Modal analysis of assumed-mode models of a flexible slewing beam

This paper compares the performances of different shape function-based models with respect to their ability to accurately represent the dynamic and the static behaviour of a flexible rotating beam. Several assumed-modes are compared, namely, the eigenfunctions of a rotating beam, the eigenfunctions of a clamped-payload beam, the eigenfunctions of a clamped-free beam, the polynomial functions, the cubic splines and the cubic B-splines. A systematic and detailed comparison of the eigenvalues, the eigenmodes and their derivatives and the static deformations and their derivatives is performed on a slewing beam in the vertical plane. Load parameters are changed from their nominal values to test for the sensitivity of the shape functions based models. The comparisons show that: (1) clamped-free eigenfunctions are mostly inadequate; (2) clamped-payload eigenfunctions are good candidates even when the payload parameters are changed; (3) compared to the clamped-payload eigenfunctions, the additional complexity of the rotating beam eigenfunctions does not improve the results; (4) polynomial functions are very attractive but are too sensitive to system parameters variations and (5) overall, the cubic splines using curvatures as generalised coordinates offer the best compromise between good precision and low calculation complexity.