Free Vibrations of a Trapezoidal Plate with an Internal Line Hinge
This paper deals with a general variational formulation for the determination of natural frequencies and mode shapes of free vibrations of laminated thin plates of trapezoidal shape with an internal line hinge restrained against rotation. The analysis was carried out by using the kinematics correspo...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/252084 |
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| _version_ | 1832545510983991296 |
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| author | María Virginia Quintana Ricardo Oscar Grossi |
| author_facet | María Virginia Quintana Ricardo Oscar Grossi |
| author_sort | María Virginia Quintana |
| collection | DOAJ |
| description | This paper deals with a general variational formulation for the determination of natural frequencies and mode shapes of free vibrations of laminated thin plates of trapezoidal shape with an internal line hinge restrained against rotation. The analysis was carried out by using the kinematics corresponding to the classical laminated plate theory (CLPT). The eigenvalue problem is obtained by employing a combination of the Ritz method and the Lagrange multipliers method. The domain of the plate is transformed into a rectangular domain in the computational space by using nonorthogonal triangular coordinates and the transverse displacements are approximated with a set of simple polynomials automatically generated and expressed in the triangular coordinates. The developed algorithm allows obtaining approximate analytical solutions for mentioned plate with different geometries, aspect ratio, position of the line hinge, and boundary conditions including translational and rotational elastically restrained edges. It allows studying the influence of the mentioned line on the vibration frequencies and respective mode shapes. The algorithm can easily be programmed and it is numerically stable. Additionally, as a particular case, the results of triangular plates can be easily generated. |
| format | Article |
| id | doaj-art-64cefbf5503a4ea28be27f282da4ada5 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-64cefbf5503a4ea28be27f282da4ada52025-02-03T07:25:36ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/252084252084Free Vibrations of a Trapezoidal Plate with an Internal Line HingeMaría Virginia Quintana0Ricardo Oscar Grossi1INIQUI-CONICET, Facultad de Ingeniería, Universidad Nacional de Salta, Av. Bolivia 5150, 4400 Salta, ArgentinaINIQUI-CONICET, Facultad de Ingeniería, Universidad Nacional de Salta, Av. Bolivia 5150, 4400 Salta, ArgentinaThis paper deals with a general variational formulation for the determination of natural frequencies and mode shapes of free vibrations of laminated thin plates of trapezoidal shape with an internal line hinge restrained against rotation. The analysis was carried out by using the kinematics corresponding to the classical laminated plate theory (CLPT). The eigenvalue problem is obtained by employing a combination of the Ritz method and the Lagrange multipliers method. The domain of the plate is transformed into a rectangular domain in the computational space by using nonorthogonal triangular coordinates and the transverse displacements are approximated with a set of simple polynomials automatically generated and expressed in the triangular coordinates. The developed algorithm allows obtaining approximate analytical solutions for mentioned plate with different geometries, aspect ratio, position of the line hinge, and boundary conditions including translational and rotational elastically restrained edges. It allows studying the influence of the mentioned line on the vibration frequencies and respective mode shapes. The algorithm can easily be programmed and it is numerically stable. Additionally, as a particular case, the results of triangular plates can be easily generated.http://dx.doi.org/10.1155/2014/252084 |
| spellingShingle | María Virginia Quintana Ricardo Oscar Grossi Free Vibrations of a Trapezoidal Plate with an Internal Line Hinge The Scientific World Journal |
| title | Free Vibrations of a Trapezoidal Plate with an Internal Line Hinge |
| title_full | Free Vibrations of a Trapezoidal Plate with an Internal Line Hinge |
| title_fullStr | Free Vibrations of a Trapezoidal Plate with an Internal Line Hinge |
| title_full_unstemmed | Free Vibrations of a Trapezoidal Plate with an Internal Line Hinge |
| title_short | Free Vibrations of a Trapezoidal Plate with an Internal Line Hinge |
| title_sort | free vibrations of a trapezoidal plate with an internal line hinge |
| url | http://dx.doi.org/10.1155/2014/252084 |
| work_keys_str_mv | AT mariavirginiaquintana freevibrationsofatrapezoidalplatewithaninternallinehinge AT ricardooscargrossi freevibrationsofatrapezoidalplatewithaninternallinehinge |