FREE VIBRATION AND BUCKLING OF CANTILEVER BEAMS UNDER LINEARLY VARYING AXIAL LOAD CARRYING AN ECCENTRIC END RIGID BODY

Abstract

Natural frequencies of a clamped axially loaded beam carrying an eccentric end rigid body are computed. A linearly varying non-follower axial force representing the beam’s own weight is taken into consideration. An analytical form of the frequency equation of the structure is obtained and solved numerically. The parameters associated with the end rigid body, the mass, the rotary inertia and the eccentricity, are shown to considerably affect the natural frequencies of the structure. The modified orthogonality conditions of the system are presented. A closed-form of the frequency equation for a beam under constant axial load carrying an eccentric end rigid body is obtained and results are compared with the distributed load case. Based on the exact and approximate computations of the critical buckling load a recommendation is made on the method of including the effect of distributed load for practical purposes.