Instability Phenomena Research Articles

An energy method for the bifurcation analysis of necking

Necking is an instability phenomenon widely observed in metallic and polymeric materials. On the basis of the minimum energy barrier criterion, we propose a theoretical method, combined with Monte Carlo simulations, to predict the linear instability and post-bifurcation behavior of materials with a non-convex constitutive law. For illustration, this method is applied to analyze the necking bifurcation behavior of a plate under uniaxial tension. Especially, we consider the effect of surface tension, which is important for the necking of polymeric materials. For soft materials with high surface energy, surface effects may greatly influence the morphological evolution of necking, such as the position and wavenumber of the consecutive necking zones. This work not only helps understand various necking phenomena in biological and engineering materials, but also can be extended to analyze some other instability problems, e.g., surface wrinkling.

Instability phenomena of lean hydrogen/oxygen/inert-gas premixed flames on a flat burner

Instability phenomena of lean hydrogen/oxygen/inert-gas premixed flames on a flat burner

Analysis of membrane instability with a two-parameter extended system

Membrane instability typically exhibits small wavelength compared to the structural size, which often leads to numerical difficulties in computational efficiency and convergence problem. Recently, the Fourier-based reduced technique that is similar to the famous Ginzburg–Landau equation has shown the potential to overcome these difficulties. However, the wrinkling wavelength, an internal parameter, should be defined a priori, and how to determine it is still questionable. In this paper, we propose a two-parameter extended system attempting to lift this restriction. In this system, a Fourier-based reduced model with the wavelength as the second path-control parameter is firstly established, and then augmented by appending a constraint equation that characterizes the critical state (i.e., bifurcation point). The resulting critical equilibrium path, where the bifurcation points and the corresponding buckling modes depend on the wavelength, is tracked by the pseudo-arclength algorithm. Numerical results show that the proposed system is able to correctly and efficiently predict the wrinkling wavelength and buckling behavior of the membrane. This study could be extended to other similar models (e.g., amplitude equations) that characterize instability phenomena with internal parameters.

Global buckling and wrinkling of variable angle tow composite sandwich plates by a modified extended high-order sandwich plate theory

The advanced Automated Fibre Placement (AFP) manufacturing technologies make the synthesis of Variable Angle Tow (VAT) composites, which enable the design of lightweight sandwich structures to possess variable stiffness facesheets. However, both global and local instability phenomena of VAT sandwich plates under in-plane compressive loads are rarely explored till now. The objective of this article is to fill this gap by developing a Rayleigh–Ritz procedure based on a modified extended high-order sandwich plate theory (EHSAPT). The original two-dimensional EHSAPT proposed by Phan et al. (2012) is extended to a three-dimensional case with a minor modification that the first-order shear deformation theory instead of the classical Kirchhoff–Love hypothesis is adopted for each facesheet, which brings several merits such as the conciseness in derivation process and the easiness in program implementation. The Rayleigh–Ritz approach combined with the principle of minimum potential energy is employed to derive the eigenvalue equation that governs the instability problem of VAT sandwich plates under in-plane compressive loads. Both global buckling and wrinkling patterns of VAT sandwich plates can be captured under this proposed analytical model framework. Before instability analysis, the nonuniform prebuckling stresses over the entire sandwich plate are determined under the assumption of membrane prebuckling state. The usage of Lagrange multiplier method in the prebuckling regime removes the restrictions inherent in conventional Rayleigh–Ritz formulation and thus provides a general way to model in-plane boundary conditions. The accuracy and effectiveness of the developed Rayleigh–Ritz procedure are validated by comparing with previously published results and FE solutions given by ABAQUS. Effects of core thickness, core orthotropy, and fibre orientation angle of the facesheets on the instability behaviour of VAT sandwich plates are investigated. Finally, the mechanism of steering the fibre trajectory over the facesheets to improve the buckling resistance for the sandwich plate is studied and discussed.

Nation-wide mapping and classification of ground deformation phenomena through the spatial clustering of P-SBAS InSAR measurements: Italy case study

The rising availability of satellite-based multi-temporal interferometric datasets covering large areas of the Earth surface constitutes a huge asset in the context of operational workflows aimed at improving land risk assessment and management. In order to cost-effectively handle huge amount of data, we design a semi-automatic procedure to quickly identify, map and inventory ground and infrastructures displacements by means of spatial clustering performed over very large-scale Differential Synthetic Aperture Radar Interferometry (DInSAR) datasets. The detected deforming areas are then evaluated against the Line of Sight (LOS) velocity vector decomposition and the accessible ancillary layers for a preliminary classification of the triggering factors. We apply our methodology to the mean ascending and descending deformation maps covering the whole Italian territory resulting from 3294 and 2868 Sentinel-1 (S1) acquisitions respectively, spanning from March 2015 to December 2018 and processed through the Parallel Small BAseline Subset (P-SBAS) technique. By setting a displacement rate threshold of ± 1 cm/year, a total number of 14,638 areas resulting from both geometries are found to suffer from instability phenomena, the origin of which are in turn preliminary sorted in 11 classes split between natural causes and man-made activities. With 2 degrees of confidence, we classified landslide and subsidence events as the main causes of deformation within the Italian territory, constituting respectively 31% and 27% of the total unstable areas, followed by volcanic-related processes (22%). Lastly, we provide a complete overview of the deformation phenomena which have recently occurred on the Italian Peninsula starting from national scale statistical analysis and ending up with local scale investigations according to the deformation patterns visible through the vertical and East-West components of motion.

Method of experimentally identifying the complex mode shape of the self-excited oscillation of a cantilevered pipe conveying fluid

The dynamics of a flexible cantilevered pipe conveying fluid have been researched for several decades. It is known that the flexible pipe undergoes self-excited vibration when the flow speed exceeds a critical speed. This instability phenomenon is caused by nonconservative forces. From a mathematical point of view, the system has a characteristic of non-selfadjointness and the linear eigenmodes can be complex and non-orthogonal to each other. As a result, such a mathematical feature of the system is directly related to the instability phenomenon. In this study, we propose a method of experimentally identifying the complex mode from experimentally obtained time histories and decomposing the linear mode into real and imaginary components. In nonlinear analysis, we show that the nonlinear effects of practical systems on the mode in the steady-state self-excited oscillation are small. The real and imaginary components identified using the proposed method for experimental steady-state self-excited oscillations are compared with those obtained in the theoretical analysis, thus validating the proposed identification method.

Numerical investigation of mode competition and cooperation on the combustion instability in a non-premixed combustor

The phenomena of combustion instabilities beyond limit cycles caused by the nonlinear interaction of various instability modes have recently received much attention. This paper numerically studied the mode competition and cooperation phenomena in the liquid rocket engines when combustion instabilities occur. The liquid rocket engine with the single-element structure is the focus of the present work, and the numerical model is developed employing the Large Eddy Simulation technology, with the complete conservation Navier-Stokes equations taken into account. The results first reveal the relationship between the acoustic mode and the intrinsic vorticity mode: the competition and cooperation between the two will result in the complex dynamic process, such as semi-stable oscillation and intermittency. What's more, a more detailed coupling process between intrinsic vortex shedding and acoustic oscillation is analyzed, indicating existence of four stability regimes in the liquid rocket engines and an important insight into combustion instability in non-premixed dump combustors is provided.

Resonantly enhanced polariton wave mixing and parametric instability in a Floquet medium.

We introduce a new theoretical approach for analyzing pump and probe experiments in non-linear systems of optical phonons. In our approach, the effect of coherently pumped polaritons is modeled as providing time-periodic modulation of the system parameters. Within this framework, propagation of the probe pulse is described by the Floquet version of Maxwell's equations and leads to phenomena such as frequency mixing and resonant parametric production of polariton pairs. We analyze light reflection from a slab of insulating material with a strongly excited phonon-polariton mode and obtain analytic expressions for the frequency-dependent reflection coefficient for the probe pulse. Our results are in agreement with recent experiments by Cartella et al. [Proc. Natl. Acad. Sci. U. S. A. 115, 12148 (2018)], which demonstrated light amplification in a resonantly excited SiC insulator. We show that, beyond a critical pumping strength, such systems should exhibit Floquet parametric instability, which corresponds to resonant scattering of pump polaritons into pairs of finite momentum polaritons. We find that the parametric instability should be achievable in SiC using current experimental techniques and discuss its signatures, including the non-analytic frequency dependence of the reflection coefficient and the probe pulse afterglow. We discuss possible applications of the parametric instability phenomenon and suggest that similar types of instabilities can be present in other photoexcited non-linear systems.

An alternative form of energy density demonstrating the severe strain-stiffening in thin spherical and cylindrical shells

The present article investigates an elastic instability phenomenon for internally pressurized spherical thin balloons and thin cylindrical tubes composed of incompressible hyperelastic material. A mathematical model is formulated by proposing a new strain energy density function. In the family of limited elastic materials, many material models exhibit strain-stiffening. However, they fail to predict severe strain-stiffening in a moderate range of deformations in the stress-strain relations. The proposed energy function contains three material parameters and shows substantially improved stain stiffening properties than the limited elastic material models. The model is further applied to explore the elastic instability phenomenon in spherical and cylindrical shells. The findings are compared with other existing models and validated with experimental results. The model shows better agreement with experimental results and exhibits a substantial strain-stiffening effect than the current models.

Numerical modelling of concrete-filled aluminium alloy 6082-T6 columns under axial compression

Aluminium alloys are characterised by numerous benefits, such as ease of fabrication, good strength-to-weight ratio, attractive appearance and high corrosion resistance. On the other hand, aluminium has low Young’s Modulus and as a result, it is susceptible to structural instability phenomena that can subsequently affect the structural integrity. Improved strength and stiffness can be achieved by combining aluminium alloys with concrete. The present work investigates numerically the response of concrete-filled aluminium tubular members under axial compression. In particular, 6082-T6 extruded aluminium alloy rectangular and square hollow sections filled with C30 concrete are examined. Finite element models are developed accounting for geometric and material non-linearities. Upon validation against experimental data, the finite element models are used to conduct a thorough parametric study over a wide range of structural members likely to occur in practice to investigate their structural behaviour under axial compression. The obtained load capacities are discussed and remarks on the structural response and on the buckling behaviour are reported. Design recommendations for the buckling strength of concrete-filled aluminium tubular columns on the basis of the numerical analyses are also made.

Machine-learning Algorithms Based on Time-series Data for Real-time Classification of Nuclear Fusion Plasmas in KSTAR

A high confinement mode (H-mode)1) was selected as one of the basic operation scenarios of ITER.2) The H-mode is a phenomenon in which the plasma confinement performance suddenly increases because a transport barrier is formed near the plasma boundary. However, although there are advantages obtained in the H-mode, instabilities at the plasma boundary also appear, such as edge localized modes (ELMs). The problem with the ELMs is that the transport barrier periodically collapses (ELM crash). As a result, high temperature energy and particles are released, damaging the plasma-facing components. Therefore, various studies for controlling the ELMs are continuously conducted in various tokamak devices worldwide. The most effective method to prevent ELM crashes is resonant magnetic perturbation (RMP). Also, the most problematic phenomenon among various instability phenomena of plasma, including the ELMs, is plasma disruption.3) The disruption is a phenomenon in which the plasma inside the tokamak loses heat and electromagnetic energy very quickly and disappears. This sudden energy loss induces a considerable heat flux to the plasma-facing components. Furthermore, it applies a strong electromagnetic force to the surrounding conductor to damage the tokamak device, so it is an unstable phenomenon that must be resolved.

Stability Phenomena Associated with the Development of Polymer-Based Nanopesticides.

Pesticides have been used in agricultural activity for decades because they represent the first defense against pathogens, harmful insects, and parasitic weeds. Conventional pesticides are commonly employed at high dosages to prevent their loss and degradation, guaranteeing effectiveness; however, this results in a large waste of resources and significant environmental pollution. In this regard, the search for biocompatible, biodegradable, and responsive materials has received greater attention in the last years to achieve the obtention of an efficient and green pesticide formulation. Nanotechnology is a useful tool to design and develop “nanopesticides” that limit pest degradation and ensure a controlled release using a lower concentration than the conventional methods. Besides different types of nanoparticles, polymeric nanocarriers represent the most promising group of nanomaterials to improve the agrochemicals' sustainability due to polymers' intrinsic properties. Polymeric nanoparticles are biocompatible, biodegradable, and suitable for chemical surface modification, making them attractive for pesticide delivery. This review summarizes the current use of synthetic and natural polymer-based nanopesticides, discussing their characteristics and their most common design shapes. Furthermore, we approached the instability phenomena in polymer-based nanopesticides and strategies to avoid it. Finally, we discussed the environmental risks and future challenges of polymeric nanopesticides to present a comprehensive analysis of this type of nanosystem.

Fouling Behavior and Dispersion Stability of Nanoparticle-Based Refrigeration Fluid

Nanofluids as heat transfer fluids have been acquiring popularity ever since their beginning. Therefore, the refrigeration research could not keep itself away from the ever-rising horizon of nanofluid applications. On the other hand, nanofluid stability remains the critical bottleneck for use. A significant reduction in nanofluids’ performance can derivate from instability phenomena. Looking to industrial applications, nanofluid long-term stability and reusability are crucial requisites. Nanoparticles’ deposits induce microchannel circuit obstruction, limiting the proper functioning of the device and negating the beneficial characteristics of the nanofluid. The aggregation and sedimentation of the particles may also determine the increased viscosity and pumping cost, and reduced thermal properties. So, there is a need to address the features of nanofluid starting from realization, evaluation, stabilization methods, and operational aspects. In this review, investigations of nanorefrigerants are summarized. In particular, a description of the preparation procedures of nanofluids was reported, followed by a deep elucidation of the mechanism of nanofluid destabilization and sedimentation, and finally, the literature results in this field were reviewed.

Post-cracking regimes in the flexural behaviour of fibre-reinforced concrete beams

The flexural behaviour of steel fibre-reinforced concrete beams is discussed in the framework of Fracture Mechanics. The Bridged Crack Model is updated by means of a cohesive softening constitutive law of the reinforcement layers, taking into account the fibre slippage within the cementitious matrix. In this way, the model is able to describe the global response of the composite, including the local instability phenomena characterizing the different post-cracking regimes. The structural response is found to be governed by two dimensionless numbers: the reinforcement brittleness number, NP, which defines the minimum reinforcement condition of the composite beam, and the pull-out brittleness number, Nw, which describes its plastic rotation capacity. The former, NP = (Vfσ¯sh1/2)/KIC, depends on the fibre volume fraction, Vf, on the fibre slippage strength, σ¯s, on the concrete fracture toughness, KIC, and on the beam depth, h. The latter, Nw = (wcE)/(KICh1/2), depends on the fibre embedment length, wc, on the concrete Young’s Modulus, E, on the concrete fracture toughness, KIC, and on the beam depth, h. These two parameters make it possible to identify a softening post-cracking response of the fibre-reinforced concrete element that is scale-dependent. Finally, the numerical analyses are compared to several experimental results reported in the scientific literature, proving the effectiveness of the described model.

Dynamic Interactions of Multiple Wall-Mounted Flexible Plates in a Laminar Boundary Layer

The interactions between large arrays of wall-mounted flexible plates and oncoming laminar boundary-layer flows are studied numerically by using the immersed boundary method. The influences of bending rigidity, mass ratio and gap distance between adjacent plates on the dynamic behaviors are explored. With the variation of control parameters, five distinct dynamic modes, namely, static reconfiguration, sectional waving, regular waving, upright oscillation and cavity oscillation, are identified. The frequency lock-in phenomenon and various types of flow instability associated with different dynamic modes are discussed. The findings of this study indicate that the coherent motions of the arrays are governed by a coupled mechanism in which the frequency of flow instability is locked onto the structural natural frequency.

Superradiance evolution of black hole shadows revisited

Black hole (BH) shadows can be used to probe new physics in the form of ultra-light particles via the phenomenon of superradiant instability. By directly affecting the BH mass and spin, superradiance can lead to a time evolution of the BH shadow, which nonetheless has been argued to be unobservable through Very Long Baseline Interferometry (VLBI) over realistic observation timescales. We revisit the superradiance-induced BH shadow evolution including the competing effects of gas accretion and gravitational wave (GW) emission and, as a first step towards modelling realistic new physics scenarios which predict the existence of multiple ultra-light species, we study the system in the presence of two ultra-light bosons, whose combined effect could help reducing the shadow evolution timescale. We find that accretion and GW emission play a negligible role in our results (justifying previous simplified analyses), and that contrary to our intuition the inclusion of an additional ultra-light boson does not shorten the BH shadow evolution timescale and hence improve detection prospects. However, we point out an important subtlety concerning the observationally meaningful definition of the superradiance-induced BH shadow evolution timescale, which reduces the latter by about an order of magnitude, opening up the possibility of observing the superradiance-induced BH shadow evolution with upcoming VLBI arrays, provided angular resolutions just below the $\mu{\rm as}$ level can be reached. As a concrete example, we show that the angular size of the shadow of SgrA$^*$ can change by up to $0.6\,\mu{\rm as}$ over a period as short as $16$ years, which further strengthens the scientific case for targeting the shadow of SgrA$^*$ with next-generation VLBI arrays.

Eigenvalue analysis of SARS-CoV-2 viral load data: illustration for eight COVID-19 patients.

Eigenvalue analysis is an important tool in economics and nonlinear physics to analyze industrial processes and instability phenomena, respectively. A model-based eigenvalue analysis of viral load data from eight symptomatic COVID-19 patients was conducted. The eigenvalues and eigenvectors of the instabilities were determined that give rise to COVID-19. For all eight patients, it was found that the virus dynamics followed the unstable eigenvectors until the viral load reached the respective peak values. At the peak virus values, the virus dynamics branched off from the directions specified by the eigenvectors. The temporal course of the unstable eigenvalues was determined as well. For all patients, it was found that the eigenvalues switched from positive to negative values just when the virus load reached peak values. These findings suggest that the fixed, instability-related eigenvalues and eigenvectors determine initial stages of SARS-CoV-2 infections during which virus load increases. In contrast, the time-dependent eigenvalues show a sign-switching phenomenon that indicates when the virus dynamics switches from the growth stage (increasing virus load) to the decay stage (decreasing virus load). The virus dynamics model was a standard three-variable virus dynamics model frequently used in the literature.

Accurate Modeling of PLL With Frequency-Adaptive Prefilter: On the Positive Feedback Effect

Phase locked loops (PLLs) with frequency-adaptive prefilters could suppress input disturbances and thus are widely studied. However, their accurate models are absent in the literature. In particular, the impact of frequency adaption (FA) is underestimated. This letter proposes the accurate and analytical modeling method with focus on the impact of frequency adaption, by taking the PLL based on dual second-order generalized integrator (DSOGI) as an example. The proposed model can precisely describe the transient behaviors of DSOGI-PLL, especially the couplings among amplitude, phase angle, and frequency. Moreover, it reveals that the FA creates a positive feedback path, which is the essential reason for the instability phenomenon and the key factor limiting the PLL performance. Experimental results have verified the accuracy of the proposed model.

Effect of pulsating flow on mild / deep surge phenomena of turbocharger compressor

Abstract It is known that a compressor causes a flow instability phenomenon called surge when the flow rate becomes reduced. Previous studies performed a compressor performance test using an apparatus that simulated a turbocharger for cars. As a result, they have confirmed that surge frequencies differ depending on the capacity of the tank. In this study, performance tests of a compressor for a turbocharger were conducted to understand a mechanism of surge phenomena and to understand differences between them under the steady flow and the pulsating flow. The apparatus which was used at this time consists of a compressor, a pulsating flow generator, a tank, and a valve. Except for the compressor, they install on the downstream side of it in this apparatus. The pulsating flow generator and the tank are equivalent to an automobile engine. First, to understand the difference between the mild surge and the deep surge under steady flow, the flow rate and the pressure of the tank were measured by controlling the valve under five different rotational speeds. And the two types of surge phenomena (i.e. the mild surge and the deep surge) were determined. Compared to the mild surge and the deep surge, it was judged that the former has smaller fluctuations of the flow rate and weaker surge phenomena. And, Fast Fourier Transform (FFT) analysis was performed on the measured pressure. It was found that the higher the rotation speed became, the lower the surge frequencies of the deep surge were, and the lower the rotation speed became, the weaker the strength of the surge phenomenon became. Next, it was investigated the difference in surge frequencies between the mild surge and the deep surge under pulsating flow with the rotation speed fixed. It was found that in the mild surge, the effect of pulsating flow on the surge phenomenon was significant, and it was confirmed that the surge frequencies were drawn into the pulsating frequencies. On the other hand, in the deep surge, the pressure fluctuation of the surge phenomenon became stronger than that of the mild surge, and a pattern of drawing was changed. In addition, unlike the mild surge, in the deep surge, the frequency range of draw in the same magnification between the given pulsating frequency and the obtained surge frequency narrowed. And, it was confirmed that the surge frequency was drawn into the pulsating frequency at half times rate and two times rate.

Instability attenuation and bifurcation studies of a non-ideal rotor involving time-delayed feedback

In non-ideal vibratory system, the excitation is a nonlinear function of system response. The dynamic behavior of such system is often characterized by an energy source with limited power. The study of instability phenomena in non-ideal rotor driven through a non-ideal energy source is of considerable current interest. The non-ideal rotor system often gets destabilized on exceeding a critical input power near the resonance. This kind of instability is termed as Sommerfeld effect marked with nonlinear jump phenomena. This paper investigates the attenuation of nonlinear jump phenomena and numerical study of bifurcations of a non-ideal unbalanced rotor system with internal damping using time-delayed feedback via active magnetic bearings. The results show that the time delay indeed plays a critical role on the suppression of the jump phenomena. Following, some new insights are also revealed through a numerical study of saddle node, Hopf and trans-critical bifurcations with time delay as a bifurcation parameter. The transient analysis confirms the results obtained analytically through the steady-state consideration.