Free Vibrations of a Trapezoidal Plate with an Internal Line Hinge. (26th February 2014)

• Record Type: Journal Article
• Authors: Quintana, María Virginia; Grossi, Ricardo Oscar
• Other Names: Lee J. Academic Editor.; Rothberg S. J. Academic Editor.; Yu J. Academic Editor.
• Is Part Of: TheScientificWorldjournal. Volume 2014(2014)
• Publication Date: 2014-02-26
• Subjects: Science -- Periodicals; Technology -- Periodicals; Medicine -- Periodicals; 505
• DOI: 10.1155/2014/252084
• Languages: English
• ISSNs: 2356-6140

Abstract

Abstract : 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.