Investigation on the Nonlinear Vibration Characteristics of Current-Carrying Crescent Iced Conductors under Aerodynamic Forces, Ampere’s Forces, and Forced Excitation Conditions

Aiming at the problem of nonlinear vibration of current-carrying iced conductors, the aerodynamic forces are introduced into the previous vibration equation of current-carrying conductors that only considered Ampere’s forces. At the same time, on this basis, a forced excitation load is further introduced to study the influence of dynamic wind on the nonlinear vibration characteristics of current-carrying iced conductors, and a new current-carrying iced conductors system under the combined action of Ampere’s forces, forced excitation, and aerodynamic forces has been established, and the improved theoretical modeling of current-carrying iced transmission lines made the model more in line with practical engineering. Firstly, the model of current-carrying iced conductors was established, and then the vibration equation of the model was derived. And the vibration equation was transformed into a finite dimensional ordinary differential equation by using the Galerkin method. The amplitude-frequency response functions of the nonlinear forced primary resonances and super-harmonic and subharmonic resonances of the system are derived by using the multiscale method. Through numerical calculation, the influence of current-carrying, spacing, wind velocity, tension, and excitation amplitude on the response amplitude when the primary resonance of the system appears is analyzed, and the difference between the two working conditions (considering the aerodynamic forces and without considering aerodynamic forces) is compared. The influence of the variation of current-carrying i on the response amplitude of super-harmonic and subharmonic resonances and the stability of the steady-state solution of forced primary resonance was analyzed. The results show that the response amplitude and the nonlinearilty of system under the action of aerodynamic forces are smaller and weaker than without the action of aerodynamic forces; the variation of line parameters has a certain influence on the response amplitude of conductor and the nonlinearity of system; the response amplitudes of the primary resonance, super-harmonic resonance, and subharmonic resonance increase with the increase in the excitation amplitudes, and the resonance peak is offset towards the negative value of the tuning parameter σ, showing the characteristics of soft spring, and the response amplitudes are accompanied by complex nonlinear dynamic behaviors such as the multivalue and jump phenomenon. The change of current-carrying i has an obvious effect on the nonlinearity of the system. The nonlinear and response amplitudes of the system are also enhanced with the increase in wind velocity. The stability of the system is judged when the primary resonance occurs, and it is found that the response amplitude shows synchronization and the out-of-step phenomenon with the change of tuning parameters. The research results obtained in this paper would help to further improve the theoretical modeling about current-carrying iced lines, and the research of line parameters can give a certain reference value to practical engineering, and it will have a positive effect on the safe operation of high-voltage transmission lines.

Non-Synchronous Vibration and Lock-in Regimes in Coupled Structures Using Reduced Models

The contribution is aimed at phenomenological modelling and analysis of fundamental properties of non-synchronous vibrations in chosen coupled structures. A van der Pol reduced-order model is employed to simulate the aero-elastic interaction between flexible bodies and fluid. Non-synchronous vibration and frequency lock-in, along with hysteresis, are captured in the main resonance area. Moreover, the model reveals subharmonic resonances accompanied by the existence of unstable solutions and frequency lock-in. The study is further extended to investigate the dynamical behaviour of a coupled cyclic structure, where different modes of vibration due to the aero-elastic interaction are analysed.

Bifurcations in a Pre-Stressed, Harmonically Excited, Vibro-Impact Oscillator at Subharmonic Resonances

This study investigates the behavior of a damped, inelastic, sinusoidally forced impact oscillator which has its barrier placed such that the oscillator always vibrates under compression about its subharmonic resonant frequencies. The Poincaré sections at near subharmonic resonance conditions exhibit finger-shaped chaotic attractors, similar to the strange attractor mapping of Hénon and the ones found by Holmes in his study of chaotic resonances of a buckled beam. The number of such fingers are observed to increase as the barrier distance from the equilibrium is decreased. These chaotic states are interspersed with regimes of periodic behavior, with the periodicity being in accordance with well defined period adding laws. This study also focuses on the ordered behavior of the one-impact period-[Formula: see text] orbits around the higher subharmonics of the oscillator.

Asymmetric Large Deformation Superharmonic and Subharmonic Resonances of Spiral Stiffened Imperfect FG Cylindrical Shells Resting on Generalized Nonlinear Viscoelastic Foundations

This paper is devoted to superharmonic and subharmonic behavior investigation of imperfect functionally graded (FG) cylindrical shells with external FG spiral stiffeners under large amplitude excitations. The structure is embedded within a generalized nonlinear viscoelastic foundation, which is composed of a two-parameter Winkler–Pasternak foundation augmented by a Kelvin–Voigt viscoelastic model with a nonlinear cubic stiffness, to account for the vibration hardening/softening phenomena and damping considerations. The von Kármán strain-displacement kinematic nonlinearity is employed in the constitutive laws of the shell and stiffeners. The external spiral stiffeners of the cylindrical shell are modeled according to the smeared stiffener technique. The coupled governing equations are solved by using Galerkin’s method in conjunction with the stress function concept. The multiple scales method is utilized to detect the subharmonic and superharmonic resonances and the frequency–amplitude relations of the 1/3 and 1/2 subharmonic and 3/1 and 2/1 superharmonic resonances of the system. Finally, the influences of the stiffeners helical angles, foundation type, coefficient of the nonlinear elastic foundation, material distribution, and excitation amplitude on the system resonances are investigated comprehensively.

Superharmonic and Subharmonic Resonances of Spiral Stiffened Functionally Graded Cylindrical Shells under Harmonic Excitation

This paper presents the superharmonic and subharmonic resonances of spiral stiffened functionally graded (SSFG) cylindrical shells under harmonic excitation. The stiffeners are considered to be externally or internally added to the shell. Also, it is assumed that the material properties of the stiffeners are continuously graded in the thickness direction. In order to model the stiffeners, the smeared stiffener technique is used. Within the context of the classical plate theory of shells, the von Kármán nonlinear equations are derived for the shell and stiffeners based on Hooke’s law and the relations of stress-strain. Using Galerkin’s method, the equation of motion is discretized. The superharmonic and subharmonic resonances are analyzed by the method of multiple scales. The influence of the material parameters and various geometrical properties on the superharmonic and subharmonic resonances of SSFG cylindrical shells is investigated. Considering these results, the hardening nonlinearity behavior and jump value of cylindrical shell is less and more than others, when the angle of stiffeners is [Formula: see text] and [Formula: see text], respectively.

Coexistence of Subharmonic Resonant Modes Obeying a Period-Adding Rule

We report numerical evidence of a novel chain of subharmonic resonances organized in period-adding domains in the parameter space. Different periodic domains are mediated by a coexisting main subharmonic motion according to a hierarchical organization rule. We consider the driven bilinear oscillator — which is the simplest system to model a range of engineering systems going from cracked mechanical structures to switching electronic circuits — and show that its parameter space is marked by multistability involving subharmonic main modes, as well as period-adding secondary modes which, through a period-doubling route, lead to coexisting chaotic attractors.