A New Trajectory Reversing Method for Estimating Stability Regions of Autonomous Nonlinear Systems

A new method is presented for estimating regions of asymptoticstability for autonomous nonlinear dynamical systems. The underlyinganalysis uses a combination of Lyapunov theory, simulation and sometopological properties of the stability boundary. The advantages of themethod are the accuracy of estimation of the true stability boundary,its numerical robustness and its applicability to wide classes ofdynamical systems. The main limitation is that a global Lyapunovfunction for the system must be available.     

Performance measures for targeted energy transfer and resonance capture cascading in nonlinear energy sinks

In vibrating mechanical systems, the targeted energy transfer mechanism (TET) of nonlinear energy sinks (NES) is employed as an alternative to linear tuned mass dampers (TMD) as passive vibrations absorbers for transient vibrations. The major advantages a NES has over a linear TMD are (1) an increased robustness to detuning and (2) the ability to dissipate multiple frequencies with only a single NES through so-called resonance capture cascading (RCC). The performance, especially the speed, of TET and RCC has rarely been a topic of research. In this research, algebraic performance measures for the speed of both TET and RCC are derived, called the pumping time and the cascading time, respectively. It shows that cascading time can be seen as a sum of single-mode pumping times, by introducing a novel modal decomposition. The strength of both measures is that they do not require numerical simulations, allowing easy optimization of the NES. The influence of different nonlinearities on the TET and RCC performance is investigated. Actual numerical simulations presented in the study validate the merit of both the pumping time and cascading time.     

The energy thresholds of nonlinear vibration absorbers

A popular means to mitigate excessive structural vibrations is the attachment of a lightweight spring-mass element, known as a vibration absorber or tuned mass damper. Designing new types of vibration absorbers that outperform the classical linear tuned mass damper is a challenging ongoing research field. This paper focuses on the absorber with a strongly nonlinear spring characteristic. A critical aspect in the design procedure of such nonlinear vibration absorber is the existence of energy thresholds below which no efficient vibration reduction is possible. This paper extends the concept of an energy threshold to a more general parameter threshold representing several threshold values. Two important contributions are obtained. First, one single bifurcation analysis covers every combination of the system parameters. Second, the results are generalized to linear main systems under impulsive load and harmonic load, nonlinear main systems, and general nonlinear spring characteristics.     

Torsional vibrations of wet clutches: influence of mechanical parameters

Using a small scale test-rig a number of experiments were performed in which the imposed disk velocity v _disk, the different mechanical parameters of the test-rig (damping c and tangential stiffness k), and normal load were varied independently.     

Crack identification method in beam-like structures using changes in experimentally measured frequencies and Particle Swarm Optimization

In this paper, a technique is presented for the detection and localization of an open crack in beam-like structures using experimentally measured natural frequencies and the Particle Swarm Optimization (PSO) method. The technique considers the variation in local flexibility near the crack. The natural frequencies of a cracked beam are determined experimentally and numerically using the Finite Element Method (FEM). The optimization algorithm is programmed in MATLAB. The algorithm is used to estimate the location and severity of a crack by minimizing the differences between measured and calculated frequencies. The method is verified using experimentally measured data on a cantilever steel beam. The Fourier transform is adopted to improve the frequency resolution. The results demonstrate the good accuracy of the proposed technique.     

External damping losses in measuring the vibration damping properties in lightly damped specimens using transient time-domain methods

The contaminating effect of external damping sources to the overall measured damping of mechanical structures has always been an issue. Although these sources are qualitatively known, they are often not considered if damping properties are experimentally determined, yielding erroneous results. The aim of this paper is to quantify some of these undesired effects on the overall measured damping value. Free vibrations of steel plate specimens are used to list up several causes of external damping sources. As small modifications to the test setup may lead to totally different results, appropriate actions are offered to design a more accurate test setup. Known observations, such as the damping value’s dependence on the specimen size and the excitation level, are confirmed. Finally, it is shown that the damping capacity of one type of steel alloy can usually not be generalised to other steel alloys.     

An application of Liapunov''s method for the analysis of neural networks

The stability is studied of a class of nonlinear dynamical systems which possess many nonlinearities and many equilibrium states. As a special case, the analyzed class of systems includes analog neural networks. Sufficient conditions for the nonoscillatory behaviour of these systems, in the form of frequency domain criteria, are presented. The main result is proved relying on a suitable Liapunov function which is subsequently used for the simultaneous computation of regions of attraction for each stable equilibrium.