Geometric Nonlinear Vibration Analysis for Pretensioned Rectangular Orthotropic Membrane

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....

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Veröffentlicht in:International applied mechanics Jg. 54; H. 1; S. 104 - 119
Hauptverfasser: Liu, C. J., Zheng, Z. L., Yang, X. Y., Guo, J. J.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.01.2018
Springer
Springer Nature B.V
Schlagworte:
Analysis
Applications of Mathematics
Classical Mechanics
Computation
Differential equations
Mathematical analysis
Membrane structures
Nonlinear analysis
Nonlinear equations
Nonlinear programming
Nonlinearity
Perturbation methods
Physics
Physics and Astronomy
Vibration
Vibration (Physics)
Vibration analysis
Vibration control
Vibration mode
membrane
nonlinear vibration
orthotropic
perturbation method
ISSN:1063-7095, 1573-8582
Online-Zugang:Volltext
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Zusammenfassung: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.
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ISSN:1063-7095
1573-8582
DOI:10.1007/s10778-018-0864-4