Dynamic Modeling and Simulation of Flexible Beam Finite Rotation with ANCF Method and FFR Method

In this paper, a method of modeling and simulating flexible beam finite rotation is investigated. Based on the assumptions of low speed and small deformation, the ANCF method is regarded as a finite element interpolation method to obtain the constant mass matrix of the flexible beam; the local coordinate system in the ANCF method is considered the floating coordinate system, and the stiffness matrix independent of the generalized coordinates is obtained. The split-iteration method is used to expand the generalized coordinates that are not contained in the constraint equations to the 2nd-order Taylor series of the generalized coordinates that are contained in the constraint equations and the Lagrange multipliers. The nonlinear constraint equations are linearized to the 1st-order Taylor series of the generalized coordinates. Then, the generalized coordinates and Lagrange multipliers can be solved quickly. The results show that the dynamic equations can be effectively simplified by combining the ANCF method with the FFR method for the small-deformation problems. The low-order Taylor approximation of generalized coordinates in both the dynamic equations and constrained equations does not lose substantial computational accuracy but can significantly reduce computational time. The results of this investigation have important reference values for dynamic analysis of cranes, aerial work platforms, and other engineering equipment.