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Strongly Nonlinear Damped Vibration of Orthotropic Membrane under Initial Displacement: Theory and Experiment

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Abstract

Introduction

Due to the small weight and large flexibility, membrane structures are prone to vibration under external excitation. Furthermore, it may affect the normal function of membrane structures.

Objectives

In view of the limitation of traditional perturbation method and small deflection theory in solving strongly nonlinear vibration problem of membranes. an improved multi-scale method is proposed in this paper to investigate the characteristics of strongly nonlinear vibration of membrane.

Methods

Firstly, based on the large deflection theory of membrane and the improved multi-scale method, the strongly nonlinear damped vibration control equation of membrane with consideration of geometrical non-linearity is solved. Then, the analytical expressions of the frequency and displacement functions of the strongly nonlinear vibration of membranes are obtained, which are compared with the numerical results. Furthermore, the vibration characteristics of the membrane under the initial displacement are explained together with the experimental results.

Results and Conclusion

The results show that the improved multi-scale method is more suitable for solving the strongly nonlinear vibration of membranes than the traditional perturbation method, since the accuracy is higher. Therefore, such a discovery exhibit exposes a more accurate theoretical method for the vibration control and design of membranes.

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Data availability

The data used to support the findings of this study are available from the corresponding author upon request.

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Funding

This research was funded by the National Natural Science Foundation of China (Grant No. 51608060), Natural Science Foundation of Hebei Province of China (Grant No. E2020402061) and the Innovation Foundation of Hebei University of Engineering (Grant No. SJ010002159).

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Authors and Affiliations

  1. School of Civil Engineering, Hebei University of Engineering, Handan, 056038, China

    Weiju Song, Yafei Zhang & Huimin Yin

  2. School of Road, Bridge and Architecture, Chongqing Vocational College of Transportation, Chongqing, 402247, China

    Lingling Du

  3. School of Civil Engineering, Guangzhou University, Guangzhou, 510006, China

    Changjiang Liu

Authors
  1. Weiju Song
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  2. Lingling Du
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  3. Yafei Zhang
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  4. Huimin Yin
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  5. Changjiang Liu
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Correspondence to Weiju Song.

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Song, W., Du, L., Zhang, Y. et al. Strongly Nonlinear Damped Vibration of Orthotropic Membrane under Initial Displacement: Theory and Experiment. J. Vib. Eng. Technol. 9, 1359–1372 (2021). https://doi.org/10.1007/s42417-021-00302-0

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  • DOI: https://doi.org/10.1007/s42417-021-00302-0

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