Analytical Relations Between the Eigenvalues of Circular Plate Based on Various Plate Theories

MA Lian-sheng; WANG Tie-jun

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MA Lian-sheng, WANG Tie-jun. Analytical Relations Between the Eigenvalues of Circular Plate Based on Various Plate Theories[J]. Applied Mathematics and Mechanics, 2006, 27(3): 253-259.

Citation:

MA Lian-sheng, WANG Tie-jun. Analytical Relations Between the Eigenvalues of Circular Plate Based on Various Plate Theories[J]. Applied Mathematics and Mechanics, 2006, 27(3): 253-259.

Citation:

MA Lian-sheng, WANG Tie-jun. Analytical Relations Between the Eigenvalues of Circular Plate Based on Various Plate Theories[J]. Applied Mathematics and Mechanics, 2006, 27(3): 253-259.

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Analytical Relations Between the Eigenvalues of Circular Plate Based on Various Plate Theories

Department of Engineering Mechanics, MOE Key Laboratory for Strength and Vibration, Xi'an Jiaotong University, Xi'an 710049, P. R. China

Received Date: 2005-02-16
Rev Recd Date: 2005-11-15
Publish Date: 2006-03-15

Abstract

Abstract

Based on the mathematical similarity of the axisymmetric eigenvalue problems of a circular plate between the classical plate theory(CPT),the first-order shear deformation plate theory(FPT) and the Reddy's third-order shear deformation plate theory(RPT),analytical relations between the eigenvalues of circular plate based on various plate theories are investigated.The eigenvalue problem was transformed to solve an algebra equation.Analytical relationships that were expressed explicitly between various theories were presented.Therefore,from these relationships obtained one can easily obtain the exact RPT and FPT solutions of critical buckling load and natural frequency for a circular plate with CPT solutions.The relationships are useful for engineering application,and can be used to check the validity,convergence and accuracy of numerical results for the eigenvalue problem of plates.
- classical plate theory,
- shear deformation plate theory,
- eigenvalue,
- buckling,
- natural frequency

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References(14)

References

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