A hybrid-dimensional modeling method for the vibration of embedding 1D rotation-free beam into 3D solid under rotating scenarios

Abstract

Hybrid-dimensional models are widely used in large-scale engineering machinery. In this paper, a hybrid-dimensional modeling method for the vibration of embedding 1D structures into 3D solids under rotating scenarios is developed. Based on the Nitsche method, a weak coupling strategy is first proposed to improve a rotation-free 1D beam, enhancing its prediction capability for complex geometries. Then, by embedding the improved 1D rotation-free beam into a 3D solid, a weak coupling method capable of considering complex vibration modes is proposed for the hybrid-dimensional problems. Both the 1D and 3D models are discretized within an isogeometric framework. Hamilton's principle is employed to derive the governing equations. The numerical accuracy and efficiency of the proposed approach are investigated in various scenarios and complex geometries, and the influence of the stability parameters, interface lengths, and rotating speeds on the solutions is discussed. The results demonstrate that the proposed method can accurately predict complex vibration modes with small computational scale under suitable stability parameters, different interface lengths, and rotating speeds. The presented method also exhibits the ability to model complex geometrical structures, making it easy to extend to complex rotor systems with multiple flexible irregular disks, shafts and general supports.