Numerical and experimental analysis of the vibration and band-gap properties of elastic beams with periodically variable cross sections |
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| Authors: | Fuchao Gao Chuanzeng Zhang |
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| Institution: | 1. College of Mechanical Engineering, Beijing University of Technology , Beijing, China;2. Department of Civil Engineering, University of Siegen , Siegen, Germany |
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| 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. |
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