Free Vibration Analysis of an Inflated Toroidal ShellSource: Journal of Vibration and Acoustics:;2002:;volume( 124 ):;issue: 003::page 387Author:Akhilesh K. Jha
,
Raymond H. Plaut
,
D. H. Pletta Professor
,
Daniel J. Inman
,
G. R. Goodson Professor and Director
DOI: 10.1115/1.1467650Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: Free vibration analysis of a free inflated torus of circular cross-section is presented. The shell theory of Sanders, including the effect of pressure, is used in formulating the governing equations. These partial differential equations are reduced to ordinary differential equations with variable coefficients using complete waves in the form of trigonometric functions in the longitudinal direction. The assumed mode shapes are divided into symmetric and antisymmetric groups, each given by a Fourier series in the meridional coordinate. The solutions (natural frequencies and mode shapes) are obtained using Galerkin’s method and verified with published results. The natural frequencies are also obtained for a circular cylinder with shear diaphragm boundary condition as a special case of the toroidal shell. Finally, the effects of aspect ratio, pressure, and thickness on the natural frequencies of the inflated torus are studied.
keyword(s): Equations , Free vibrations , Frequency , Shapes , Shells , Pressure , Stress , Boundary-value problems , Thickness , Functions , Waves AND Fourier series ,
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| contributor author | Akhilesh K. Jha | |
| contributor author | Raymond H. Plaut | |
| contributor author | D. H. Pletta Professor | |
| contributor author | Daniel J. Inman | |
| contributor author | G. R. Goodson Professor and Director | |
| date accessioned | 2017-05-09T00:09:06Z | |
| date available | 2017-05-09T00:09:06Z | |
| date copyright | July, 2002 | |
| date issued | 2002 | |
| identifier issn | 1048-9002 | |
| identifier other | JVACEK-28862#387_1.pdf | |
| identifier uri | http://yetl.yabesh.ir/yetl/handle/yetl/127704 | |
| description abstract | Free vibration analysis of a free inflated torus of circular cross-section is presented. The shell theory of Sanders, including the effect of pressure, is used in formulating the governing equations. These partial differential equations are reduced to ordinary differential equations with variable coefficients using complete waves in the form of trigonometric functions in the longitudinal direction. The assumed mode shapes are divided into symmetric and antisymmetric groups, each given by a Fourier series in the meridional coordinate. The solutions (natural frequencies and mode shapes) are obtained using Galerkin’s method and verified with published results. The natural frequencies are also obtained for a circular cylinder with shear diaphragm boundary condition as a special case of the toroidal shell. Finally, the effects of aspect ratio, pressure, and thickness on the natural frequencies of the inflated torus are studied. | |
| publisher | The American Society of Mechanical Engineers (ASME) | |
| title | Free Vibration Analysis of an Inflated Toroidal Shell | |
| type | Journal Paper | |
| journal volume | 124 | |
| journal issue | 3 | |
| journal title | Journal of Vibration and Acoustics | |
| identifier doi | 10.1115/1.1467650 | |
| journal fristpage | 387 | |
| journal lastpage | 396 | |
| identifier eissn | 1528-8927 | |
| keywords | Equations | |
| keywords | Free vibrations | |
| keywords | Frequency | |
| keywords | Shapes | |
| keywords | Shells | |
| keywords | Pressure | |
| keywords | Stress | |
| keywords | Boundary-value problems | |
| keywords | Thickness | |
| keywords | Functions | |
| keywords | Waves AND Fourier series | |
| tree | Journal of Vibration and Acoustics:;2002:;volume( 124 ):;issue: 003 | |
| contenttype | Fulltext |