Vibration and Buckling of Composite Beams

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Abstract
The eigenvalue problem corresponding to the vibration and buckling of a composite beam under the action of a conservative axial force is considered. The material properties of the beam or its cross-sectional dimension may vary continuously or discontinuously along its length. The eigen-frequencies and the buckling load are estimated by means of the method of the new quotient which has been recently proposed by Nemat-Nasser, and the results are compared with those obtained by means of the usual Rayleigh quotient and its dual. A scheme of improving the test functions is also presented. This gives very accurate lower and upper bounds for the vibration frequencies, as well as for the buckling load. Results are illustrated by means of several numerical examples which include both the determinate and the indeterminate cases. These examples tend to suggest that the new quotient gives very accurate estimates for this class of problems.

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