Vibrations of short beams

The paper presents a new formulation for transverse oscillations of uniform beams. The governing equations are two SUnultaneous partial integro-dilferential equations. From these equations, simpler governing equations to various orders of approximation are deduced. Well-known beam equations correspond to some special cases in the present formulation.Introduction of refined shear coefficient in the Timosbenko's theory seems to increase the discrepancy between theory and experiment, whereas the present formulation reduces this discrepancy. Second-order approximation equations are believed to be adequate for most engineering applications; for more accurate determination of the natural frequency higher-order approximations can be used