AN ELEMENT FOR STUDYING THE VIBRATION OF UNRESTRAINED CURVED TIMOSHENKO BEAMS

A Timoshenko beam finite element is developed using trigonometric basis functions. The properties and performance of these new elements as applied to the vibration of beams are explored through a series of illustrative problems that treat both straight and curved geometries. The effect of using a consistent mass matrix vs. a diagonal mass matrix has been investigated, as has the effect of the wave content of the basis functions. For specific wave parameter values, trigonometric basis functions are shown to allow the recovery of rigid body modes in the case of straight and circular arc curved beams. They are also shown to exhibit good convergence and accuracy characteristics in both geometries. Natural frequency results for a complete series of free-free curved beams are reported. © 1992.