Oscillatory Instability Research Articles

Shimmy Suppression of an Aircraft Nose Landing Gear Using Torsional Nonlinear Energy Sink

Abstract Shimmy motion may occur for an aircraft nose landing gear (NLG) during its takeoff, landing, and taxiing procedure, which is an undesirable motion and should be suppressed. Here, a novel torsional nonlinear energy sink (NES) based on the cam-roller mechanism is proposed and applied in the NLG to improve its shimmy performance. The torsional NES is connected with the upper and lower struts of the NLG and its mechanical characteristic is studied. A seven-dimensional dynamic model of the NLG coupled with NES is built, which considers the NLG torsional and lateral motions, and the nonlinear tire model. The numerical continuation method is applied to analyze its shimmy performance, the stable area and limit cycle oscillation (LCO) amplitude are acquired, further compared with those of the original NLG without using the NES. The results show that as the NES is used in the NLG, the torsional shimmy dominated unstable area reduces significantly and the lateral shimmy dominated unstable area decreases slightly, which results in the increase of the stable area of the NLG; the maximum LCO amplitudes for the NLG torsional and lateral shimmy become smaller, the forward speed ranges as the torsional and lateral shimmy occur become narrower, which indicates that the stable forward speed ranges of the NLG become wider; the NLG shimmy performance improves as the NES has larger torsional inertia and damping, and smaller torsional linear stiffness. Thus, the NES can suppress the NLG shimmy motion and enhance its shimmy performance effectively.

The dynamics of imperfectly supported hanging pipes conveying fluid: An experimental study

An experimental investigation was conducted to examine the effect of imperfection in the clamping of cantilevered pipes discharging or aspirating fluid. Interest in fluid-conveying cantilevered pipes stems not only from their capability to display rich dynamical behaviour but also from their presence in industrial applications; in the latter, geometric imperfections allowing for translational and rotational motions at their supported end may well be present. Six cases were studied, with three of them involving water-discharging pipes surrounded by air and three involving water-aspirating pipes submerged in water. The discharging pipe cases studied involved (i) a perfectly supported cantilevered pipe, while cases (ii) and (iii) utilized imperfectly supported pipes with the positive clamping replaced by a short flexible rubber tube, which allowed non-zero lateral and rotational motion at the clamped end. Cases (iv) – (vi) of the cantilevered aspirating pipes were analogous to those of the discharging pipes, but the pipes were submerged in water. Imperfectly supported discharging pipes developed larger static deformations, leading to a static instability, prior to the onset of oscillatory instability. Imperfect cantilevered aspirating pipes behaved similarly. However, the source of the increased static deformation for the imperfectly hanging discharging pipes appeared to be related to added translational motion, whilst for imperfectly supported aspirating pipes the increased static deformation was mainly due to rotation at the support.

Equilibria and oscillations in cheat-cooperator dynamics.

Cooperative societies can be threatened by cheats, who invest less in cooperation and exploit the contributions of others. The impact of cheats depends on the extent to which they are maintained in the population. However, different empirical studies, across organisms ranging from RNA replicators to bacteria, have shown diverse cheat-cooperator dynamics. These vary from approaching a stable equilibrium to dynamic cyclical oscillations. The reason for this variation remains unclear. Here, we develop a theoretical model to identify the factors that determine whether dynamics should tend toward stable equilibria or cyclical oscillations. Our analyses show that (1) a combination of both periodic population bottlenecks and density-dependent selection on cheating is required to produce cyclical oscillations and (2) the extent of frequency-dependent selection for cheating can influence the amplitude of these oscillations but does not lead to oscillations alone. Furthermore, we show that stochastic group formation (demographic stochasticity) can generate different forms of oscillation, over a longer time scale, across growth cycles. Our results provide experimentally testable hypotheses for the processes underlying cheat-cooperator dynamics.

The stable and unstable oscillations of a rod attached to many springs

The oscillation equations of a multi-spring system connected to a rod are developed. Oscillations can be stable or unstable depending on the distribution of the spring constant and the number of springs. The symmetrical spring distribution with respect to the rod center tends to stabilize. The system becomes more stable as the number of springs increases. The equations of motion are identified to satisfy the Mathieu’s equation. The system could be thought of as a rough imitation of the crazy bamboo attraction, a traditional attraction by old civilization that is frequently associated with the mystical phenomenon. One spring represents one performer. The behavior of the performer’s force (opposite to the direction of the bamboo movement and providing a stronger force as the displacement of the bamboo increases) is similar to that of the spring force.

110 MW thin-disk oscillator.

A compact Kerr-lens mode-locked thin-disk oscillator reproducibly delivering 110 MW output peak power, the highest among all oscillators, is reported. This simple and stable femtosecond oscillator delivering a unique combination of high average power (202 W) and peak power, is an ideal driver and an important milestone for the development of extreme ultraviolet transportable frequency comb sources.

Dynamics of cavitating tip vortex

The three-dimensional dynamic behaviour of a tip vortex generated by a NACA $66_2$ -415 hydrofoil is investigated under wetted flow and cavitating conditions using time-resolved tomographic particle image velocimetry. Two main cavitation modes are studied, namely the breathing and double-helical modes. The time-averaged flow field consists of a system of two streamwise vortices for all three conditions. The shape of the tip vortex resembles that of the cavitation mode, instead of a circular cylinder. Multi-scale vortical structures are captured in the instantaneous flow field. The surface oscillation of the cavity contributes to the growth of Kelvin–Helmholtz instability over the tip vortex, leading to the onset of hairpin vortices. Stronger spanwise interaction between the tip vortex and flow separation of the hydrofoil is produced by cavitation, further intensifying the perturbation growth. The proper orthogonal decomposition analysis gives insight into the relationship between cavity oscillation and vortex instability. Two major types of unstable modes of the tip vortex are obtained, leading to serpentine centreline displacement and elliptical deformation motion. The selection of the dominant unstable mode is associated with cavity surface oscillation. For the wetted flow condition, the displacement mode dominates the growth of vortex perturbation, while for breathing mode cavitation, the most energetic unstable mode changes into an elliptical deformation pattern, the disturbance energy of which is negligible in the wetted flow condition. Consistency is found between the peak frequency of the deformation mode and the cavity resonance frequency, indicating the contribution of cavity oscillation to the disturbance growth and breakdown of the tip vortex.

Coupled instabilities drive quasiperiodic order-disorder transitions in Faraday waves.

We present an experimental study of quasiperiodic transitions between a highly ordered square-lattice pattern and a disordered, defect-riddled state, in a circular Faraday system. We show that the transition is driven initially by a long-wave amplitude modulation instability, which excites the oscillatory transition phase instability, leading to the formation of dislocations in the Faraday lattice. The appearance of dislocations dampens amplitude modulations, which prevents further defects from being created and allows the system to relax back to its ordered state. The process then repeats itself in a quasiperiodic manner. Our experiments reveal an unexpected mechanism for temporal quasiperiodicity that results from a coupling between two distinct instabilities on the route to chaos.

Oscillation Suppression Strategy of Three-Phase Four-Wire Grid-Connected Inverter in Weak Power Grid

As the penetration of renewable energy increases year by year, the risk of high-frequency oscillation instability increases when a three-phase, four-wire split capacitor inverter (TFSCI) is connected to the grid with complementary capacitors in weak grids. Compared to the three-phase, three-wire inverter, the TFSCI has an additional zero-sequence current loop. To improve the accuracy of the modeling and stability analysis, the effect of the zero-sequence loop needs to be considered in the impedance-based stability analysis. Therefore, a correlation model considering multi-perturbation variables is first established, based on which the inverter positive, negative, and zero sequence admittance models are derived, solving the difficult problem of impedance modeling under small perturbations. Secondly, an admittance remodeling strategy based on a negative third-order differential element and a second-order generalized integrator (SOGI) damping controller is proposed, which can improve the stability of positive, negative, and zero-sequence systems simultaneously. Finally, the effectiveness of the oscillation suppression strategy is verified by simulation and experiment.

A Q-Band CMOS Image-Rejection Receiver Integrated with LO and Frequency Dividers

This paper presents a Q-band image-rejection receiver using a 65 nm CMOS technology. For a high image-rejection ratio (IMRR), the Q-band receiver employs the Hartley architecture which consists of a Q-band low-noise amplifier, two down-conversion mixers, a 90° hybrid coupler, and two IF baluns. In addition, a Q-band fundamental voltage-controlled oscillator (VCO) and a frequency divider chain divided by 256 are integrated into the receiver for LO. A charge injection technique is employed in the mixers to reduce the DC power while maintaining a high conversion gain and linearity. The VCO adopts a cross-coupled topology to secure stable oscillation with high output power in the Q-band. The frequency divider chain is composed of an injection-locked frequency divider (ILFD) and a multi-stage current-mode logic (CML) divider to achieve a high division ratio of 256, which facilitates the LO signal locking to an external phase-locked loop. An inductive peaking is employed in the ILFD to widen the locking range. The Q-band image-rejection receiver exhibits a peak conversion gain of 16.4 dB at 43 GHz. The IMRR is no less than 35.6 dBc at the IF frequencies from 1.5 to 5 GHz.

Transverse mode instability in fiber laser oscillators.

What we believe to be a first theoretical study of transverse mode instability (TMI) in oscillators based on a stimulated thermal Rayleigh scattering (STRS) model is conducted. Higher order mode (HOM) lasing is found to happen at high powers. Further fundamental mode (FM) growth is limited once HOM lasing takes place, with further increase of pump power mostly going to HOM growth, a fundamentally different phenomenon from that in fiber amplifiers. TMI thresholds defined as when the HOM lasing condition is met is studied. The results are consistent with the measured TMI thresholds and their dependence on pumping configurations and pump wavelengths.

Experimental and Kinetic Study on Laminar Burning Velocities of High Ratio Hydrogen Addition to CH4+O2+N2 and NG+O2+N2 Flames

In 2020, energy-related CO2 emissions reached 31.5 Gt, leading to an unprecedented atmospheric CO2 level of 412.5 ppm. Hydrogen blending in natural gas (NG) is a solution for maximizing clean energy utilization and enabling long-distance H2 transport through pipelines. However, insufficient comprehension concerning the combustion characteristics of NG, specifically when blended with a high proportion of hydrogen up to 80%, particularly with minority species, persists. Utilizing the heat flux method at room temperature and 1 atm, this experiment investigated the laminar burning velocities of CH4/NG/H2/air/He flames incorporating minority species, specifically C2H6 and C3H8, within NG. The results point out the regularity of SL enhancement, reaching its maximum at an equivalence ratio of 1.4. Furthermore, the propensity for the enhancement of laminar burning velocity aligned with the observed thermoacoustic oscillation instability during fuel-rich regimes. The experimental findings were contrasted with kinetic simulations, utilizing the GRI 3.0 and San Diego mechanisms to facilitate analysis. The inclusion of H2 augments the chemical reactions within the preheating zone, while the thermal effect from temperature is negligible. Both experimental and simulated results revealed that CH4 and NG with a large proportion of H2 had no difference, no matter whether from a laminar burning velocity or a kinetic analysis aspect.

A Data-Driven approach for oscillatory stability assessment misclassification restriction using Neyman-Pearson umbrella classifiers

With the gradual growth of the scale of power systems, the system operating conditions are becoming increasingly complex, and the requirements for oscillatory stability assessment (OSA) are also increasing. Considering that the misclassification of OSA may lead to serious consequences, this article proposes a data-driven approach to restrict the misclassification of OSA for industrial applications. The approach includes a feature extraction procedure and an OSA model. The former is constructed on the basis of Pearson correlation coefficient (PCC) and partial mutual information (PMI), and the latter is constructed on the basis of the Neyman-Pearson umbrella (NPU) algorithm. In the feature extraction procedure, the relevancies between operating variables and the oscillatory stability indicator (OSI) are detected through PCC and PMI, and the pivotal features highly correlated with the OSI are extracted. In the OSA model, the first category error in OSA can be efficiently restricted by regulating the first category error threshold of the NPU classifiers. Additionally, a process for model updating is designed to enhance the applicability to various operating conditions for the approach. The performance of the OSA approach is verified by a series of tests on a 23-bus system and a practical 1648-bus system.

Experimental and Numerical Nonlinear Stability Analysis of Wings Incorporating Flared Folding Wingtips

Recent studies have considered the use of wings incorporating flared folding wingtips (FFWTs) to enable higher aspect ratios (reducing overall induced drag) while also reducing gust loading and meeting airport operational requirements. This paper presents the first experimental research into the nonlinear dynamic behavior of a wing incorporating an FFWT. Wind-tunnel tests were conducted at a range of velocities below and beyond the linear flutter boundary. The experimental findings are compared with results obtained from continuation and bifurcation analyses on a representative low-fidelity numerical model. The results show that beyond the linear flutter boundary, stable limit cycle oscillations form, which is dependent on the flare angle, are bounded by either geometric or aerodynamic nonlinearities. Also presented is the effect of a wingtip trim tab on the stability boundary of a wing incorporating FFWTs. It is found that the tab angle can significantly alter the stability boundary of the system, indicating that the choice of camber is an important parameter when considering the stability boundary of FFWTs and that a moveable control surface on an FFWT could be used “in flight” to extend the stability boundary of an aircraft.

Stability of mass oscillations in hydropower plants with brook intakes

The need for more energy storage in the transition to a renewable energy system leads to increasing interest in upgrading existing hydropower plants to pumped storage plants. Such upgrades result in stronger hydraulic transients in the tunnel system, including increased mass oscillation amplitudes. In this study, a generalized tunnel system with multiple brook intakes/surge tanks is analysed to assess the influence of the brook intakes on the mass oscillation stability. The variables that are assessed are the number of brook intakes, cross section area, the amount of inflow, and throttling of the brook intakes/surge tanks. The study is carried out using frequency-response analysis, where the excitation is the oscillation of the guide vane position, and the response is the product of the measured head and discharge (equivalent to the hydraulic power). The results show that brook intakes are generally beneficial for the stability of the mass oscillations. Existing hydropower plants with brook intakes may have sufficient stability margins to allow upgrade and reconstruction without the need for upgrading of the surge tank with regard to mass oscillation stability.

Simple criterion for evaluating stability of hydraulic oscillation based on water-hammer reflection coefficients

Hydraulic oscillation is a fluctuating phenomenon of pressure and discharge in pipes, which can threaten the safety of hydropower, pumping and water conveyance systems. To analyse the associated problems, new methods with simple form and clear physics are needed. This paper presents a water-hammer reflection coefficient-based criterion for stability evaluation of free-vibration of hydraulic systems. The stability (or attenuation) condition for a single pipe system is that the modulus of the product of the reflection coefficients at the inlet and outlet should be smaller than 1. For a complex pipe system, the condition necessary for stability is that every single pipe system is stable. To apply this new criterion to stabilizing the reservoir-single pipe-constant power turbine system by adding a head loss valve in the pipe, a formula for the critical head loss is proposed and verified. This new method is theoretically consistent with conventional methods, but more convenient in application.

On the rising and sinking motion of bouncing oil drops in strongly stratified liquids

When an immiscible oil drop is immersed in a stably stratified ethanol–water mixture, the Marangoni flow on the surface of the drop can experience an oscillatory instability, so that the drop undergoes a transition from levitating to bouncing. The onset of the instability and its mechanisms have been studied previously (Li et al., Phys. Rev. Lett., vol. 126, 2021, 124502; Li et al., J. Fluid Mech., vol. 932, 2022, A11), yet the bouncing motion of the drop itself, which is a completely different problem, has not yet been investigated. Here we study how the bouncing characteristics (jumping height, rising and sinking time) depend on the control parameters (drop radius, stratification strength, drop viscosity). We first record experimentally the bouncing trajectories of drops of different viscosities in different stratifications. Then a simplified dynamical analysis is performed to get the scaling relations of the jumping height and the rising and sinking times. The rising and sinking time scales are found to depend on the drag coefficient $C_D^S$ of the drop in the stratified liquid, which is determined empirically for the current parameter space (Zhang et al., J. Fluid Mech., vol. 875, 2019, 622–656). For low-viscosity (5 cSt) oil drops, the results on the drag coefficient match those from the literature (Yick et al., J. Fluid Mech., vol. 632, 2009, pp. 49–68; Candelier et al., J. Fluid Mech., vol. 749, 2014, pp. 184–200). For high-viscosity (100 cSt) oil drops, the parameter space had not been explored and the drag coefficients are not readily available. Numerical simulations are therefore performed to provide external verification for the drag coefficients, which well match with the experimental results.

Electrohydrodynamic instability in dielectric rotating Oldroydian nanofluid layer

The influence of rheology on the initiation of thermal convection in a rotating nanofluid layer heated beneath with the inclusion of a vertical alternating current (AC) electric field is studied by employing linear stability analysis in which bounding surfaces are taken as stress-free. The stationary and oscillatory convective stability of the rheological nanofluid is customarily established utilizing the Buongiorno model for nanoparticles and the Oldroyd model for the rheological behaviour of the regular fluid. The Buongiorno model deployed for nanofluids incorporates the impact of thermophoresis and the Brownian motion. The eigen-value problem is solved for exact solutions analytically by using single term Galerkin technique and the expressions of the thermal Rayleigh number for the start of both stationary and oscillatory convection for both bottom-heavy and top-heavy nanoparticles configuration are obtained and are presented graphically.

The Frequency Spectrum Analysis of Wideband Oscillations of Grid-Connected Voltage Source Converter

With the widespread application of voltage source converters (VSCs) in power systems with high renewable resource penetration, the problem of wideband oscillations caused by interactions between power converters and the power grid has drawn great attention. This paper presents a new methodology for simplifying the mathematical derivations of the impedance model of a VSC. Using the new simplified model, the stability and spectrum characteristics of the performance of the VSC can be clearly analyzed. The proposed second-order d-q impedance model of a grid-connected VSC in the presence of a PLL not only mathematically demonstrates that wideband oscillatory modes always occur in conjugate pairs, but also delivers a clear vision of the physical essence of these wideband oscillations. A classic modal analysis is executed in this paper to demonstrate the stability and frequency spectral characteristics of wideband oscillations in a VSC integrated system. The impact of the control parameters of the VSC on wideband oscillatory stability is thoroughly analyzed by modal analysis using ‘DIgSILENT PowerFactory’ as well as hardware-in-the-loop experiments. This methodology can be considered a powerful tool for the control design of VSCs in the modern power system.

Numerical study on the nonlinear characteristics of shock induced two-dimensional panel flutter in inviscid flow

For an aeroelastic system of a two-dimensional elastic panel subjected to an impinging inviscid oblique shockwave, the nonlinear flutter characteristics are affected by many factors such as shock impingement location, cavity pressure and initial perturbation. The effects of the above factors on the variation of system bifurcation type and dynamic behaviors are investigated numerically. A low-fidelity computational method coupled with local piston theory and van Karman plate model, and a high-fidelity computational method coupled with Euler equations and finite element model are used for fluid-structure interaction simulations. Two sets of new findings are unveiled. First, either the variation of shock impingement location or cavity pressure can induce the aeroelastic system to transition between a subcritical bifurcation and a supercritical bifurcation. For some cases, the system bifurcation characteristics exhibit strong sensitivity to these two factors. Second, it is found that in addition to the limit cycle oscillation in the form of a combination of the second and third structural modes, multiple stable limit cycle oscillations due to the coupling of higher-order modes can be triggered by suitable initial perturbations. These limit cycle oscillations have high frequencies and amplitudes, which suggest a higher risk of structural fatigue failure.

The dynamics of corruption under an optional external supervision service

External supervision services play an important role in combating corruption by detecting potential collusive bribery. This work aims at studying the dynamics of collusive bribery when participants have the option of engaging the external supervision services. To do so, we construct a basic model where collusive bribery can happen between the defecting participants who aim to escape from a punishment by offering a bribe to rule enforcers who monitor interactions among all participants. Among rule enforcers, only the corrupt ones accept the bribe and ignore the violations. The cooperative participants can engage the external supervision service at a certain cost to avoid the risk of potential collusive bribery. Under the framework of evolutionary game theory, we find that a higher initial fraction of honest enforcers is more likely to lead to a trusting cooperating equilibrium. We also find that, when allowing random exploration of available strategies, increasing the exploration rate of rule enforcers is effective in combating corruption for both infinite and finite populations. Lastly, we find that minimizing the cost of external supervision services is not always good. When the system evolves into a cooperating equilibrium, a low cost of external supervision service induces unnecessary costs of seeking external supervision. When the strategy profiles exhibit stable oscillations, there exists an optimal cost of external supervision, considering the trade-off between minimizing the chance of exposing cooperative participants to collusive bribery and strengthening the punishment on the corrupt enforcers. Premised on the results, we discuss practical management suggestions.