Analysis of the free vibration of rectangular plates with central cut-outs using the discrete Ritz method

International Journal of Mechanical Sciences

Volumn 45, Issue 5, 2003, Pages 941-959

  Liew, K M ^a   Kitipornchai, S ^b,c   Leung, A Y T ^b   Lim, C W ^b  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^c UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

Cut out; Free vibration; Orthogonal polynomials; Perforated plates; Ritz method

Indexed keywords

BOUNDARY CONDITIONS; DEFLECTION (STRUCTURES); KINETIC ENERGY; PERFORATING; POLYNOMIALS; STRAIN; VIBRATIONS (MECHANICAL);

RITZ METHOD;

PLATES (STRUCTURAL COMPONENTS);

EID: 0141459619     PISSN: 00207403     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7403(03)00109-7     Document Type: Article

References (23)

1. Boay C.G. Free vibration of laminated plates with a central circular hole. Composite Structures. 35:1996;357-368.
2. Sabir A.B., Davies T.G. Natural frequencies of square plates with reinforced central holes subjected to inplane loads. Thin-Walled Structures. 28:1997;337-353.
3. Sivakumar K., Iyengar N.G.R., Deb K. Free vibration of laminated composite plates with cutout. Journal of Sound and Vibration. 221:1999;443-470.
4. Sivakumar K., Iyengar N.G.R., Deb K. Optimum design of laminated composite plates with cutouts undergoing large amplitude oscillations. Advanced Composite Materials. 8:1999;295-316.
5. Pan E.N. A general boundary element analysis of 2-D linear elastic fracture mechanics. International Journal of Fracture. 88:1997;41-59.
6. Chau K.T., Wang Y.B. A new boundary integral formulation for plane elastic bodies containing cracks and holes. International Journal of Solids and Structures. 36:1999;2041-2074.
7. Liu F.L., Liew K.M. Vibration analysis of discontinuous Mindlin plates by differential quadrature element method. Trans. ASME Journal of Vibration and Acoustics. 121:1999;204-208.
8. Liu F.L., Liew K.M. Differential quadrature element method. a new approach for free vibration analysis of polar Mindlin plates having discontinuities Computer Methods in Applied Mechanics and Engineering. 179:1999;407-423.
9. Yang B., Zhou J. Semi-analytical solution of 2-D elasticity problems by the strip distributed transfer function method. International Journal of Solids and Structures. 33:1996;3983-4005.
10. Yang B., Park D.H. Analysis of plates with curved boundaries using isoparametric strip distributed transfer functions. International Journal for Numerical Methods in Engineering. 44:1999;131-146.
11. Geannakakes G.N. Vibration analysis of arbitrarily shaped plates using beam characteristic orthogonal polynomials in the semi-analytical finite strip method. Journal of Sound and Vibration. 137:1990;283-303.
12. Laura P.A.A., Romanelli E., Rossi R.E. Transverse vibrations of simply supported rectangular plates with rectangular cutouts. Journal of Sound and Vibration. 202:1997;275-283.
13. Liew K.M., Hung K.C., Lim M.K. Method of domain decomposition in vibrations of mixed edge anisotropic plates. International Journal of Solids and Structures. 30:1993;3281-3301.
14. Liew K.M., Hung K.C., Lim M.K. Roles of domain decomposition method in plate vibrations - treatment of mixed discontinuous periphery boundaries. International Journal of Mechanical Sciences. 35:1993;615-632.
15. Liew K.M., Hung K.C., Sum Y.K. Flexural vibration of polygonal plates. treatments of sharp re-entrant corners Journal of Sound and Vibration. 183:1995;221-238.
16. Liew K.M., Sum Y.K. Vibration of plates having orthogonal straight edges with clamped boundaries. Journal of Engineering Mechanics, ASCE. 124:1998;184-192.
17. Liew K.M., Ng T.Y., Kitipornchai S. A semi-analytical solution for vibration of rectangular plates with abrupt thickness variation. International Journal of Solids and Structures. 38:2001;4937-4954.
18. Aksu G., Ali R. Determination of dynamic characteristics of rectangular plates with cut-outs using finite difference formulation. Journal of Sound and Vibration. 44:1976;147-158.
19. Lam K.Y., Hung K.C. Vibration analysis of plates with cutouts by the modified Rayleigh-Ritz method. Applied Acoustics. 28:1989;49-60.
20. Chihara T.S. An introduction to orthogonal polynomials. 1978;Gordon and Breach, New York.
21. Grandin H. Jr. Fundamentals of the finite element method. 1986;Macmillan, New York.
22. Rao C.R., Mitra S.K. Generalized inverse of matrices and its applications. 1971;Wiley, New York.
23. Rajamani A., Prabhakaran R. Dynamic-response of composite plates with cut-outs - 1. Simply-supported plates. Journal of Sound and Vibration. 54:1977;549-564.