Abstract
An exact solution for the natural frequencies of transverse vibration of free beams with rectangular cross-section is used as a basis of comparison for the Timoshenko beam theory and a plane stress approximation which is developed herein. The comparisons clearly show the range of applicability of the approximate solutions as well as their accuracy. The choice of a best shear coefficient for use in the Timoshenko beam theory is considered by evaluation of the shear coefficient that would make the Timoshenko beam theory match the exact solution and the plane stress solution. The plane stress solution is shown to provide excellent accuracy within its range of applicability.
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