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Analytical Solution for Free Vibrations of a Moderately Thick Rectangular Plate
Joint Authors
Senjanović, Ivo
Tomić, Marko
Vladimir, Nikola
Cho, Dae Seung
Source
Mathematical Problems in Engineering
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-07-31
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
In the present thick plate vibration theory, governing equations of force-displacement relations and equilibrium of forces are reduced to the system of three partial differential equations of motion with total deflection, which consists of bending and shear contribution, and angles of rotation as the basic unknown functions.
The system is starting one for the application of any analytical or numerical method.
Most of the analytical methods deal with those three equations, some of them with two (total and bending deflection), and recently a solution based on one equation related to total deflection has been proposed.
In this paper, a system of three equations is reduced to one equation with bending deflection acting as a potential function.
Method of separation of variables is applied and analytical solution of differential equation is obtained in closed form.
Any combination of boundary conditions can be considered.
However, the exact solution of boundary value problem is achieved for a plate with two opposite simply supported edges, while for mixed boundary conditions, an approximate solution is derived.
Numerical results of illustrative examples are compared with those known in the literature, and very good agreement is achieved.
American Psychological Association (APA)
Senjanović, Ivo& Tomić, Marko& Vladimir, Nikola& Cho, Dae Seung. 2013. Analytical Solution for Free Vibrations of a Moderately Thick Rectangular Plate. Mathematical Problems in Engineering،Vol. 2013, no. 2013, pp.1-13.
https://search.emarefa.net/detail/BIM-1008698
Modern Language Association (MLA)
Senjanović, Ivo…[et al.]. Analytical Solution for Free Vibrations of a Moderately Thick Rectangular Plate. Mathematical Problems in Engineering No. 2013 (2013), pp.1-13.
https://search.emarefa.net/detail/BIM-1008698
American Medical Association (AMA)
Senjanović, Ivo& Tomić, Marko& Vladimir, Nikola& Cho, Dae Seung. Analytical Solution for Free Vibrations of a Moderately Thick Rectangular Plate. Mathematical Problems in Engineering. 2013. Vol. 2013, no. 2013, pp.1-13.
https://search.emarefa.net/detail/BIM-1008698
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1008698