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Application of the Liouville–Green transformation to free vibrations of non-homogeneous rectangular membranes

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Abstract

We use the Liouville-Green transformation to derive a new approximate solution to Liouville’s problem. This approximate solution is then applied to the eigenvalue problem of free vibrations of non-homogeneous rectangular membranes. The examples show that the fundamental natural frequencies obtained in this work are in good agreement with those of previous studies. The main advantage of our method is that it is simple, easy to implement.

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Authors and Affiliations

  1. School of Civil Engineering, Hunan University of Science and Technology, Xiangtan, Hunan, 411201, People’s Republic of China

    Hui Hu, Yuan-Jun Guo & Da-Qing Xu

Authors
  1. Hui Hu
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  2. Yuan-Jun Guo
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  3. Da-Qing Xu
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Correspondence to Hui Hu.

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Hu, H., Guo, YJ. & Xu, DQ. Application of the Liouville–Green transformation to free vibrations of non-homogeneous rectangular membranes. Arch Appl Mech 84, 999–1006 (2014). https://doi.org/10.1007/s00419-014-0844-z

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  • DOI: https://doi.org/10.1007/s00419-014-0844-z

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