Open AccessFree Vibration Analysis of a Rectangular Plate with Kelvin Type Boundary Conditions
Author(s) -
R. Kırışık,
Ş. Yüksel
Publication year - 2006
Publication title -
shock and vibration
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.418
H-Index - 45
eISSN - 1875-9203
pISSN - 1070-9622
DOI - 10.1155/2007/307575
Subject(s) - eigenfunction , bending of plates , plate theory , boundary value problem , vibration , modal , modal analysis , stiffness , equations of motion , separation of variables , transverse plane , mathematical analysis , spring (device) , vibration of plates , physics , mathematics , structural engineering , classical mechanics , materials science , engineering , acoustics , bending , eigenvalues and eigenvectors , quantum mechanics , polymer chemistry
The transverse vibrations of a rectangular plate with the Kelvin type boundary conditions at four corners are investigated. The plate is modeled as being attached to four lumped spring-damper systems at the corners. An analytical procedure is proposed based on the modal analysis. The completely free case of the plate is first studied. The expressions for the eigenfrequencies and eigenfunctions of the plate are obtained by utilizing the separation of variables. Then, the case in which the stiffness and the viscous damping as external forces acting at the corners of the plate is studied. Following the modal analysis procedure, the general solution for the equation of motion of the rectangular plate is derived. Some numerical results are presented
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