Study the Transverse Vibration of a Beam With Different Length

Abstract

A numerical solution to the frequency equation for the transverse vibration of a beam (Simply Supported with symmetric overhang) is done. It is proposed two limiting cases of a beam with no overhang, and no span. This agrees with the cases in which the supports are at the nodal Points of a freely vibrating beam. Also the numerical results compared with the analytical solutions for this study are coincident. An approximation to the solution of the frequency equation for beams with small overhang is presented and compared with the numerical solution. This approximation is quite useful to determine a beam's flexural stiffness (EI), or modulus of elasticity (E), by free vibrating of a simply supported beam.