Reduced-order modeling and solution method for nonlinear frequency response analysis of large space truss structures

• Published in: Nonlinear dynamics 2024-06, Vol.112 (12), p.10127-10145
• Main Authors: Liu, Fushou, Jin, Dongping, Li, Xinyuan, Wei, Guo
• Format: Article
• Language: English
• Subjects: Algorithms; Automotive Engineering; Civil engineering; Classical Mechanics; Complex variables; Continuation methods; Control; Dynamical Systems; Engineering; Equivalence; Finite element method; Frequency analysis; Frequency response; Harmonic response; Mathematical models; Mechanical Engineering; Methods; Nonlinear response; Nonlinearity; Original Paper; Stiffness; Time response; Trussed structures; Vibration; Vibration damping
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-024-09572-1

This study presented a comprehensive reduced-order modeling and solution method for multi-harmonic nonlinear frequency response analysis of large space truss structures with nonlinear joints. In the modeling method, the multi-harmonic describing function method was used to obtain the equivalent linearized model of the nonlinear joint, then a condensed two-node hybrid element model considering the high-order harmonic response was derived for the truss member with two nonlinear joints at its ends, at last the condensed truss model and the equivalent beam model were established for the truss structures. In the solution method, the application of the arc-length continuation method on solution of the nonlinear frequency responses of large space truss structures was elaborated in detail, and the modification of the formulas in the arc-length method and the bordering algorithm for solving nonlinear algebraic equation system with complex variables was presented for the first time. In the numerical studies, a planar truss structure with rotational nonlinear joints and a spatial truss structure with axial nonlinear joints were studied, the cubic stiffness model and piece-wise linear stiffness model were used for modeling the joint nonlinearity. The influences of joint parameters and excitation amplitude, as well as the closely spaced modes, the coupling vibration, and the damping on the frequency response of the truss structures were investigated. The correctness of the presented method was verified by the time response evaluated by the nonlinear finite element model of the original truss structure established in ANSYS.