Jump bifurcation phenomenon during varying wind speeds in floating offshore wind turbines

Floating Offshore Wind Turbines (FOWTs) are susceptible to an instability which has come to be called negative damping. Conventional land based wind turbine controllers when used with FOWTs may cause large amplitude platform pitch oscillations. Most controllers have since been improved to reduce motions due to this phenomenon. In this paper, the motions induced using one of the original controllers is studied. The current study is performed using the coupled time domain program FAST-SIMDYN that was developed in Marine Dynamics Laboratory (MDL) at Texas A&M University. It is capable of studying large amplitude motions of Floating Offshore Wind Turbines. FOWTs use various controller algorithms of operation based on the available wind speed depending on various power output objectives i.e., to either maximize or level out power absorption. It is observed that the transition region for controllers is often chaotic. So most studies focus on operations away from the transition region below and above the transition wind speeds. Here we study the transition region using the theoretical insight of non-linear motion response of structures. This study reveals the presence of a very interesting and potentially hazardous nonlinear phenomenon, bifurcation. This finding could help explain the chaotic motion response that is observed in the transition region of controllers. Understanding the nature and cause of bifurcation could prove very useful for future design of FOWT controllers.

Negative self-feedback induces enhancement and transition of spiking activity for class 3 excitability

Post-inhibitory rebound (PIR) spike, which has been widely observed in diverse nervous systems with different physiological functions and simulated in theoretical models with class 2 excitability, presents a counterintuitive nonlinear phenomenon in that the inhibitory effect can facilitate neural firing behavior. In this study, a PIR spike induced by inhibitory stimulation from the resting state corresponding to class 3 excitability that is not related to bifurcation is simulated in the Morris-Lecar neuron. Additionally, the inhibitory self-feedback mediated by an autapse with time delay can evoke tonic/repetitive spiking from phasic/transient spiking. The dynamical mechanism for the PIR spike and the tonic/repetitive spiking is acquired with the phase plane analysis and the shape of the quasi-separatrix curve. The result extends the counterintuitive phenomenon induced by inhibition to class 3 excitability, which presents a potential function of inhibitory autapse and class 3 neuron in many neuronal systems such as the auditory system.

Maintaining Constant Pulse-Duration in Highly Dispersive Media Using Nonlinear Potentials

A method is shown for preventing temporal broadening of ultrafast optical pulses in highly dispersive and fluctuating media for arbitrary signal-pulse profiles. Pulse pairs, consisting of a strong-field control-pulse and a weak-field signal-pulse, co-propagate, whereby the specific profile of the strong-field pulse precisely compensates for the dispersive phase in the weak pulse. A numerical example is presented in an optical system consisting of both resonant and gain dispersive effects. Here, we show signal-pulses that do not temporally broaden across a vast propagation distance, even in the presence of dispersion that fluctuates several orders of magnitude and in sign (for example, within a material resonance) across the pulse’s bandwidth. Another numerical example is presented in normal dispersion telecom fiber, where the length at which an ultrafast pulse does not have significant temporal broadening is extended by at least a factor of 10. Our approach can be used in the design of dispersion-less fiber links and navigating pulses in turbulent dispersive media. Furthermore, we illustrate the potential of using cross-phase modulation to compensate for dispersive effects on a signal-pulse and fill the gap in the current understanding of this nonlinear phenomenon.

Nonlinear thermal vibration of a nanoplate attached to a cavity

Dynamic problems of a nanocircular plate-cavity system are investigated using molecular dynamics (MD) method. A nonlinear plate model considering gas action is developed. The results of the MD simulation show that the helium atoms adsorb on the wall of the cavity at low temperature, resulting in a negative deflection of the molybdenum disulfide (MoS2) plate. As the temperature increases, the pressure in the cavity increases, leading to a gradual rise in the deflection of the plate. A nonlinear phenomenon of stiffness hardening is shown with increasing temperature. The nonlinear plate model can give a relatively good prediction compared with the results of MD simulations. The natural frequency of the plate is affected by temperature and the presence of gas in the cavity. The phenomenon of stiffness hardening and softening can be well simulated by the nonlinear plate model and MD method. The present study provides a reference for vibration experiments of two-dimensional nanostructures.

Influence of Selected Non-Ideal Aspects on Active and Reactive Power MRAS for Stator and Rotor Resistance Estimation

Mathematical models of induction motor (IM) used in direct field-oriented control (DFOC) strategies are characterized by parametrization resulting from the IM equivalent circuit and model-type selection. The parameter inaccuracy causes DFOC detuning, which deteriorates the drive performance. Therefore, many methods for parameter adaptation were developed in the literature. One class of algorithms, popular due to their simplicity, includes estimators based on the model reference adaptive system (MRAS). Their main disadvantage is the dependence on other machines’ parameters. However, although typically not considered in the respective literature, there are other aspects that impair the performance of the MRAS estimators. These include, but are not limited to, the nonlinear phenomenon of iron losses, the effect of necessary discretization of the algorithms and selection of the sampling time, and the influence of the supply inverter nonlinear behavior. Therefore, this paper aims to study the effect of the above-mentioned negative aspects on the performance of selected MRAS estimators: active and reactive power MRAS for the stator and rotor resistance estimation. Furthermore, improved reduced-order models and MRAS estimators that consider the iron loss phenomenon are also presented to examine the iron loss influence. Another merit of this paper is that it shows clearly and in one place how DFOC, with the included effect of iron losses and inverter nonlinearities, can be modeled using simulation tools. The modeling of the IM and DFOC takes place in MATLAB/Simulink environment.

Investigation of the nonlinear phenomena of a Langevin ultrasonic transducer caused by high applied voltage

In the field of power ultrasound, Langevin ultrasonic transducers (LUTs) usually operate at a large displacements output power by applying high voltages. However, empirically, a LUT exhibits nonlinearities such as amplitude jumping and peak hysteresis for high voltages in actual operations. The nonlinearities would reduce the efficiency and output accuracy of an LUT. In this research, the burst-mode method was used to measure the longitudinal vibration velocity of the LUT, which gradually decreased with time after the excitation voltage was turned off. The equivalent mechanical losses and equivalent spring constants were determined using the velocity attenuation rate and resonant frequency and they were found to be the linear functions of velocity, helping to develop a novel nonlinear model. This model contained two quadratic nonlinear terms based on the linear model. Furthermore, the developed nonlinear model was analyzed using the Lagrangian method as well as the multiscale method, which confirmed that the model was effective in describing the nonlinear behavior. It was also found that the frequency-amplitude curve bent when the nonlinear term was taken into account, which resembled the nonlinear phenomenon tested experimentally. From a physical point of view, this bending was meaningful because it led to the formation of multi-valued response regions with jumping phenomena. Additionally, according to the obtained results, the maximum value of the system response was independent of the degree of nonlinearity of the system.

Effects of Weakly Nonlinear Waves on Acoustic Scattering from the Ocean Surface

The elevation of ocean waves is always modeled in linear theory as a superposition of the sinusoidal components with crests and troughs of identical heights. However, under some circumstances, the wave amplitude is outside the linear range and presents as a weakly nonlinear asymmetrical waveform with sharper crests and shallower troughs. We studied the impact of the weakly nonlinear effect of ocean waves in deep and intermediate waters on acoustic scattering from the surface of the ocean using two rough surface models with fractal geometry and power law spectral behavior in the equilibrium range. The classic Weierstrass–Mandelbrot function was used to model the linear waves and a new fractal function, the fractional Weierstrass function developed in studies of electromagnetism, was used to model the weakly nonlinear waves. We evaluated these two models using the Pierson–Moskowitz spectrum and the incident wavelength. The bistatic scattering strength was obtained via a numerical method based on the “exact” solution of the integral equation. The weakly nonlinear phenomenon led to a very small reduction in the narrow area around the specular reflection angle and a small increase in the remaining wide area, including the backpropagation area with a scattering angle [Formula: see text]. The differences in backscattering strength between the two models were similar to the bistatic scattering strength in the backpropagation area and did not depend on the incident grazing angle.

Mid-Infrared Ultra-Short Pulse Generation in a Gas-Filled Hollow-Core Photonic Crystal Fiber Pumped by Two-Color Pulses

We show numerically that ultra-short pulses can be generated in the mid-infrared when a gas filled hollow-core fiber is pumped by a fundamental pulse and its second harmonic. The generation process originates from a cascaded nonlinear phenomenon starting from a spectral broadening of the two pulses followed by an induced phase-matched four wave-mixing lying in the mid-infrared combined with a dispersive wave. By selecting this mid-infrared band with a spectral filter, we demonstrate the generation of ultra-short 60 fs pulses at a 3–4 µm band and a pulse duration of 20 fs can be reached with an additional phase compensator.