Stability Map Research Articles

Stability and Dynamics of Viscoelastic Moving Rayleigh Beams with an Asymmetrical Distribution of Material Parameters

In this article, vibration of viscoelastic axially functionally graded (AFG) moving Rayleigh and Euler–Bernoulli (EB) beams are investigated and compared, aiming at a performance improvement of translating systems. Additionally, a detailed study is performed to elucidate the influence of various factors, such as the rotary inertia factor and axial gradation of material on the stability borders of the system. The material properties of the beam are distributed linearly or exponentially in the longitudinal direction. The Galerkin procedure and eigenvalue analysis are adopted to acquire the natural frequencies, dynamic configuration, and instability thresholds of the system. Furthermore, an exact analytical expression for the critical velocity of the AFG moving Rayleigh beams is presented. The stability maps and critical velocity contours for various material distributions are examined. In the case of variable density and elastic modulus, it is demonstrated that linear and exponential distributions provide a more stable system, respectively. Furthermore, the results revealed that the decrease of density gradient parameter and the increase of the elastic modulus gradient parameter enhance the natural frequencies and enlarge the instability threshold of the system. Hence, the density and elastic modulus gradients play opposite roles in the dynamic behavior of the system.

On the Vibrations and Stability of Moving Viscoelastic Axially Functionally Graded Nanobeams.

In this article, size-dependent vibrations and the stability of moving viscoelastic axially functionally graded (AFG) nanobeams were investigated numerically and analytically, aiming at the stability enhancement of translating nanosystems. Additionally, a parametric investigation is presented to elucidate the influence of various key factors such as axial gradation of the material, viscosity coefficient, and nonlocal parameter on the stability boundaries of the system. Material characteristics of the system vary smoothly along the axial direction based on a power-law distribution function. Laplace transformation in conjunction with the Galerkin discretization scheme was implemented to obtain the natural frequencies, dynamical configuration, divergence, and flutter instability thresholds of the system. Furthermore, the critical velocity of the system was evaluated analytically. Stability maps of the system were examined, and it can be concluded that the nonlocal effect in the system can be significantly dampened by fine-tuning of axial material distribution. It was demonstrated that AFG materials can profoundly enhance the stability and dynamical response of axially moving nanosystems in comparison to homogeneous materials. The results indicate that for low and high values of the nonlocal parameter, the power index plays an opposite role in the dynamical behavior of the system. Meanwhile, it was shown that the qualitative stability of axially moving nanobeams depends on the effect of viscoelastic properties in the system, while axial grading of material has a significant role in determining the critical velocity and natural frequencies of the system.

Nonlinear dynamics and gust response of a two-dimensional wing

In this paper, aeroelastic equations for a two-dimensional wing encountering a wind gust are presented and solved numerically. The indicial aerodynamic theory based on Wagner’s function is adopted to obtain aerodynamic forces and moments acting on the wing in the time domain. The dynamics of the wing is approximated via two degrees-of-freedom, i.e. pitch and plunge. The structural stiffness is modeled by a linear translational and a nonlinear torsional spring. Two different types of stiffness nonlinearities are examined: (i) flat spot or dead zone to model free-play, and (ii) hysteresis. For given system parameters, bifurcation diagrams are presented, and time-history, power-spectral density, phase-plane and Poincaré diagrams are shown at different flow velocities. We show that the dynamics of the system with the free-play nonlinearity may be very complex with the possibility of the occurrence of chaos through period-doubling bifurcations. In contrast, the dynamics with the hysteresis nonlinearity is found to be rather simple, where a Hopf bifurcation is the only bifurcation observed. The response of the nonlinear system to sharp-edged and 1-cosine gust profiles are also obtained at different flow velocities and compared to the time response of the system with no gust input. It was found that the gust input may cause the nonlinear system to get attracted to a periodic orbit in the subcritical flow regime. In addition, basin of attraction is obtained for various amplitudes of the sharp-edged gust. It is discussed that as the gust becomes stronger, the likelihood of the occurrence of limit-cycle oscillation increases while the stable points become less dispersed inside the stability map and form a finite region confined to large values of initial conditions.

Fabrication of ball-milled MgO–Mg(OH)2-hydromagnesite composites and evaluation as an air-stable hydrogen storage material

A phase stability map of metallic magnesium powder, exposed to environmental conditions for 12 months (Mg-12M) and subjected to different high-energy ball-milling speeds and milling times, was constructed. Mg-12M−160 [½MgO-⅓Mg(OH)2-⅙hydromagnesite] and Mg-12M−640 [¼MgO-⅝Mg(OH)2-⅛hydromagnesite] composites were obtained changing the milling conditions. The correlation among the accumulated energy (ΔEaccum), the impact energy (ΔEhit), and the phase stability under different high-energy ball-milling conditions were generated. The Mg-12M−160 composite had a hydrogen storage capacity of 0.63 wt% at −196 °C and 8.3 bar, although further hydrogen adsorption at higher pressures is expected. Structural defects play a significant role in the adsorption capacity. A representation of the possible absorption mechanism is proposed.

Thermodynamic modelling of polycrystalline multicomponent multiphase metal alloys

The present work explores the thermodynamic stability of multicomponent multiphase polycrystalline metal alloys using a theoretical approach based on the regular solution model. We extend the definition of ‘phase’ to homogeneous bodies of any dimensionality, which allows grain boundaries to take on phase-like, or complexion, properties, with energy and chemical composition different from grain interiors. Accordingly, we examine the possible attainment of structural stability due to grain boundary segregation within the framework of equilibrium thermodynamics, making use of a Gibbs free energy function. We also derive a dimensionless version of the model for greater generality, and to properly compare the factors determining the thermodynamic stability of polycrystalline structures. Model predictions are summarized with the help of suitably defined stability maps and a few case studies concerning binary and ternary alloys are discussed.

Road vehicles travelling with time-dependent speed: theoretical study on the directional stability

In this paper, directional stability of road vehicles travelling at time-dependent forward velocity is investigated. The dynamical behaviour of the system is governed by a set of linear ordinary-differential equations with time-varying coefficients. A simple two degrees of freedom (DOF) model is considered, in order to better understand the effects of such a perturbation on the well-established bicycle model, which is frequently used in the literature as a first approach to get useful physical insights on vehicle dynamics. Numerical simulations show significative differences with respect to the prediction of the stability analysis in the case of constant forward speed. A moderately large variation on the forward velocity, indeed, can stabilise the vehicle which is statically unstable. Stability maps are obtained by means of the Floquet theory, with the aim to shed light on the modified vehicle dynamics. A final discussion is provided, which leads to outline the possible practical applications of the present investigation, together with future comprehensive studies.

Influence of bit design on the stability of a rotary drilling system

This paper extends the RGD model originally proposed by Richard et al. (J Sound Vib 305(3):432–456, 2007, https://doi.org/10.1016/j.jsv.2007.04.015) to investigate drilling-induced vibrations, by considering idealized drag bits characterized either by multiple angular offsets between the blades or by a combination of full and partial blades, a departure from the symmetric bit of the RGD model consisting of multiple continuous blades. The RGD model is built on a two-degrees of freedom discrete representation of the drillstring combined with a rate-independent bit/rock interaction law. By relaxing the original constraints on the bit geometry, the coupled state-dependent delay differential equations governing the angular and axial motions of the bit now contain multiple state-dependent time delays. A linear stability analysis leads to explicit expressions for the critical rotational speed(s) defining two different regimes of stability of the coupled dynamics. Stability maps indicate that both groups of bits have a better axial stability than their RGD counterparts. It is also found that multiple critical rotation speeds exist for certain bit geometries, in contrast to the single axial stability boundary of the original RGD model. Time simulations confirm the predictions of the linear stability analysis and show evidence of the existence of different types of quasi-periodic responses before the establishment of a limit cycle characterized by both axial and torsional stick-slip events.

Landslide Vulnerability Mapping for Landslide Victim Relocation

some victims of landslides must be relocated if the location affected by a landslide impossible to be occupied again. The relocation site of the Sijeruk-Banjarnegara landslide victims had experienced a landslide again, due to the inappropriate location selection. It was necessary to mapping the landslide vulnerability for the selection of relocation sites so that the new location must safe from landslides. Settlements that were still located in the high-risk landslide were as the danger the occupants. The selection of relocation sites must be appropriate and the risk of landslides was low. This study aims to produce a vulnerability landslide map so that land suitability can be obtained for the development of settlements by referring to the threat of landslide hazards. Slope stability modelling uses the TRIGRS (Transient Rainfall Infiltration and Grid-Based Regional Slope-Stability) program version 2.0. The principles are modelling the effect of rainfall on regional slope stability. The data needed in modelling was digital elevation model (DEM), soil data index properties, soil engineering properties, and rainfall. The modelling results show that the safety factor values in the study were ranged from 0.8 to 10. Safe numbers below 1.2 means are prone to landslides. Slope stability map can be used to determine the location of the relocation of landslide victims.

Unstable crop yields reveal opportunities for site-specific adaptations to climate variability

Water deficit and water excess constitute severe stresses that limit crop yield and are likely to intensify as climate becomes more variable. Regional crop production aggregates for the US Midwest indicate widespread yield losses in past decades due to both extreme rainfall and water limited conditions, though the degree to which these weather impacts are related to site-specific factors such as landscape position and soils has not been examined in a systematic manner. This study offers observational evidence from a large sample of commercial crop fields to support the hypothesis that landscape position is the primary mediator of crop yield responses to weather within unstable field zones (i.e., zones where yields tend to fluctuate between high and low, depending on the year). Results indicate that yield losses in unstable zones driven by water excess and deficits occur throughout a wide range of seasonal rainfall, even simultaneously under normal weather. Field areas prone to water stress are shown to lag as much as 23–33% below the field average during drought years and 26–33% during deluge years. By combining large-scale spatial datasets, we identify 2.65 million hectares of water-stress prone cropland, and estimate an aggregated economic loss impact of $536M USD yr−1, 4.0 million tons yr−1 of less CO2 fixed in crop biomass, and 52.6 Gg yr−1 of more reactive N in the environment. Yield stability maps can be used to spatially implement adaptation practices to mitigate weather-induced stresses in the most vulnerable cropland.

Porosity predictions during co-cure of honeycomb core prepreg sandwich structures

Honeycomb core sandwich structures are co-cured to bond partially cured thermoset prepreg facesheets with an adhesive layer to either side of the honeycomb core under a prescribed pressure and temperature cycle in an autoclave. Defects such as porosity and poorly formed fillets of the adhesive bond-line can compromise the mechanical properties of the sandwich structure. High defect levels during the co-cure are common as the process development cycle is strongly dependent on complex relationships among material properties, part geometry and process parameters. A process model to predict bond-line porosity is formulated based on the understanding gathered about the physics of the co-cure process and the physics of bond-line formation. A three-step approach is adopted to simulate the bond-line porosity. The first step uses the knowledge of the diffusion-induced void growth in the form of a stability map to guide the design of the co-cure cycle. The second step develops the void growth model accounting for the diffusion of volatiles within the adhesive and the prepreg resin. In the final step, the voids that escape into the core from the bond-line are taken into account to calculate the porosity of the bond-line. With the help of two examples, it is shown that in addition to the initial radius of voids and the initial porosity of the bond-line, the interplay between the stability map and the process cycle also play an important role in prediction of the final porosity within the bond-line. This process model should prove useful in reducing or eliminating voids by optimizing the co-cure cycle.

Experimental Study of Continuous H2/Air Rotating Detonations

ABSTRACT An experimental study of a lab scale rotating detonation combustor (RDC) has been conducted to identify and classify its modes of operation under different feeding conditions. The chamber uses air as oxidizer and hydrogen as fuel. The stability diagram of the RDC has been determined based on the detonation chamber Reynolds number and reactants mixture equivalence ratio values. The Reynolds number is based on the air volume flow rate, chamber annulus size, and the reactants mixture feeding slot area. Hence the effects of geometrical parameters and operational parameters on the detonation wave stability can be presented in a single stability map. This diagram identifies different zones in terms of the stability, propagation characteristics, and the number of detonation waves. Absence of a stable detonation wave at low Reynolds numbers and observation of different detonation modes with increasing Reynolds number, in different ranges of equivalence ratios, have been established in this research. This paper describes the various modes of rotating detonation wave propagation in the RDC. These modes include the single-wave detonation mode, the dual-waves unidirectional detonation mode, the dual-waves colliding detonation mode, extinguishing and re-initiating detonation mode, and the deflagration mode

Thermo-mechanical stability of axially graded Rayleigh pipes

Thermo-mechanical vibrations of axially functionally graded (AFG) pipes conveying fluid are investigated, aiming at stability enhancement of fluid–interaction systems. Material properties of the pipe vary continuously in the longitudinal direction based on a power-law distribution function. The governing equation of motion of the system was derived using Rayleigh beam theory by considering both linear and nonlinear stress–temperature relations. The Galerkin discretization procedure and eigenvalue analysis were implemented to solve the equation, and stability regions were identified accordingly. The model is validated and compared with the available results in the literature. The influence of material gradient, power index, boundary conditions, rotary inertia factor, temperature rise, and different boundary conditions on the dynamic configuration of the system was elucidated. It was demonstrated that the detached stable regions emerge and develop by increasing the power index at sufficiently high mass ratios. It was shown that either S-shaped or Z-shaped segments may appear on the stability borders. Moreover, the thermal stability map of the supported pipes was also examined, and it was concluded that the AFG power index has a reverse effect on the critical temperature rise of the system at the low and high material gradients. Results of this study may help engineers to design inhomogeneous piping systems optimally. Communicated by Francesco Tornabene.

Rate dependent transition to thermoacoustic instability via intermittency in a turbulent afterburner

Experiments were conducted to study the rate dependent transition to thermoacoustic instability in a turbulent afterburner rig. The afterburner rig contains v-gutters as flame stabilizers and simulates elevated inlet gas temperature using a preheater. Under quasi-static increase in flow Reynolds number of the afterburner, screech is not observed; on the contrary, screech onsets when the Reynolds number is increased at a higher rate. Such a phenomenon is known as rate induced tipping or R-tipping. When the Reynolds number is increased at a lower rate, screech appears as a few bursts of high-amplitude periodic oscillations amidst low-amplitude aperiodic oscillations, a state known as intermittency. As the rate of change of Reynolds number is increased, more bursts appear and with further increase in the rate, the proportion of periodic oscillations of the bursts increases in the time series of pressure fluctuations, approaching a state of limit-cycle oscillations. We show for the first time, a rate-dependent transition to thermoacoustic instability in a turbulent afterburner happening through intermittency, with respect to increasing the rate of change of Reynolds number. The onset of burst occurs earlier, i.e. bursts occurring at a lower Reynolds number as the rate of change of Reynolds number is increased. The amplitude of bursts during intermittency is higher than that of the limit cycle oscillations. The rate dependent transition to screech through intermittency is analyzed by studying the variation of probability density function (PDF) of the amplitude of pressure, variation of the amplitude of bursts, variation of the number of bursts of periodic oscillations, and the inlet conditions corresponding to the onset of bursts, with respect to different rates of change of Reynolds number. Rate dependent transition observed in the model afterburner suggests that combustion system of a gas turbine engine should be subjected to different engine throttling rates to define the thermoacoustic stability map.

Identifying drug targets in tissues and whole blood with thermal-shift profiling.

Monitoring drug-target interactions with methods such as the cellular thermal-shift assay (CETSA) is well established for simple cell systems but remains challenging in vivo. Here we introduce tissue thermal proteome profiling (tissue-TPP), which measures binding of small-molecule drugs to proteins in tissue samples from drug-treated animals by detecting changes in protein thermal stability using quantitative mass spectrometry. We report organ-specific, proteome-wide thermal stability maps and derive target profiles of the non-covalent histone deacetylase inhibitor panobinostat in rat liver, lung, kidney and spleen and of the B-Raf inhibitor vemurafenib in mouse testis. In addition, we devised blood-CETSA and blood-TPP and applied it to measure target and off-target engagement of panobinostat and the BET family inhibitor JQ1 directly in whole blood. Blood-TPP analysis of panobinostat confirmed its binding to known targets and also revealed thermal stabilization of the zinc-finger transcription factor ZNF512. These methods will help to elucidate the mechanisms of drug action in vivo.

Modal interactions for spindle, holders, and tools

This paper describes the interaction between vibration modes associated with the machine-spindle and those associated with the holder-tool when the holder-tool combination is inserted in the milling machine spindle. It is shown that when the bending natural frequency of the holder-tool is near a machine-spindle natural frequency, there is a combined two mode frequency response (similar to a dynamic absorber) for the assembly that exhibits increased dynamic stiffness over those situations when the interaction is absent. Experimental results are provided. The variation in tool point frequency response with tool extension length is then used to calculate the corresponding stability maps. These maps are evaluated to determine the effect of interactions between machine-spindle and holder-tool modes on milling stability. Conclusions are presented.

Исследование устойчивости тонкого слоя жидкости в задаче Ландау–Левича

The stability of the liquid layer in the Landay–Levich problem is theoretically investigated. The free energy of this layer is the sum of the dispersion (van der Waals) interaction and the specific electrical interaction caused by the presence of two electric layers at both interphase boundaries. In the framework of long-wave approximation, the stability of such a system with respect to perturbations is studied in the system of Navier–Stokes equations. A stability map is provided for different layer thicknesses.

A Novel Frequency-Domain Approach for the Exact Range of Imaginary Spectra and the Stability Analysis of LTI Systems With Two Delays

This paper presents a novel frequency-domain approach to reveal the exact range of the imaginary spectra and the stability of linear time-invariant systems with two delays. First, an exact relation, i.e., the Rekasius substitution, is used to replace the exponential term caused by the delays in order to transform the transcendental characteristic equation to a quasi-polynomial. Second, this quasi-polynomial is uniquely tackled by our proposed Dixon resultant and discriminant theory, leading to the elimination of delay-related elements and the revelation of the exact range of the frequency spectra of the original system of interest. Then, by sweeping the frequency over this obtained range, the stability switching curves are declared exhaustively. Last, we deploy the cluster treatment of characteristic roots (CTCR) paradigm to reveal the exact and complete stability map. The proposed methodologies are tested and verified by a numerical method called Quasi-Polynomial mapping-based Root finder (QPmR) over an example case.

Application of Wiedeburg linearization for solving the stability problem of a two-layer mixture with concentration-dependent diffusion

In this paper, we consider the problem of the stability of an isothermal system of two miscible fluids in a gravity field. Fluids are aqueous solutions of non-reacting substances with different diffusion coefficients. At the very beginning, the solutions uniformly fill half-spaces, which are separated from each other by an infinitely thin horizontal contact surface. Such a configuration can be easily realized experimentally, although it is more difficult for theoretical analysis. We assume that the initial configuration of the system is statically stable. After the start of evolution, the solutions begin to mix, penetrating each other, and creating conditions for the development of the convective instability of double diffusion. An important complicating factor of the problem is the functional dependence of the diffusion coefficients of solutions on their concentration. In recent years, this effect has been actively studied, since its significant influence on convective stability has been proven experimentally. For simplicity, we assume that the diffusion coefficients of solutions depend linearly on concentration. The problem of the stability of a mixture includes the equation of motion in the Darcy and Boussinesq approximation, the continuity equation, and two transport equations for the concentrations. The solution to this problem in the absence of the effect of concentration-dependent diffusion is well known from the literature. If we take into accountsuch a dependence, then we have to deal with the problem of nonlinear diffusion, which can only be solved numerically. To find an analytical solution to the problem, we propose to apply the method of preliminary linearization of Wiedeburg (1890). The method is well known in the theory of thermal conductivity, although it was originally developed specifically for solutions of substances. In our case, we demonstrate that the conditions for convective stability of the base state can be obtained analytically. The comparative analysis of the discrepancy between the Wiedeburg solution and the numerical solution is given. Based on the closed-form analytical solution, we obtain a stability map for the problem under the consideration. We show how the effect of concentration-dependent diffusion affects stability.

Onset of Thermal Buoyancy Convection in a Two-Layer System with Deformable Interface and Fixed Heat Flux at the Boundaries under Terrestrial and Microgravity Conditions

The stability of a conductive state of a system of two horizontal layers of immiscible fluids of close densities with a fixed heat flux at external boundaries is studied. The problem is solved in the framework of the generalized Boussinesq approximation, which correctly takes into account the deformations of the interface. The onset of convection at heating from above or below is investigated. Main attention is paid to the effect of layer thickness ratio and gravity level on instability. Two long-wave instability modes related the presence of a deformable interface and to a fixed heat flux at the external boundaries are found out. They are analyzed analytically. The behavior of the system with respect to monotonic and oscillatory perturbations of finite wavelength is studied numerically. The complete stability map is obtained. It is found that for very different layer thicknesses, as well as for single layers with fixed heat flux at the boundaries, a long-wavelength instability is observed. The presence of a long-wave instability domain at close thicknesses of layers is also found, which is associated with a strong stabilization of finite-wavelength instability in this parameter range. In the case of Earth gravity, the monotonic perturbations are most dangerous at any ratios of layer thicknesses, the oscillatory mode of instability is responsible for the onset of convection only in microgravity conditions.

Tetragonal phase stability maps of ceria-yttria co-doped zirconia: From powders to sintered ceramics

Ceria-Yttria co-doped tetragonal zirconia is an attractive class of materials having high strength, toughness and thermal stability. In this study, several co-doped zirconia powders with different stabilizers contents were synthesized via continuous hydrothermal flow synthesis (CHFS). The CHFS was concluded as a suitable method in synthesizing ultrafine tetragonal zirconia particles with controlled morphology. The synthesized powders as well as some commercial powders were heat-treated both in the form of powders and pellets between 1150 and 1500 °C and their crystalline structure after cooling to room temperature was studied. The results were used to map out the stability range of the tetragonal phase. The developed diagrams are useful tools to select the appropriate amounts of stabilizers applicable for different sintering temperatures and for samples with different target densities.