A new exact analytical approach for free vibration of Reissner–Mindlin functionally graded rectangular plates

An exact closed-form procedure is presented for free vibration analysis of moderately thick rectangular plates having two opposite edges simply supported (i.e. Lévy-type rectangular plates) based on the Reissner–Mindlin plate theory. The material properties change continuously through the thickness...

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Bibliographic Details
Published in:International journal of mechanical sciences 2011, Vol.53 (1), p.11-22
Main Authors: Hosseini-Hashemi, Sh, Fadaee, M., Atashipour, S.R.
Format: Article
Language:English
Subjects:
Benchmarking
Exact closed form solution
Exact sciences and technology
Exact solutions
Free vibration
Functionally graded rectangular plates
Functionally gradient materials
Fundamental areas of phenomenology (including applications)
Mathematical analysis
Mathematical models
Physics
Power law
Rectangular plates
Reissner–Mindlin plate theory
Solid mechanics
Structural and continuum mechanics
Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
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Summary:An exact closed-form procedure is presented for free vibration analysis of moderately thick rectangular plates having two opposite edges simply supported (i.e. Lévy-type rectangular plates) based on the Reissner–Mindlin plate theory. The material properties change continuously through the thickness of the plate, which can vary according to a power law distribution of the volume fraction of the constituents. By introducing some new potential and auxiliary functions, the displacement fields are analytically obtained for this plate configuration. Several comparison studies with analytical and numerical techniques reported in literature are carried out to establish the high accuracy and reliability of the solutions. Comprehensive benchmark results for natural frequencies of the functionally graded (FG) rectangular plates with six different combinations of boundary conditions (i.e. SSSS–SSSC–SCSC–SCSF–SSSF–SFSF) are tabulated in dimensionless form for various values of aspect ratios, thickness to length ratios and the power law index. Due to the inherent features of the present exact closed-form solution, the present results will be a useful benchmark for evaluating the accuracy of other analytical and numerical methods, which will be developed by researchers in the future.
ISSN:0020-7403
1879-2162
1879-2162
DOI:10.1016/j.ijmecsci.2010.10.002