High-Precision Approximate Analytical Solutions for Free Bending Vibrations of Thin Plates and an Improvement

BAO Si-yuan; DENG Zi-chen

doi:10.21656/1000-0887.370005

Volume 37 Issue 11

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Article Navigation > Applied Mathematics and Mechanics > 2016 > 37(11): 1169-1180

BAO Si-yuan, DENG Zi-chen. High-Precision Approximate Analytical Solutions for Free Bending Vibrations of Thin Plates and an Improvement[J]. Applied Mathematics and Mechanics, 2016, 37(11): 1169-1180. doi: 10.21656/1000-0887.370005

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High-Precision Approximate Analytical Solutions for Free Bending Vibrations of Thin Plates and an Improvement

doi: 10.21656/1000-0887.370005

BAO Si-yuan¹,
DENG Zi-chen²

¹Department of Engineering Mechanics, School of Civil Engineering, Suzhou University of Science and Technology, Suzhou, Jiangsu 215011, P.R.China;²Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an 710072, P.R.China

Funds: The National Natural Science Foundation of China（11202146）

Received Date: 2016-01-04
Rev Recd Date: 2016-06-30
Publish Date: 2016-11-15

Abstract

Abstract

For free bending vibrations of thin plates, based on the variable separation method, the analytical solutions of deflection functions were obtained in the Hamiltonian system, and the eigenvalue equations about the 2 coordinate axes were established. Then the vibration frequencies were solved as parametrical variables, and the mode shapes of different orders were got. The analytical form of the deflection function was in fact a high-precision approximate solution satisfying the displacement boundary conditions. From the approximate frequency values calculated with the Rayleigh-Ritz method, it is found that the previous analytical method had great precision, thus the effectiveness was demonstrated. In addition, for clamped or simply supported boundary conditions, different points were properly selected as the coordinate origins. The unified forms of the frequency equations were given. These forms were used to discuss the rectangular plates with 4 edges clamped, or 4 edges simply supported, or some clamped and the other(s) simply supported, and so on. The correctness of the frequency equation forms was verified with the symmetry of the plates’ deformations. The linkage and transformation between the frequency equations under different boundary conditions were obtained.
- Hamiltonian system,
- thin plate,
- free vibration,
- deflection,
- frequency,
- symmetry

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References(18)

References

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