Nonlinear finite element modeling of a high speed rotating timoshenko beam structure

The demand for designing high speed turbomachinery has led to intensive research in dynamic modeling of rotating elastic mechanisms in recent years. Such a demand in the design arena is usually addressed by better computational schemes. A nonlinear finite element modeling scheme is presented in this paper to address this demand. The proposed modeling scheme incorporates three new features to improve computational accuracy and efficiency. First, the rotating beam is modeled as a Timoshenko beam with the inclusion of gyroscopic inertia and geometric stiffness. The geometric stiffness is modeled with exact tangent matrix as opposed to conventional pseudo-tangent matrix approximation. Second, the time separation concept is introduced to allow time-independent terms being computed separately and assembled with time-dependent terms in each integration time step. This separation concept is applicable to both linear and nonlinear time-independent terms. Third, the computational scheme is formulated in homogeneous coordinates that provide a natural and efficient vector representation for dynamic modeling of a rotating structure. Kane's classic rotating beam problem is used to test the accuracy and efficiency of the proposed computational scheme. The numerical solution of the present formulation agrees well with that of Simo's. Moreover, the computer time required for the present formulation is reduced by a factor of 70%.