Frequency equations for the in-plane vibration of orthotropic circular annular plate

Orthotropic circular annular plates have a lot of applications in engineering such as space structures and rotary machines. In this paper, frequency equations for the in-plane vibration of the orthotropic circular annular plate for general boundary conditions were derived. To obtain the frequency eq...

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Bibliographic Details
Published in:Archive of applied mechanics (1991) 2011-09, Vol.81 (9), p.1307-1322
Main Authors: Karamooz Ravari, M. R., Forouzan, M. R.
Format: Article
Language:English
Subjects:
Annular plates
Boundary conditions
Classical Mechanics
Displacement
Engineering
Equations of motion
Mathematical analysis
Original
Spacecraft
Theoretical and Applied Mechanics
Vibration
Wave equations
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Summary:Orthotropic circular annular plates have a lot of applications in engineering such as space structures and rotary machines. In this paper, frequency equations for the in-plane vibration of the orthotropic circular annular plate for general boundary conditions were derived. To obtain the frequency equation, first the equation of motion for the circular annular plate in the cylindrical coordinate is derived by using the stress-strain- displacement expressions. Helmholtz decomposition is used to uncouple the equations of motion. The wave equation is obtained by assumption a harmonic solution for the uncoupled equations. Using the separation of the variables leads to the general wave equation solution and the in-plane displacements in the r and θ directions. Finally, boundary conditions are exerted and the natural frequency is derived for general boundary conditions. The obtained results are validated by comparing with the previously reported and those from finite element analysis.
ISSN:0939-1533
1432-0681
DOI:10.1007/s00419-010-0488-6