No abstract

Summary Connecting stay cables with cross‐ties is the most promising solution for vibration control of long cables in cable‐stayed bridges. Existing studies have been focusing on the influences of the cross‐tie configurations and properties on the dynamics of the formed cable networks, mostly based on the taut‐string model of cables. However, the cross‐ties are particularly aimed at long cables whose in‐plane vibrations can be significantly affected by the sag effect. This paper therefore presents an analytical method to investigate free in‐plane vibrations of shallow cable networks with cross‐ties, using the linear theory of shallow cables. A two‐shallow‐cable network with one viscoelastic cross‐tie is studied in detail to appreciate the sag effect on the dynamics of the cable network. It is shown that the sag effect couples vibrations of the cable segments divided by the cross‐ties and changes the modal interactions substantially. When the cross‐tie is rigid, curve veering occurs between frequency curves of the system with respect to varying cross‐tie location, as compared with curve intersection in the absence of the sag effect. When the cross‐tie is flexible, generally, mode shapes of the cable segments and the whole cable are not antisymmetric nor symmetric, and the sag then affects nearly all the vibration modes. Furthermore, taking into account the damping effect of the cross‐tie, the frequency loci in the complex plane regarding the increment of cross‐tie damping coefficient can still be categorized by the corresponding undamped and clamped frequencies while the modal interaction becomes more complicated. Quantitatively speaking, when the sag parameter is in the practical range of existing cable‐stayed bridges, the first and second vibration modes of the cable networks are considerably affected and need to be considered for practice.

Isolated backbone curves represent significant dynamic responses of nonlinear systems; however, as they are disconnected from the primary responses, they are challenging to predict and compute. To explore the conditions for the existence of isolated backbone curves, a generalized two-mode system, which is representative of two extensively studied examples, is used. A symmetric two-mass oscillator is initially studied and, as has been previously observed, this exhibits a perfect bifurcation between its backbone curves. As this symmetry is broken, the bifurcation splits to form an isolated backbone curve. Here, it is demonstrated that this perfect bifurcation, indicative of a symmetric structure, may be preserved when the symmetry is broken under certain conditions; these are derived analytically. With the symmetry broken, the second example—a single-mode nonlinear structure with a nonlinear tuned mass damper—is considered. The evolution of the system's backbone curves is investigated in nonlinear parameter space. It is found that this space can be divided into several regions, within which the backbone curves share similar topological features, defining the conditions for the existence of isolated backbone curves. This allows these features to be more easily accounted for, or eliminated, when designing nonlinear systems.

Nonlinear normal modes (NNMs) are a widely used tool for studying nonlinear mechanical systems. The most commonly observed NNMs are synchronous (i.e. single-mode, in-phase and anti-phase NNMs). Additionally, asynchronous NNMs in the form of out-of-unison motion, where the underlying linear modes have a phase difference of 90°, have also been observed. This paper extends these concepts to consider general asynchronous NNMs , where the modes exhibit a phase difference that is not necessarily equal to 90°. A single-mass, 2 d.f. model is firstly used to demonstrate that the out-of-unison NNMs evolve to general asynchronous NNMs with the breaking of the geometrically orthogonal structure of the system. Analytical analysis further reveals that, along with the breaking of the orthogonality, the out-of-unison NNM branches evolve into branches which exhibit amplitude-dependent phase relationships. These NNM branches are introduced here and termed phase-varying backbone curves . To explore this further, a model of a cable, with a support near one end, is used to demonstrate the existence of phase-varying backbone curves (and corresponding general asynchronous NNMs) in a common engineering structure.

In this paper, the novel approach for the rotating machine as diagnosis method in detecting the faults during its operation was proposed based upon the infrared thermograph technique. As experimental works, by performing the test of operation at several lubrication conditions for the ball bearing applied in the rotating machine which there has been used broadly, diagnosis evaluation and fault analysis for temperature distributions provided from infrared thermogrphy were carried out. As results, the local region defect of the bearing to use the infrared thermal image technique was analyzed. Also, it was concluded that the location of the exact crack and size and lubrication condition could be confirmed.