The Efficiency of the Rayleigh-Ritz Method Applied to In-Plane Vibrations of Circular Arches Elastically Restrained against Rotation at the Two Ends
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International Journal of Engineering Trends and Technology (IJETT) |  |
| © 2021 by IJETT Journal | ||
| Volume-69 Issue-2 |
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| Year of Publication : 2021 | ||
| Authors : Ahmed. Babahammou, Rhali. Benamar |
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| DOI : 10.14445/22315381/IJETT-V69I2P207 |
Citation
MLA Style: Ahmed. Babahammou, Rhali. Benamar "The Efficiency of the Rayleigh-Ritz Method Applied to In-Plane Vibrations of Circular Arches Elastically Restrained against Rotation at the Two Ends" International Journal of Engineering Trends and Technology 69.2(2021):42-52.
APA Style:Ahmed. Babahammou, Rhali. Benamar. The Efficiency of the Rayleigh-Ritz Method Applied to In-Plane Vibrations of Circular Arches Elastically Restrained against Rotation at the Two Ends. International Journal of Engineering Trends and Technology, 69(2),42-52.
Abstract
The natural frequencies and mode shapes of in-plane vibration of thin circular arches elastically restrained against rotation at their ends are determined using the Rayleigh-Ritz method; the trial functions obtained is taken as particular solutions of the sixth order differential equation of arch vibrations corresponding to an opening angle equal to 1 rad. The arch axis is assumed to be inextensible, and the dimensions of the cross-section are supposed constant and small in comparison with the radius. The first frequency parameters of arches with different opening angles and torsional spring stiffnesses are determined and shown to compare well with the available literature. The effect of the rotational stiffness on the frequency parameter and mode shapes are determined and illustrated in the joint plots. The accuracy and relative simplicity of the RRM applied in a systematic way to such complicated problems is established, making it ready to use in more complex situations, such as those of arches with one or more added masses, with non-uniform cross-section, with variable radius or with point supports
Reference
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Keywords
In-plane linear vibration, circular arches, Rayleigh-Ritz method, elastically restrained, frequency parameters, mode shapes.