A semi-analytical solution for forced vibrations response of rectangular orthotropic plates with various boundary conditions

다국어 초록 (Multilingual Abstract)

Orthotropic plates form an essential part of many marine, aerospace, and automobile structures. The recent increase in the use of composite materials for plate-type structures intensified the need for solutions utilizing orthotropic plates. These structural components, in many instances, are subjected to vibration. The main purpose of this paper is to present a semi-analytical analysis of the response of orthotropic plates to forced vibrations with different combinations of boundary conditions subjected to a general distributed excitation.
The solution of the partial differential equation was reduced to an iterative sequential solution of ordinary differential equations using extended Kantorovich method. The efficiency and accuracy of the proposed method were examined through comparison with available literature and was in good agreement with them.

참고문헌 (Reference)

1 C. Mei, "finite element method for non-linear forced vibrations of rectangular plates" 23 : 1104-1110, 1985

2 R. Szilard, "Theory and analysis of plates. Englewood Cliffs" Prentice-Hall 1974

3 R. B. Bhat, "Plate characteristic functions and natural frequencies of vibration of plates by iterative reduction of partial differential equation" 115 (115): 177-181, 1993

4 M. Dalaei, "Natural vibration analysis of clamped rectangular orthotropic plates" 189 (189): 399-406, 1996

5 R. B, Bhat, "Natural frequencies of rectangular plates using characteristic orthogonal polynomials in the Rayleigh–Ritz method" 102 (102): 493-499, 1985

6 T. Sakata, "Natural frequencies of orthotropic rectangular plates obtained by iterative reduction of the partial differential equation" 189 (189): 89-101, 1996

7 S. D. Yu, "Generic free vibration of orthotropic rectangular plates with clamped and simply supported edge" 163 (163): 439-450, 1993

8 A. N. Bercin, "Free vibration solution for clamped orthotropic plates using the Kantorovich method," 196 (196): 243-247, 1996

9 R. L. Ramkumar, "Free vibration solution for clamped orthotropic plates using Lagrangian multiplier technique" 25 (25): 146-151, 1987

10 M. Huang, "Free vibration analysis of orthotropic rectangular plateswith variable thickness and general boundary conditions" 931-955, 2005

11 R. E. Rossi, "Forced vibrations of rectangular plates subjected to harmonic loading distributed over a rectangular subdomain," 28 : 1575-1584, 2001

12 E. Romanelli, "Forced transverse vibrations of a simply supported rectangular orthotropic plate in the case where the force acts over a plate subdomain" 28 : 1135-1144, 2001

13 L. V. Kantorovich, "Approximate methods of higher analysis" The Netherlands 1964

14 R. Jones, "Application of the extended Kantorovich method to the vibration of clamped rectangular plates" 45 : 309-316, 1976

15 S. G. Lekhnitskii, "Anisotropic plates" Gordon &Breach 1968

16 A. D. Kerr, "An extension of the Kantorovich method" 26 : 219-129, 1968

17 C. R. Wylie, "Advanced Engineering Mathematics" McGraw-Hill 1985

18 D. J. Gorman, "Accurate free vibration analysis of clamped orthotropic plates by the method of superposition" 140 (140): 391-411, 1990

19 S. M. Dickinson, ", On the use of orthogonal polynomials in the Reyleigh- Ritz method for the study of the flexural vibration and buckling of isotropic and orthotropic rectangular plates" 108 (108): 51-62, 1986