Application of the Reissner Method to a Timoshenko Beam

The Reissner and the potential energy methods have been applied to a Timoshenko beam vibrating in flexure. Frequency equations are developed using shape functions for bending moment, shearing force, deflection, and slope in series form through the Ritz process. Natural frequencies and mode shapes are obtained and comparison is made between the results of the two approaches from which it is observed that the Reissner method indicates a quicker convergence and gives better mode shapes.