TRANSVERSE VIBRATION OF A SIMPLY SUPPORTED BEAM WITH SYMMETRICAL OVERHANG OF ARBITRARY LENGTH

The numerical solution to the frequency equation for the transverse vi bration of a simple beam with symmetric overhang is found. The numeric al results converge to the analytical solutions for the two limiting c ases of a beam with no overhang and a beam with no span and agree with the case in which the supports are at the nodal points of a freely vi brating beam. An approximation to the solution of the frequency equati on for beams with small overhang is presented and compared to the nume rical solution. This simple yet accurate approximation is most useful to determine a beam's flexural stiffness, EI or modulus of elasticity, E, by freely vibrating a simply supported beam.