Modal characteristics of sagged-cable-crosstie systems. Part 1: Modeling and validation

• Published in: Applied mathematical modelling 2023-07, Vol.119, p.698-716
• Main Authors: Sun, Ceshi, Jiao, Dewang, Lin, Junqiang, Li, Cong, Tan, Chao
• Format: Article
• Language: English
• Subjects: Crosstie; General model; Modal characteristic; Sagged cable; Vibration mitigation
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2023.03.007

•A general model of sagged-cable-crosstie is established by introducing spatial and temporal nondimensionalization.•The general expression of the characteristic equation’s 2N(M+1)-order coefficient matrix is given for the first time.•A minimal set of fundamental key dimensionless parameters that govern the system’s modal characteristics are intuitively found.•The general model is degenerated into three models and is high-precisely verified by literature and FEM. Though crosstie has become a promising approach for vibration mitigation of long cables, its mechanism is yet to be fully understood, restricting the set of engineering design theory. Scholars worldwide have continuously proposed various mechanical models to investigate modal characteristics of cable-crosstie structures. However, first, dynamic equations were dimensional or not fully dimensionalized, hindering the definition of essential independent key parameters that govern the modal characteristics of the system; second, no general expression of the coefficient matrix in characteristic equations was given. This paper proposes a general sagged-cable-crosstie model applicable to structures with a generic number of cables and crossties. A universal dimensionless dynamic equation is derived by thorough dimensionless treatment, and the universal expression of a 2N(M+1)-order coefficient matrix is obtained by introducing boundary, equilibrium, and continuity conditions. A minimal set of dimensionless parameters that govern modal characteristics of any sagged-cable-crosstie system is found, i.e., crosstie positions εj,p, Irvine parameters of cables λj2, dimensionless wave speed parameters αj, and dimensionless crosstie stiffnesses kj,p. Subsequently, the general model degenerates into three representative models: double-cable-single-crosstie, three-cable-single-crosstie, and double-cable-double crosstie. Frequencies of each degenerated model are compared with that of literature and FEM, and good consistency is obtained.