Flexural Vibrations in Uniform Beams According to the Timoshenko Theory

Abstract The general series solution is given for the flexural vibrations in a uniform beam according to the Timoshenko equations, which include the secondary effects of shear and rotatory inertia. In addition, the series solution is presented for the case of a pin-ended beam. For the special case of a concentrated transient force at the mid-point of a pin-ended beam, the bending-moment and shear-force solutions according to the Timoshenko and elementary equations are compared.