Coupled bending-torsion vibration of beams including rotary inertia: a Galerkin-based mesh reduction dynamic finite element method
by
Seyed M. Hashemi
Department of Aerospace Engineering, Ryerson University, Toronto, Canada

The free vibration analysis of linear, uniform geometrically coupled beams, including Rotary Inertia (RI) effect, is addressed. A Galerkin-based FEM formulation is then presented where the frequency dependent basis functions (of the approximation space) are chosen to be the closed-form solutions of the uncoupled ODEs governing the beam bending and torsion. The beam displacements are then interpolated using the resulting shape functions and the nodal variables. The implementation of the Principle of Virtual Work then leads to the frequency dependent element matrices. The resulting nonlinear eigenvalue problem is then solved using a dedicated root counting technique and based on the Sturm sequence properties of the element Dynamic Stiffness Matrix (DSM). The application of the theory is illustrated for a semi-circular cross section beam where the influence of RI on the natural frequencies is demonstrated by numerical results. Since the DFE formulation leads to very high convergence rates, it can be considered as a ‘Mesh Reduction’ method.

Date received: March 5, 2004

Copyright © 2004 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # canw-00.