures subject to harmonic excitations by using topology optimization method. Therein, the design objective is to minimize the structural vibration level at specified positions by distributing a given amount of damping material. An artificial damping material model that has a similar form as in the SIMP approach is suggested and the relative densities of the damping material are taken as design variables. The vibration equation of the structure has a non-proportional damping matrix. A system reduction procedure is first performed by using the eigenmodes of the undamped system. The complex mode superposition method in the state space, which can deal with the non-proportional damping, is then employed to calculate the steady-state response of the vibrating structure. In this context, an adjoint variable scheme for the response sensitivity analysis is developed. Numerical examples are presented for illustrating validity and efficiency of this approach. Impacts of the excitation frequency as well as the damping coefficients on topology optimization results are also discussed.
ISSN:1615-147X
1615-1488
DOI:10.1007/s00158-011-0746-4