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Articles

Numerical and experimental analysis of the vibration and band-gap properties of elastic beams with periodically variable cross sections

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Pages 299-316 | Received 04 Jul 2017, Accepted 16 Jan 2018, Published online: 01 Feb 2018
 

ABSTRACT

The band-gap properties of non-uniform periodic beams are analyzed using numerical and experimental methods. The flexural wave equations are established based on the Euler–Bernoulli and Timoshenko beam theories. The beams with periodically variable cross sections are investigated. The transfer matrix method is used to explore the dynamic behaviors of the periodic beams, that is, the natural frequencies of the finite periodic beams with different cross-section ratios between the adjacent sub-cells and the band-gaps of the infinite periodic beams based on the Bloch theory. The validity and accuracy of the band-gaps acquired by the present method are verified by comparing the results with those obtained from the finite element method and the vibration experiments. The effects of the different lengths of adjacent sub-cells on the band-gap properties are then investigated. The research results and conclusions should be useful in the study of vibration control applications.

Acknowledgments

Fengming Li is grateful to the financial support by the Alexander von Humboldt Foundation for his scientific visit at the Chair of Structural Mechanics, University of Siegen, Germany.

Additional information

Funding

This research is supported by the Key Laboratory of Vibration and Control of Aero-Propulsion System Ministry of Education, Northeastern University [grant number VCAME201703], the National Natural Science Foundation of China [grant numbers 11761131006, 11602065 and 11572007] and the Fundamental Research Funds for the Central Universities [grant numbers HEUCFJ170203 and HEUCFM170201]. Fengming Li is supported by the Alexander von Humboldt Foundation.

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