Geometrically nonlinear transient analysis of a rotating beam structure carrying a static payload

This paper presents a nonlinear finite element method for the transient dynamic analysis of a rotating flexible beam carrying a static payload. The proposed method incorporates several new features to enhance computational efficiency and modeling accuracy for nonlinear transient dynamic analysis. The method makes use of the Lagrange formulation in homogeneous coordinates. This allows the element matrices and nodal forces to be obtained by matrix operations supported by symbolic manipulators. The exact nonlinear stiffness is derived and implemented as opposed to the conventional iterative approximation. This results in a computational scheme that has fast convergence and high accuracy. A time separation concept is introduced to allow time independent terms to be coputed separately and assembled into system equations with time dependent terms in each integration time step. The proposed modeling procedure is systematic and can be accomplished with a symbolic program. A rotating steel beam problem is used to test for accuracy and to measure the effects of the spin-up speed and the payload on gyroscopic inertia, geometric nonlinearity and system dynamics.