Eventos Anais de eventos
COBEM 2021
26th International Congress of Mechanical Engineering
Analysis and Modeling of the Dynamic Behavior of Cylindrical Cables under Transient Excitation
Submission Author:
Marcos Fabrício de Souza Aleixo Filho , DF
Co-Authors:
Marcos Fabrício de Souza Aleixo Filho, Francisco Ricardo Cunha, JOSE ALEXANDER ARAUJO, Remy Kalombo Badibanga
Presenter: Marcos Fabrício de Souza Aleixo Filho
doi://10.26678/ABCM.COBEM2021.COB2021-1627
Abstract
The present work brings a theoretical investigation of vortex-induced vibration, a phenomenon that commonly occurs in cylindrical bodies subjected to wind, such as aerial cables in power transmission lines. Mathematical models are proposed in order to predict the oscillatory motion of a cylindrical cable undergoing a wind current. In this paper we use: (i) a Duffing type model non-linear harmonic oscillator; (ii) a concentrated model of a prototype cylinder suspended by non-linear springs and forcing by a transverse flow; (iii) and the vibrating cylinder cable model. When the nondimensional physical parameter of the oscillatory system is much smaller than unity, a perturbation method provides an asymptotic solution for the prototype cable displacement. An excellent agreement is observed between the asymptotic and numerical solutions based on a standard Runge-Kutta algorithm. A dynamic analysis is presented for the non-linear oscillator by using phase-space diagrams and amplitude-frequency plots, and by exploring the chaotic response of the system for nonlinear regimes with high amplitudes of excitation. In addition, experiments with a real transmission cable undergoing harmonic oscillations are carried out in order to measure the time-response at different longitudinal positions. When adjusting the system parameters of the theoretical model for the real values of the experiments, the non-linear harmonic oscillator successfully fits the experimental data. For appropriate condition of damping and excitation, and after few manipulations, the concentrated cylinder model is seen to be equivalent to the nonlinear harmonic oscillator model. Finally, the vibrating motion of the prototype cylindrical cable is examined for the homogeneous case of an impulse forcing. The results are shown for discrete longitudinal points through the cable, as well as some vibrating modes. From a scaling analysis of the nondimensional second order partial differential governing equation of the cable motion in space-time, the equivalence and consistency between the continuous and the concentrated models are demonstrated. We show that for small values of tensions applied to the cable, the wave propagation velocity is sufficiently small, and consequently the space second derivative along the length of the cable is only a weak contribution, resulting in a concentrated mass-spring-damper system.
Keywords
conductive cables, wind vibration, Von Kárman vortex shedding, perturbation method, concentrated models
