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Improved Homotopy Perturbation Solution for Nonlinear Transverse Vibration of Orthotropic Membrane

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Abstract

Objective

Due to its characteristics of being light and flexible, membrane has been widely used in long-span stadiums and other buildings. However, under the effect of external loads, it will produce relatively large deformation. Therefore, the large deflection vibration of membrane has been of concern to researchers.

Methods

To obtain the efficient and accurate solution of the nonlinear vibration problem of membrane, the governing equations of strongly nonlinear vibration of orthotropic membrane structures are derived based on the Von Karman large deflection theory and Galerkin method, then its analytical solution is gained by employing the homotopy perturbation method and the improved homotopy perturbation method, respectively.

Results

The vibration characteristics of strongly nonlinear vibration of orthotropic membranes under displacement excitation were investigated, in which parameters considered in the analysis were vibration amplitude, thickness, surface density, and geometric.

Conclusion

In addition, the results are compared with those obtained by the existing methods, which shows that the improved homotopy perturbation method is more accurate and suitable than the studied methods, and has good application ability in the strong nonlinear vibration of orthotropic 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 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

    Yafei. Zhang, Weiju. Song, Huimin. Yin & Jinsheng Ma

Authors
  1. Yafei. Zhang
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  2. Weiju. Song
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  3. Huimin. Yin
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  4. Jinsheng Ma
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Correspondence to Weiju. Song.

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Zhang, Y., Song, W., Yin, H. et al. Improved Homotopy Perturbation Solution for Nonlinear Transverse Vibration of Orthotropic Membrane. J. Vib. Eng. Technol. 10, 995–1005 (2022). https://doi.org/10.1007/s42417-021-00424-5

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  • DOI: https://doi.org/10.1007/s42417-021-00424-5

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