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Similitude design for the vibration problems of plates and shells: A review

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Abstract

Similitude design plays a vital role in the analysis of vibration and shock problems encountered in large engineering equipment. Similitude design, including dimensional analysis and governing equation method, is founded on the dynamic similitude theory. This study reviews the application of similitude design methods in engineering practice and summarizes the major achievements of the dynamic similitude theory in structural vibration and shock problems in different fields, including marine structures, civil engineering structures, and large power equipment. This study also reviews the dynamic similitude design methods for thin-walled and composite material plates and shells, including the most recent work published by the authors. Structure sensitivity analysis is used to evaluate the scaling factors to attain accurate distorted scaling laws. Finally, this study discusses the existing problems and the potential of the dynamic similitude theory for the analysis of vibration and shock problems of structures.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11572082), the Excellent Talents Support Program in Institutions of Higher Learning in Liaoning Province of China (Grant No. LJQ2015038), the Fundamental Research Funds for the Central Universities of China (Grant Nos. N150304004 and N140301001), and the Key Laboratory for Precision & Non-traditional Machining of Ministry of Education, Dalian University of Technology (Grant No. JMTZ201602).

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Authors and Affiliations

  1. Department of Automatic Control and System Engineering, Sheffield University, Sheffield, S13JD, UK

    Yunpeng Zhu

  2. School of Mechanical Engineering and Automation, Northeastern University, Shenyang, 110819, China

    You Wang & Zhong Luo

  3. School of Mechanical Engineering, Dalian University of Technology, Dalian, 116023, China

    Qingkai Han

  4. AECC Shenyang Aero-engine Institute, Shenyang, 110042, China

    Deyou Wang

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  1. Yunpeng Zhu
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  2. You Wang
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  3. Zhong Luo
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  4. Qingkai Han
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  5. Deyou Wang
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Correspondence to Zhong Luo.

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Zhu, Y., Wang, Y., Luo, Z. et al. Similitude design for the vibration problems of plates and shells: A review. Front. Mech. Eng. 12, 253–264 (2017). https://doi.org/10.1007/s11465-017-0418-1

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