Dynamic modeling and simulation of flexible beam finite rotation with ANCF method and FFR method
Keywords: ANCF, FFR, small deformation, split-iteration
AbstractIn this paper, a method of modeling and simulatingflexible beam finite rotation is investigated. Based on theassumptions of low speed and small deformation, theANCF method is regarded as a finite element interpolationmethod to obtain the constant mass matrix of the flexiblebeam; the local coordinate system in the ANCF method isconsidered the floating coordinate system, and thestiffness matrix independent of the generalizedcoordinates is obtained. The split-iteration method is usedto expand the generalized coordinates that are notcontained in the constraint equations to the 2nd -orderTaylor series of the generalized coordinates that arecontained in the constraint equations and the Lagrangemultipliers. The nonlinear constraint equations arelinearized to the 1st -order Taylor series of the generalizedcoordinates. Then, the generalized coordinates andLagrange multipliers can be solved quickly. The resultsshow that the dynamic equations can be effectivelysimplified by combining the ANCF method with the FFRmethod for the small-deformation problems. Thelow-order Taylor approximation of generalizedcoordinates in both the dynamic equations and constrainedequations does not lose substantial computationalaccuracy but can significantly reduce computational time.The results of this investigation have important referencevalues for dynamic analysis of cranes, aerial workplatforms, and other engineering equipment.
DYNAMICS OF MECHANICAL SYSTEMS