General analytical solution of transverse vibration for orthotropic rectangular thin plates

Abstract

A general solution of differential equation for transverse displacement function of orthotropic rectangular thin plates in free vibration is established in this paper. It can be used to solve the vibration problem of plate with arbitrary boundaries. As an example, the frequencies of a composite laminated plate with four free edges have been solved. The result as compared with the experiment is satisfactory.

Keywords

orthotropic plate / vibration / frequency

References

[1] Dana Young. Vibration of rectangular plates by the Ritz method[J]. J Appl Mech, 1950, 17(4): 448-453

[2] Gorman D J. Free vibration analysis of the completely free rectangular plate by the method of superposition[J]. J Sound and Vibration, 1978, 57(3): 437-447

[3] Huang Yan. A general analytical solution for elastic vibration of rectangular thin plates[J]. Applied mathematics and mechanics, 1988, 9(11): 1057-1065

[4] Dickinson S M, Blasin A D. On use of orthogonal polynomials in the Rayleigh-Rittz method for the study of the flexural vibration and buckling of isotropic and orthotropic rectangular plates[J]. J Sound and vibration, 1986, 108: 51-62

[5] Al-Khaiat H. Free vibration analysis of orthotropic plates by the initial value method[J]. Comput Struct, 1989, 33: 1431-1439

[6] Jayaraman G, Chen D, Snyder V W. Free vibration of rectangular orthotropic plates with a pair of parallel edges simply supported[J]. Comput Struct, 1990, 34: 203-214

[7] Goman D J. Accurate free vibration analysis of completely free orthotropic plate by method of superposition[J]. J Sound and Vibration, 1990, 140: 391-411

[8] Goman D J. Accurate free vibration analysis of completely free orthotropic rectangular plate by the method of superposition[J]. J Sound and Vibration, 1993, 65: 409-420

[9] Sakata T, Takahashi K, Bhat R B. Natural frequencies of orthotropic rectangular plates obtained by iterative reduction of the partial differential equation[J]. J Sound and Vibration, 1996, 189: 89-101

[10] Jones R M. Mechanics of Composite Materials[M]. 1975, New York: McGraw-Hill