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.
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Robert A. Anderson (1953) studied this question.
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