Abstract
This paper presents vibration analysis of plates by the Rayleigh-Ritz method with orthogonal polynomials derived by the Gram-Schmidt Process as displacement functions, and Gauss-Legendre Quadrature as an integration scheme. A computer program was developed and numerical results by this computation were in good accord with those obtained by using other beam functions. Furthermore, the present method was shown to resolve various problems encountered in the application of existing methods.
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Abbreviations
- a, b :
-
Length scale of rectangular plate inx andy directions, respectively
- C :
-
Clamped edge indicater
- D :
-
Flexural rigidity,Eh 3/{12(1−ν 2)}
- E :
-
Young’s modulus
- F :
-
Free edge indicator
- S :
-
Simply-supported edge indicator
- T max :
-
Maximum total kinetic energy
- U max :
-
Maximum total strain energy
- X m (x),Y n (y):
-
Orthogonal set of polynomials
- °:
-
Aspect ratio
- ϕ(x):
-
Orthogonal polynomial
- ω:
-
Circular frequency
- λ:
-
Frequency parameter
- ν:
-
Poisson’s ratio
- π:
-
Mass density per unit area of plate
References
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Han, B.K., Chung, K. & Han, D.S. Vibration analysis on plates by orthogonal polynomials. KSME Journal 3, 95–102 (1989). https://doi.org/10.1007/BF02953594
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DOI: https://doi.org/10.1007/BF02953594