Finite Element Study of the Geometric Centrifugal Stiffening Effect

摘要

The finite element absolute nodal coordinate formulation is used in this investigation to study the centrifugal stiffening effects on rotating two- dimensional beams. It is demonstrated that the geometric stiffening effects can be automatically accounted for in the above mentioned finite element formulation by using an expression for the elastic forces obtained with a general continuum mechanics approach. The Hill equation that governs the vibration of the rotating beam is obtained in terms of a set of generalized coordinates that describe the beam displacements and slopes. Under the assumption of small deformation, the Hill equation is linearized, and the complete solution is obtained and used to demonstrate analytically that such a solution does not exhibit instabilities as the angular velocity of the beam increases. The results obtained using this finite element procedure are compared with the results reported in the literature.