Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
Study of the first mode of vibration of transmission line cables via Rayleigh’s method and elastic line equation
Submission Author:
Alexandre de Macêdo Wahrhaftig , BA , Brazil
Co-Authors:
Alexandre de Macêdo Wahrhaftig, Iago Gonçalves de Oliveira, Rodrigo Oliveira da Silva Conceição , Cibele Mota Menezes, Eduardo Márcio de Oliveira Lopes, Kevin Mauricio Menon Ribeiro, Gabriel do Amaral, José Manoel Balthazar
Presenter: Cibele Mota Menezes
doi://10.26678/ABCM.COBEM2023.COB2023-0454
Abstract
Throughout their useful life, overhead cables of power transmission lines and communication lines are subjected to climatic conditions whose effects are capable of activating their vibration modes. The study of the vibration of these cables is a relevant topic for the Brazilian and world industry. The first mode is considered of particular importance, because it is especially influenced by the initial deformed configuration of the cable when subjected to the acceleration of gravity. Under these conditions, the initial configuration is subordinated to the geometric and material properties of the element itself, potentially including its viscoelastic behavior. Therefore, it is legitimate to infer that these mechanical systems are intrinsically non-linear, both from a geometric and material point of view. Cables are extraordinarily slender and eminently flexible structural elements by their own nature, reason why their balance can only be found in the deformed configuration. The magnitude of the traction force to which they are subjected in operation modifies their natural frequencies by introducing the portion of geometric stiffness into the total stiffness of the system. In determining these frequencies, analytical models are particularly desired because they are traditional processes in the field of mathematical analysis. In this sense, the main aspect of this work is the proposition of an analytical solution for the first natural mode of vibration that considers the traction in the cable and the eventual viscoelasticity of the material. The elaboration of this solution is based on the Rayleigh method. In a first approach, the approximate elastic line equation is considered as a shape function, which, in the second approach, is replaced by the exact equation. In this case, it is imperative to use numerical methods to solve the differential equations based on the boundary conditions of the problem. The validation of the analytical solution is done in comparison with modal analysis, of non-linear characteristics, from computational modeling based on the finite element method. The object of study is a cable of 18.30 mm in diameter, 13.285 m long, subjected to a tension of 15.86 kN.
Keywords
Cables, Transmission lines, Rayleigh’s Method, Elastic line equations, Analytical Solution, Finite Element Method, Viscoelastic behavior
