Free Transverse Vibration of Orthotropic Thin Trapezoidal Plate of Parabolically Varying Thickness Subjected to Linear Temperature Distribution
The present paper deals with the free transverse vibration of orthotropic thin trapezoidal plate of parabolically varying thickness in x-direction subjected to linear temperature distribution in x-direction through a numerical method. The deflection function is defined by the product of the equation...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2014/392325 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832559052537724928 |
|---|---|
| author | Arun Kumar Gupta Shanu Sharma |
| author_facet | Arun Kumar Gupta Shanu Sharma |
| author_sort | Arun Kumar Gupta |
| collection | DOAJ |
| description | The present paper deals with the free transverse vibration of orthotropic thin trapezoidal plate of parabolically varying thickness in x-direction subjected to linear temperature distribution in x-direction through a numerical method. The deflection function is defined by the product of the equations of the prescribed continuous piecewise boundary shape. Rayleigh-Ritz method is used to evaluate the fundamental frequencies. The equations of motion, governing the free transverse vibrations of orthotropic thin trapezoidal plates, are derived with boundary condition CSCS. Frequency corresponding to the first two modes of vibration is calculated for the orthotropic thin trapezoidal plate having CSCS edges for different values of thermal gradient, taper constant, and aspect ratio. The proposed method is applied to solve orthotropic thin trapezoidal plate of variable thickness with C-S-C-S boundary conditions. Results are shown by figures for different values of thermal gradient, taper constant, and aspect ratio for the first two modes of vibrations. |
| format | Article |
| id | doaj-art-0ea528d9d1114f5e8383f63be1d51ed0 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-0ea528d9d1114f5e8383f63be1d51ed02025-02-03T01:30:49ZengWileyShock and Vibration1070-96221875-92032014-01-01201410.1155/2014/392325392325Free Transverse Vibration of Orthotropic Thin Trapezoidal Plate of Parabolically Varying Thickness Subjected to Linear Temperature DistributionArun Kumar Gupta0Shanu Sharma1Department of Mathematics, M.S. College, Saharanpur 247001, IndiaDepartment of Mathematics, M.S. College, Saharanpur 247001, IndiaThe present paper deals with the free transverse vibration of orthotropic thin trapezoidal plate of parabolically varying thickness in x-direction subjected to linear temperature distribution in x-direction through a numerical method. The deflection function is defined by the product of the equations of the prescribed continuous piecewise boundary shape. Rayleigh-Ritz method is used to evaluate the fundamental frequencies. The equations of motion, governing the free transverse vibrations of orthotropic thin trapezoidal plates, are derived with boundary condition CSCS. Frequency corresponding to the first two modes of vibration is calculated for the orthotropic thin trapezoidal plate having CSCS edges for different values of thermal gradient, taper constant, and aspect ratio. The proposed method is applied to solve orthotropic thin trapezoidal plate of variable thickness with C-S-C-S boundary conditions. Results are shown by figures for different values of thermal gradient, taper constant, and aspect ratio for the first two modes of vibrations.http://dx.doi.org/10.1155/2014/392325 |
| spellingShingle | Arun Kumar Gupta Shanu Sharma Free Transverse Vibration of Orthotropic Thin Trapezoidal Plate of Parabolically Varying Thickness Subjected to Linear Temperature Distribution Shock and Vibration |
| title | Free Transverse Vibration of Orthotropic Thin Trapezoidal Plate of Parabolically Varying Thickness Subjected to Linear Temperature Distribution |
| title_full | Free Transverse Vibration of Orthotropic Thin Trapezoidal Plate of Parabolically Varying Thickness Subjected to Linear Temperature Distribution |
| title_fullStr | Free Transverse Vibration of Orthotropic Thin Trapezoidal Plate of Parabolically Varying Thickness Subjected to Linear Temperature Distribution |
| title_full_unstemmed | Free Transverse Vibration of Orthotropic Thin Trapezoidal Plate of Parabolically Varying Thickness Subjected to Linear Temperature Distribution |
| title_short | Free Transverse Vibration of Orthotropic Thin Trapezoidal Plate of Parabolically Varying Thickness Subjected to Linear Temperature Distribution |
| title_sort | free transverse vibration of orthotropic thin trapezoidal plate of parabolically varying thickness subjected to linear temperature distribution |
| url | http://dx.doi.org/10.1155/2014/392325 |
| work_keys_str_mv | AT arunkumargupta freetransversevibrationoforthotropicthintrapezoidalplateofparabolicallyvaryingthicknesssubjectedtolineartemperaturedistribution AT shanusharma freetransversevibrationoforthotropicthintrapezoidalplateofparabolicallyvaryingthicknesssubjectedtolineartemperaturedistribution |