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

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.

Graphical abstract

Keywords

review / dynamic / similitude / vibration / model test

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Acknowledgments

This work was supported by the National 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).

Conflict of Interest

The authors declare no conflict of interest, including specific financial interests and relationships relevant to the subject of this paper.

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