A One-Dimensional Dynamic Model for a Thin-Walled U-Shaped Boom Segment Considering Cross-Section Deformation

Abstract

This article presents a one-dimensional dynamic model for a thin-walled U-shaped telescopic crane boom segment, considering cross-section deformation, to address complex and inefficient dynamic modeling issues. The symmetric U-shaped cross-section provides a uniform distribution of mass and stress, enhancing the beam’s stability and bending stiffness. This symmetry allows for a simplified analysis in dynamic modeling, reducing the number of variables that need to be considered. The cross-section deformation is captured by basis functions satisfying displacement continuity conditions, which lays the foundation for constructing the initial model formulation based on the Hamilton principle. The variation forms of the cross-section are obtained by the decoupling eigenvalue problem, and then the principal component analysis is carried out to identify major cross-section deformation. The identified cross-section deformation features are hierarchically structured and have real physical significance. Finally, the initial one-dimensional higher-order dynamics model is improved by using the identified deformation mode. Numerical examples are presented in order to validate the three-dimensional dynamic properties and transient dynamic behavior of the U-shaped boom segment. The proposed model demonstrated high accuracy compared to ANSYS models, with relative errors below 2%. In addition, the method can be widely applied to a thin-walled U-shaped boom segment with a slenderness ratio of more than four.