Boundary Characteristic Orthogonal Polynomials in the Study of Transverse Vibrations of Nonhomogeneous Rectangular Plates with Bilinear Thickness Variation
The free transverse vibrations of thin nonhomogeneous rectangular plates of variable thickness have been studied using boundary characteristic orthogonal polynomials in the Rayleigh-Ritz method. Gram-Schmidt process has been used to generate these orthogonal polynomials in two variables. The thickne...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.3233/SAV-2010-0635 |
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| author | R. Lal Yajuvindra Kumar |
| author_facet | R. Lal Yajuvindra Kumar |
| author_sort | R. Lal |
| collection | DOAJ |
| description | The free transverse vibrations of thin nonhomogeneous rectangular plates of variable thickness have been studied using boundary characteristic orthogonal polynomials in the Rayleigh-Ritz method. Gram-Schmidt process has been used to generate these orthogonal polynomials in two variables. The thickness variation is bidirectional and is the cartesian product of linear variations along two concurrent edges of the plate. The nonhomogeneity of the plate is assumed to arise due to linear variations in Young's modulus and density of the plate material with the in-plane coordinates. Numerical results have been computed for four different combinations of clamped, simply supported and free edges. Effect of the nonhomogeneity and thickness variation with varying values of aspect ratio on the natural frequencies of vibration is illustrated for the first three modes of vibration. Three dimensional mode shapes for all the four boundary conditions have been presented. A comparison of results with those available in the literature has been made. |
| format | Article |
| id | doaj-art-2cadc1537d35433bbe628b135ae1bcb7 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-2cadc1537d35433bbe628b135ae1bcb72025-02-03T01:23:52ZengWileyShock and Vibration1070-96221875-92032012-01-0119334936410.3233/SAV-2010-0635Boundary Characteristic Orthogonal Polynomials in the Study of Transverse Vibrations of Nonhomogeneous Rectangular Plates with Bilinear Thickness VariationR. Lal0Yajuvindra Kumar1Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, IndiaDepartment of Mathematics, Indian Institute of Technology Roorkee, Roorkee, IndiaThe free transverse vibrations of thin nonhomogeneous rectangular plates of variable thickness have been studied using boundary characteristic orthogonal polynomials in the Rayleigh-Ritz method. Gram-Schmidt process has been used to generate these orthogonal polynomials in two variables. The thickness variation is bidirectional and is the cartesian product of linear variations along two concurrent edges of the plate. The nonhomogeneity of the plate is assumed to arise due to linear variations in Young's modulus and density of the plate material with the in-plane coordinates. Numerical results have been computed for four different combinations of clamped, simply supported and free edges. Effect of the nonhomogeneity and thickness variation with varying values of aspect ratio on the natural frequencies of vibration is illustrated for the first three modes of vibration. Three dimensional mode shapes for all the four boundary conditions have been presented. A comparison of results with those available in the literature has been made.http://dx.doi.org/10.3233/SAV-2010-0635 |
| spellingShingle | R. Lal Yajuvindra Kumar Boundary Characteristic Orthogonal Polynomials in the Study of Transverse Vibrations of Nonhomogeneous Rectangular Plates with Bilinear Thickness Variation Shock and Vibration |
| title | Boundary Characteristic Orthogonal Polynomials in the Study of Transverse Vibrations of Nonhomogeneous Rectangular Plates with Bilinear Thickness Variation |
| title_full | Boundary Characteristic Orthogonal Polynomials in the Study of Transverse Vibrations of Nonhomogeneous Rectangular Plates with Bilinear Thickness Variation |
| title_fullStr | Boundary Characteristic Orthogonal Polynomials in the Study of Transverse Vibrations of Nonhomogeneous Rectangular Plates with Bilinear Thickness Variation |
| title_full_unstemmed | Boundary Characteristic Orthogonal Polynomials in the Study of Transverse Vibrations of Nonhomogeneous Rectangular Plates with Bilinear Thickness Variation |
| title_short | Boundary Characteristic Orthogonal Polynomials in the Study of Transverse Vibrations of Nonhomogeneous Rectangular Plates with Bilinear Thickness Variation |
| title_sort | boundary characteristic orthogonal polynomials in the study of transverse vibrations of nonhomogeneous rectangular plates with bilinear thickness variation |
| url | http://dx.doi.org/10.3233/SAV-2010-0635 |
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