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

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Abstract

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.

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Acknowledgments

The support from the Natural Science Foundation of China (Grant 90816025, 11072047), the Major Project of Chinese National Programs for Fundamental Research and Development (Grant 2010CB832703) and National High-tech R&D Program of China (Grant 2009AA044501) is gratefully acknowledged.

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024, China

    Zhan Kang, Xiaopeng Zhang, Shigang Jiang & Gengdong Cheng

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  1. Zhan Kang
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  2. Xiaopeng Zhang
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  3. Shigang Jiang
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  4. Gengdong Cheng
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Correspondence to Zhan Kang.

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Kang, Z., Zhang, X., Jiang, S. et al. On topology optimization of damping layer in shell structures under harmonic excitations. Struct Multidisc Optim 46, 51–67 (2012). https://doi.org/10.1007/s00158-011-0746-4

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  • DOI: https://doi.org/10.1007/s00158-011-0746-4

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