Resonances and bifurcations in systems with elliptical equipotentials

We present a general analysis of the orbit structure of 2D potentials with self-similar elliptical equipotentials by applying the method of Lie transform normalization. We study the most relevant resonances and related bifurcations. We find that the 1:1 resonance is associated only to the appearance of the loops and leads to the destabilization of either one or the other normal modes, depending on the ellipticity of equipotentials. Inclined orbits are never present and may appear only when the equipotentials are heavily deformed. The 1:2 resonance determines the appearance of bananas and anti-banana orbits: the first family is stable and always appears at a lower energy than the second, which is unstable. The bifurcation sequence also produces the variations in the stability character of the major axis orbit and is modified only by very large deformations of the equipotentials. Higher-order resonances appear at intermediate or higher energies and can be described with good accuracy.Comment: Accepted for publication on MNRA

Equivariant singularity analysis of the 2:2 resonance

We present a general analysis of the bifurcation sequences of 2:2 resonant reversible Hamiltonian systems invariant under spatial $\Z_2\times\Z_2$ symmetry. The rich structure of these systems is investigated by a singularity theory approach based on the construction of a universal deformation of the detuned Birkhoff normal form. The thresholds for the bifurcations are computed as asymptotic series also in terms of physical quantities for the original system

Best parameter choice of Stochastic Resonance to enhance fault signature in bearings

Stochastic Resonance (SR) is a phenomenon studied and exploited for telecommunication, which permits the detection and amplification of weak signals by the assistance of noise. The first papers on this topic date back to the early 80s and were developed to explain some periodic natural phenomena. Other applications are in neuroscience, biology, medicine and, obviously, mechanics. Recently, a few researchers have tried to apply this technique for detecting faults in mechanical systems and also bearings. In this paper we discuss the best way to select the parameters to augment the performance of the algorithm. This is probably the main drawback of SR, since in system identification the procedure should be as blind as possible to be efficient and widely applicable. The classical bi-stable potential form is adopted in our study, with three parameters to be selected. Based on numerical tests, a characteristic trend of the amplification factor has been found with respect to the parameters variation, so that a general rule is consequently determined which gives the best performances in terms of detection and amplification. The SR algorithm is tested on both simulated and experimental data showing a good capacity of increasing the signal to noise ratio

A time-varying inertia pendulum: Analytical modelling and experimental identification

In this paper two of the main sources of non-stationary dynamics, namely the time-variability and the presence of nonlinearity, are analysed through the analytical and experimental study of a time-varying inertia pendulum. The pendulum undergoes large swinging amplitudes, so that its equation of motion is definitely nonlinear, and hence becomes a nonlinear time-varying system. The analysis is carried out through two subspace-based techniques for the identification of both the linear time-varying system and the nonlinear system. The flexural and the nonlinear swinging motions of the pendulum are uncoupled and are considered separately: for each of them an analytical model is built for comparisons and the identification procedures are developed. The results demonstrate that a good agreement between the predicted and the identified frequencies can be achieved, for both the considered motions. In particular, the estimates of the swinging frequency are very accurate for the entire domain of possible configurations, in terms of swinging amplitude and mass positio

Nonlinear Dynamics of a Duffing-Like Negative Stiffness Oscillator: Modeling and Experimental Characterization

In this paper, a negative stiffness oscillator is modelled and tested to exploit its nonlinear dynamical characteristics. The oscillator is part of a device designed to improve the current collection quality in railway overhead contact lines, and it acts like an asymmetric double-well Duffing system. Thus, it exhibits two stable equilibrium positions plus an unstable one, and the oscillations can either be bounded around one stable point (small oscillations) or include all the three positions (large oscillations). Depending on the input amplitude, the oscillator can exhibit linear and nonlinear dynamics and chaotic motion as well. Furthermore, its design is asymmetrical, and this plays a key role in its dynamic response, as the two natural frequencies associated with the two stable positions differ from each other. The first purpose of this study is to understand the dynamical behavior of the system in the case of linear and nonlinear oscillations around the two stable points and in the case of large oscillations associated with a chaotic motion. To accomplish this task, the device is mounted on a shaking table and it is driven with several levels of excitations and with both harmonic and random inputs. Finally, the nonlinear coefficients associated with the nonlinearities of the system are identified from the measured data

Fault diagnosis of wind turbine gearboxes through on-site measurements and vibrational signal processing

Condition monitoring of wind turbine gearboxes has attracted an impressive amount of attention in the wind energy literature. This happens for practical issues, as gearbox damages account for at least the 20% of wind turbines operational unavailability, and for scientific issues as well, because the condition monitoring of gear-based mechanical systems undergoing non-stationary operation is particularly challenging. The present work is devoted to the diagnosis of gearbox damages through a novel approach, designed exclusively for this study, based on on-site measurements and data post-processing. The main point of this method is the relatively easy repeatability, also for wind turbine practitioners, and its low impact on wind turbine operation: actually, the measuring site is not the gearbox itself, but the tower, further from the gearbox but in an easily accessible place. A real test case has been considered: a multi mega-watt wind turbine sited in Italy and owned by the Renvico company. The vibration measurements at the wind turbine suspected to be damaged and at a reference wind turbine are processed through a multivariate Novelty Detection algorithm in the feature space. The application of this algorithm is justified by univariate statistical tests on the time-domain features selected and by a visual inspection of the dataset via Principal Component Analysis. Finally, the novelty indices based on such time-domain features, computed from the accelerometric signals acquired inside the turbine tower, prove to be suitable to highlight a damaged condition in the wind-turbine gearbox, which can be then successfully monitored

IL-17 and its role in inflammatory, autoimmune, and oncological skin diseases. State of art

Recent data support the theory of the involvement of IL-17 in the pathogenesis of several chronic inflammatory skin diseases (psoriasis, atopic dermatitis, acne, hidradenitis suppurativa) and autoimmune skin diseases (alopecia areata, vitiligo, bullous diseases). Even if the role of IL-17 in inflammatory and autoimmune diseases has been reported extensively, its role in tumor is still controversial. Some reports show that Th17 cells eradicate tumors, while others reveal that they promote the initiation and early growth of tumors. Herein, we review the role of IL-17 in the involvement of some common dermatologic diseases: psoriasis, atopic dermatitis, hidradenitis suppurativa, acne, vitiligo, melanoma, and nonmelanoma skin cancers