FREE VIBRATION ANALYSIS OF ISOTROPIC AND ORTHOTROPIC CLAMPED PLATES USING ENERGY APPROACH
Keywords:
Free vibration, Isotropic, Orthotropic, Plate, Natural frequency, fundamental frequency, F.E.M, ClampedAbstract
The free vibration of isotropic, orthotropic clamped rectangular plates using the Rayleigh-Ritz energy approach has been studied. The solution of the eigenvalue problem is obtained by assuming a deflected shape in the form of series functions that satisfy the edge boundary conditions of the plate. Simplified analytical expressions for frequencies are obtained that describe the vibrational characteristics of the plate. To demonstrate the accuracy of the present approach the same plate is discritisated and analyzed using the finite element method and the corresponding frequencies are obtained. The frequencies obtained with energy approach agree closely with those of the conventional finite element method.References
- Warburton G.B., "The vibration of rectangular plates", Proceeding of the institute of Mechanical engineers, Series A, 168, (1954), pp.371-384.
- Leissa A.W., "Vibration of Plates", NASA SP-160, Washington DC, (1969).
- Leissa A.W., "Plate vibration research 1976-1980: classical theory", Shock vibration Digest, 13, (1981), pp.11-12.
- Hearmon R.F.S., "The frequency of flexural vibration of rectangular plates with clamped or simply supported edges", Journal of applied Mechanics, 26, (1959), pp.537-540.
- Aksu G. and Ali R., "Free vibration analysis of stiffened plates using finite difference method", Journal of sound and vibration, 48(1), (1976), pp.15-25.
- Sriniva S., Rao A.K., "Bending, vibration and buckling of simply supported thick orthotropic rectangular plate and laminates", Int. J. Solids Struct., 6, (1970), pp.1463-1481.
- Sakata T., Hosokawa K., "Vibrations of analysis of clamped orthotropic rectangular plates", J. Sound Vibr., 125(3), (1988), pp.429-439.
- Gorman D.J., "Accurate free vibration of the clamped orthotropic plates by the method of superposition", J. sound Vibr., 140(3), (1990), pp.341-391.
- Gutrérez R.H., Laura P.A.A. and Rossit C.A., "Fundamental frequency of transverse vibration of a clamped rectangular orthotropic plate with a free-edge hole", Journal of sound Vibration, 235(4), (2000), pp.697-701.
- Ahmadian M.T., Sherafati Zangeneh M., "Vibration analysis of orthotropic rectangular plates using superelement", Comput. Methods Appl. Mech. Engrg., 191, (2002), pp.2069-2075
- Lee S.J., "Free Vibration analysis of plates by using a four-node finite element formulated with assumed natural transverse shear strain", Journal of sound Vibration, 2003; 278, (2004), pp.657-684.
- Karim S. Numayr, Rami H. Haddad, Madhar A. Haddad, "Free vibration of composite plates using the finite difference method", Thin–Walled Structures, 42, (2004), pp.399-414.
- Mbakogu F.C., Pavlovich M.N., "Bending of clamped orthotropic rectangular plates: A variational symbolic solution", Computers and structures, 77, (2000), pp. 117-128.
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