An Analytical Approach on Thermally Induced Vibrations of Nonhomogeneous Tapered Plate
A mathematical model to control the vibrations of a rectangular plate is constructed with an aim to assist engineers in designing and fabrication of various structures used in the field of science and technology, mostly used in satellite and aeronautical engineering. The present study is related to...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/721868 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832555515649982464 |
|---|---|
| author | Anupam Khanna Ashish Singhal |
| author_facet | Anupam Khanna Ashish Singhal |
| author_sort | Anupam Khanna |
| collection | DOAJ |
| description | A mathematical model to control the vibrations of a rectangular plate is constructed with an aim to assist engineers in designing and fabrication of various structures used in the field of science and technology, mostly used in satellite and aeronautical engineering. The present study is related to the analysis of free vibrations of nonhomogeneous rectangular plate clamped at all the four edges. Authors studied the bilinear effect of thickness as well as temperature variations in both and directions. Variation in Poisson's ratio is also considered linearly in -direction due to nonhomogeneity. Rayleigh-Ritz method is used to analyze the frequencies for the first two modes of vibrations for different values of thermal gradient, nonhomogeneity constant, taper constants and aspect ratio. All the numerical computations have been performed for an alloy of aluminum, that is, duralumin. All the results are presented in the form of graphs. |
| format | Article |
| id | doaj-art-213f95e0c1eb4fa78fbdbfc074dd9313 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-213f95e0c1eb4fa78fbdbfc074dd93132025-02-03T05:47:58ZengWileyJournal of Mathematics2314-46292314-47852013-01-01201310.1155/2013/721868721868An Analytical Approach on Thermally Induced Vibrations of Nonhomogeneous Tapered PlateAnupam Khanna0Ashish Singhal1Department of Mathematics, Maharishi Markandeshwar University, Mullana, Haryana, Ambala 133203, IndiaDepartment of Mathematics, KIIT College of Engineering, Haryana, Gurgaon 122001, IndiaA mathematical model to control the vibrations of a rectangular plate is constructed with an aim to assist engineers in designing and fabrication of various structures used in the field of science and technology, mostly used in satellite and aeronautical engineering. The present study is related to the analysis of free vibrations of nonhomogeneous rectangular plate clamped at all the four edges. Authors studied the bilinear effect of thickness as well as temperature variations in both and directions. Variation in Poisson's ratio is also considered linearly in -direction due to nonhomogeneity. Rayleigh-Ritz method is used to analyze the frequencies for the first two modes of vibrations for different values of thermal gradient, nonhomogeneity constant, taper constants and aspect ratio. All the numerical computations have been performed for an alloy of aluminum, that is, duralumin. All the results are presented in the form of graphs.http://dx.doi.org/10.1155/2013/721868 |
| spellingShingle | Anupam Khanna Ashish Singhal An Analytical Approach on Thermally Induced Vibrations of Nonhomogeneous Tapered Plate Journal of Mathematics |
| title | An Analytical Approach on Thermally Induced Vibrations of Nonhomogeneous Tapered Plate |
| title_full | An Analytical Approach on Thermally Induced Vibrations of Nonhomogeneous Tapered Plate |
| title_fullStr | An Analytical Approach on Thermally Induced Vibrations of Nonhomogeneous Tapered Plate |
| title_full_unstemmed | An Analytical Approach on Thermally Induced Vibrations of Nonhomogeneous Tapered Plate |
| title_short | An Analytical Approach on Thermally Induced Vibrations of Nonhomogeneous Tapered Plate |
| title_sort | analytical approach on thermally induced vibrations of nonhomogeneous tapered plate |
| url | http://dx.doi.org/10.1155/2013/721868 |
| work_keys_str_mv | AT anupamkhanna ananalyticalapproachonthermallyinducedvibrationsofnonhomogeneoustaperedplate AT ashishsinghal ananalyticalapproachonthermallyinducedvibrationsofnonhomogeneoustaperedplate AT anupamkhanna analyticalapproachonthermallyinducedvibrationsofnonhomogeneoustaperedplate AT ashishsinghal analyticalapproachonthermallyinducedvibrationsofnonhomogeneoustaperedplate |