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Free vibration analysis of multi-span Timoshenko beams using the assumed mode method

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Abstract

Although some investigations on the vibration properties of multi-span beams have been conducted, studies on multi-span Timoshenko beams by using the assumed mode method have been relatively few. In this paper, the multi-span Timoshenko beams are investigated, and the mode shapes of the beams are modified by the interpolation functions to model the vibration modes of the multi-span beams. Hamilton’s principle is applied to establish the equation of motion of the structure, and the natural circular frequencies and the free vibration responses of the multi-span beams are obtained. The numerical results demonstrate good agreement between the present results and those from the open literature and the ANSYS software. The influences of the length–thickness ratio, the disorder degree and the span number on the free vibration of the structure are also analyzed. It is observed that the displacement amplitude and the vibration period at the midpoint of the three-span Timoshenko beams are reduced when the disorder degree and the length–thickness ratio are reduced. The increase in the span number of the multi-span beams with equal spans leads to the decrease in the displacement amplitude and the period of the structures. Furthermore, some interesting phenomena are found, e.g., the same even-order frequencies of different three-span beams are equal under specific disorder degree.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant Nos. 11761131006 and 11572007. Fengming Li is also 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.

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Authors and Affiliations

  1. College of Mechanical Engineering, Beijing University of Technology, Beijing, 100124, China

    Zhao Zhao & Fengming Li

  2. College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin, 150001, China

    Shurui Wen & Fengming Li

  3. Department of Civil Engineering, University of Siegen, 57068, Siegen, Germany

    Fengming Li & Chuanzeng Zhang

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  1. Zhao Zhao
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  2. Shurui Wen
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Correspondence to Shurui Wen or Fengming Li.

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Zhao, Z., Wen, S., Li, F. et al. Free vibration analysis of multi-span Timoshenko beams using the assumed mode method. Arch Appl Mech 88, 1213–1228 (2018). https://doi.org/10.1007/s00419-018-1368-8

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