International Applied Mechanics

, Volume 54, Issue 1, pp 104–119 | Cite as

Geometric Nonlinear Vibration Analysis for Pretensioned Rectangular Orthotropic Membrane

  • C. J. Liu
  • Z. L. Zheng
  • X. Y. Yang
  • J. J. Guo

The geometric nonlinear vibrations of pretensioned orthotropic membrane with four edges fixed, which is commonly applied in building membrane structure, are studied. The nonlinear partial differential governing equations are derived by von Kármán’s large deflection theory and D’Alembert’s principle. Because of the strong nonlinearity of governing equations, the homotopy perturbation method (HPM) to solve them is applied. The approximate analytical solution of the vibration frequency and displacement function is obtained. In the computational example, the frequency, vibration mode and displacement as well as the time curve of each feature point are analyzed. It is proved that HPM is an effective, simple and high-precision method to solve the geometric nonlinear vibration problem of membrane structures. These results provide some valuable computational basis for the vibration control and dynamic design of building and other analogous membrane structures.


nonlinear vibration orthotropic membrane perturbation method 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • C. J. Liu
    • 1
    • 2
  • Z. L. Zheng
    • 3
  • X. Y. Yang
    • 4
  • J. J. Guo
    • 5
  1. 1.State Key Laboratory of Geohazard Prevention and Geoenvironment ProtectionChengdu University of TechnologyChengduChina
  2. 2.College of Environment and Civil EngineeringChengdu University of TechnologyChengduChina
  3. 3.College of Civil EngineeringChongqing UniversityChongqingChina
  4. 4.College of nuclear technology and automation EngineeringChengdu University of TechnologyChengduChina
  5. 5.Chongqing Water Resources and Electric Engineering CollegeChongqingChina

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