Vibration of Clamped Visco-Elastic Rectangular Plate with Parabolic Thickness Variations
Most of the machines and engineering structures experience vibration and their design generally requires consideration for their dynamic behavior. Due to this, the study of vibration, as it deals with the vibratory behavior of bodies, is acquiring increasingly importance in several engineering appli...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2008/873049 |
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| author | A.K. Gupta Anupam Khanna |
| author_facet | A.K. Gupta Anupam Khanna |
| author_sort | A.K. Gupta |
| collection | DOAJ |
| description | Most of the machines and engineering structures experience vibration and their design generally requires consideration for their dynamic behavior. Due to this, the study of vibration, as it deals with the vibratory behavior of bodies, is acquiring increasingly importance in several engineering applications, nuclear reactor technology and aeronautical field etc. Most of the work has been done in the field of elastic and non-elastic behavior of the bodies but a very little work is done in the field of visco-elastic bodies with varying thickness. The analysis presented here is to study the effect of taper constants on free vibration of a clamped visco-elastic rectangular plate with parabolically varying thickness. The two-dimensional thickness variation is taken as the Cartesian product of parabolic variations along the two concurrent edges of the plate. Using Rayleigh-Ritz method, frequency equation derives. Logarithmic decrement, time period and deflection for the first two modes of vibration are calculated for various values of taper constants and aspect ratio. |
| format | Article |
| id | doaj-art-f6dfa81aeb3f47c880093feb36e6f74c |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-f6dfa81aeb3f47c880093feb36e6f74c2025-02-03T00:59:30ZengWileyShock and Vibration1070-96221875-92032008-01-0115671372310.1155/2008/873049Vibration of Clamped Visco-Elastic Rectangular Plate with Parabolic Thickness VariationsA.K. Gupta0Anupam Khanna1Department of Mathematics, M.S. College, Saharanpur, Pin-247001, (U. P.), IndiaMathematics Department, S.I.E.T. Gangoh, Saharanpur, Pin-247001, (U. P.), IndiaMost of the machines and engineering structures experience vibration and their design generally requires consideration for their dynamic behavior. Due to this, the study of vibration, as it deals with the vibratory behavior of bodies, is acquiring increasingly importance in several engineering applications, nuclear reactor technology and aeronautical field etc. Most of the work has been done in the field of elastic and non-elastic behavior of the bodies but a very little work is done in the field of visco-elastic bodies with varying thickness. The analysis presented here is to study the effect of taper constants on free vibration of a clamped visco-elastic rectangular plate with parabolically varying thickness. The two-dimensional thickness variation is taken as the Cartesian product of parabolic variations along the two concurrent edges of the plate. Using Rayleigh-Ritz method, frequency equation derives. Logarithmic decrement, time period and deflection for the first two modes of vibration are calculated for various values of taper constants and aspect ratio.http://dx.doi.org/10.1155/2008/873049 |
| spellingShingle | A.K. Gupta Anupam Khanna Vibration of Clamped Visco-Elastic Rectangular Plate with Parabolic Thickness Variations Shock and Vibration |
| title | Vibration of Clamped Visco-Elastic Rectangular Plate with Parabolic Thickness Variations |
| title_full | Vibration of Clamped Visco-Elastic Rectangular Plate with Parabolic Thickness Variations |
| title_fullStr | Vibration of Clamped Visco-Elastic Rectangular Plate with Parabolic Thickness Variations |
| title_full_unstemmed | Vibration of Clamped Visco-Elastic Rectangular Plate with Parabolic Thickness Variations |
| title_short | Vibration of Clamped Visco-Elastic Rectangular Plate with Parabolic Thickness Variations |
| title_sort | vibration of clamped visco elastic rectangular plate with parabolic thickness variations |
| url | http://dx.doi.org/10.1155/2008/873049 |
| work_keys_str_mv | AT akgupta vibrationofclampedviscoelasticrectangularplatewithparabolicthicknessvariations AT anupamkhanna vibrationofclampedviscoelasticrectangularplatewithparabolicthicknessvariations |