TRANSVERSE VIBRATIONS OF A ROTATING TWISTED TIMOSHENKO BEAM UNDER AXIAL LOADING

Transverse bending vibrations of a rotating twisted beam subjected to an axial load and spinning about its axial axis are established by usi ng the Timoshenko beam theory and applying Hamilton's Principle. The e quations of motion of the twisted beam are derived in the twist nonort hogonal coordinate system. The finite element method is employed to di scretize the equations of motion into time-dependent ordinary differen tial equations that have gyroscopic terms. A symmetric general eigenva lue problem is formulated and used to study the influence of the twist angle, rotational speed, and axial force on the natural frequencies o f Timoshenko beams. The present model is useful for the parametric stu dies to understand better the various dynamic aspects of the beam stru cture affecting its vibration behavior.