Instability Zones Research Articles

Pull-in instability and nonlinear vibration of microbeam with piezoelectric patch driven by electrostatic force using modified couple stress theory

The static and dynamic pull-in characteristics of electrostatically and piezo-electrically actuated microbeam are investigated. The static pull-in voltage is evaluated using analytical methods based on MCST, CCMT and validated through the use of FE based COMSOL multiphysics tools. The dynamic pull-in voltage obtained from numerical technique and verified with existing literature, lower than the static pull-in voltage. The piezoelectric patch has a significant influence on the pull-in voltage and an effect on the aspect ratio. Moreover, the pull-in band and instability zone of the microbeam with weak and hard forcing function have been investigated using multiple scale method.

Analyzing the Stability of a Connected Moving Cart on an Inclined Surface with a Damped Nonlinear Spring

This paper examines the stability behavior of the nonlinear dynamical motion of a vibrating cart with two degrees of freedom (DOFs). Lagrange’s equations are employed to establish the mechanical regulating system of the examined motion. The proposed approximate solutions (ASs) of this system are estimated through the use of the multiple-scales method (MSM). These solutions are considered novel as the MSM is being applied to a new dynamical model. Secular terms have been eliminated to meet the solvability criteria, and every instance of resonance that arises is categorized, where two of them are examined concurrently. Therefore, the modulation equations are developed based on the representations of the unknown complex function in polar form. The solutions for the steady state are calculated using the corresponding fixed points. The achieved solutions are displayed graphically to illustrate the impact of manipulating the system’s parameters and are compared to the numerical solutions (NSs) of the system’s original equations. This comparison shows a great deal of consistency with the numerical solution, which indicates the accuracy of the applied method. The nonlinear stability criteria of Routh–Hurwitz are employed to assess the stability and instability zones. The value of the proposed model is exhibited by its wide range of applications involving ship motion, swaying architecture, transportation infrastructure, and rotor dynamics.

Robustness and dynamical features of fractional difference spacecraft model with Mittag–Leffler stability

Abstract Spacecraft models that mimic the Planck satellite’s behaviour have produced information on cosmic microwave background radiation, assisting physicists in their understanding of the composition and expansion of the universe. For achieving the intended formation, a framework for a discrete fractional difference spacecraft model is constructed by the use of a discrete nabla operator of variable order containing the Mittag–Leffler kernel. The efficacy of the suggested framework is evaluated employing a numerical simulation of the concerning dynamic systems of motion while taking into account multiple considerations such as exterior disruptions, parameterized variations, time-varying feedback delays, and actuator defects. The implementation of the Banach fixed-point approach provides sufficient requirements for the presence of the solution as well as a distinctive feature for such mechanisms Furthermore, the consistent stability is examined. With the aid of discrete nabla operators, we monitor the qualitative behavioural patterns of spacecraft systems to provide justification for structure’s chaos. We acquire the fixed points of the proposed trajectory. At each fixed point, we calculate the eigenvalue of the spacecraft system’s Jacobian matrix and check for zones of instability. The outcomes exhibit a wide range of multifaceted behaviours resulting from the interaction with various fractional orders in the offered system. To maintain stability and synchronize the system, nonlinear controllers are additionally provided. The study highlights the technique’s vulnerability to fractional-order factors, resulting in exclusive, changing trends and equilibrium frameworks. Because of its diverse and convoluted behaviour, the spacecraft chaotic model is an intriguing and crucial subject for research.

Irregular fixation: I. Fixed points and librating orbits of the Brown Hamiltonian

ABSTRACT In hierarchical triple systems, the inner binary is slowly perturbed by a distant companion, giving rise to large-scale oscillations in eccentricity and inclination, known as von-Zeipel–Lidov–Kozai oscillations. Stable systems with a mild hierarchy, where the period ratio is not too small, require an additional corrective term, known as the Brown Hamiltonian, to adequately account for their long-term evolution. Although the Brown Hamiltonian has been used to accurately describe the highly eccentric systems on circulating orbits where the periapse completes a complete revolution, the analysis near its elliptical fixed points had been overlooked. We derive analytically the modified fixed points including the Brown Hamiltonian and analyse its librating orbits (where the periapse motion is limited in range). We compare our result to the direct three-body integrations of millions of orbits and discuss the regimes of validity. We numerically discover the regions of orbital instability, allowed and forbidden librating zones with a complex, fractal, structure. The retrograde orbits, where the mutual inclination is $\iota \ \gt\ 90\ \rm deg$, are more stable and allowed to librate for larger areas of the parameter space. We find numerical fits for the librating-circulating boundary. Finally, we discuss the astrophysical implications for systems of satellites, stars, and compact objects. In a companion paper (Paper II), we apply our formalism to the orbits of irregular satellites around giant planets.

Research on coal wall failure and stability control technology of large coal seams with a soft and thick seam

AbstractTo address the issues of coal rib instability and high occurrence of roof falls in high extraction height fully mechanized coal mining of soft coal seams, this study comprehensively employs theoretical analysis, numerical calculations, and field industrial experiments. By analyzing the distribution characteristics of coal rib displacement and deformation instability zones under different mechanical parameters of soft coal seams, the instability mechanism of coal ribs in high extraction height mining of thick and soft coal seams is revealed, and corresponding stability control techniques for high extraction height coal ribs and supports are developed. The study shows that the stability of coal ribs in high extraction height mining fields of soft and thick coal seams decreases as the values of mechanical parameters decrease. In other words, the smaller the cohesion and deformation parameters of the coal body, the more prone the coal rib is to roof falls. By utilizing advanced deep‐hole static water infusion technology, the frequency of roof falls in extremely soft high extraction height working faces is reduced by 80%, the average depth of roof falls is decreased by 35%, and the average length of roof falls is reduced by 50%. The stability of the coal ribs is effectively improved.

Study on stability evaluation of goaf based on AHP and EWM—taking the northern new district of Liaoyuan city as an example

Throughout the history of coal mining in all countries of the world, large areas of goaf have been left behind, and sudden collapses and surface subsidence of large areas of goaf may occur, especially for mining areas with long mining cycles. The northern new district of the Liaoyuan mining area has been subjected to nearly half a century of mining activities, accompanied by a gradual accumulation of disasters, which have occurred frequently in recent years. In order to assess the stability of the goaf in the study area, this paper proposes a hybrid decision-making multi-factor integrated evaluation method. The distribution of underground goafs was determined using geophysical exploration techniques (seismic survey and transient electromagnetic method) and geological drilling exploration. First, an evaluation index system was established based on the specifications of the goaf, the ecological and geological environment, and the mining conditions; the system included 14 indicators. Two weight calculation methods, AHP-EWM, were employed to determine the comprehensive weight of each indicator by combining subjective and objective weights on the basis of improved game theory. Subsequently, the fuzzy comprehensive evaluation method was utilised to complete the stability rating of each block in the study area, and MapGIS and ArcGIS were employed to complete the drawing of the stability zoning map of the northern new district goaf. The study area was divided into three zones of stability, basic stability and instability, according to the critical value. These zones accounted for 23.03%, 36.45% and 40.52% of the total area of the study area, respectively. The comprehensive on-site investigation revealed a decrease in the size and number of collapse pits and the rate of damage to the houses from the unstable zone to the stable zone. This indicates that the results of the division are consistent with the actual situation. The classification results are consistent with the actual ground disaster situation, thus verifying the rationality and validity of the evaluation method. The results indicate that the stability of the study area is generally at the lower middle level.

Understanding the isothermal compression behavior of Al-Mg-Si alloy based on hot deformation parameters and instability criteria

This work comprehensively studied the microstructure evolution and thermodynamic behavior of homogenized cast Al-Mg-Si alloy by using the dynamic materials model (DMM) of hot deformation activation energy (Q) and power dissipation efficiency (η), which were influenced by Zener-Holomon (Z) parameters of temperature-compensated strain rate. The Q varies with the material constitutive parameters n(T) and sε̇ and leads to a non-monotonic trend in the Z parameter. These coupling relationships have profound significance for revealing plastic deformation. The microstructure and microtexture evolution under four representatively Z parameters had been characterized, and it was found that the deformation mechanism under higher lnZ was mainly dynamic recovery (DRV) and a typical <101>//TD texture with a maximum strength of 14.41 was exhibited. As lnZ decreased, the volume fraction of high angle grain boundaries (HAGBs) and recrystallized grains increased from 20.89 % and 1.5 % to 49.47 % and 40.9 %, the geometrically necessary dislocation (GNDs) density dropped from 1.55 × 1014/m2 to 0.40 × 1014/m2, and the softening mechanism gradually shifted to dynamic recrystallization (DRX), with the volume fraction of Cube texture {001} <100> increasing and Goss texture {011} <110> decreasing. Hot processing maps were established based on the Prasad and Murty instability criterion. The results showed that the instable and stable zones had a strong correlation with η. Lower η often implies microcracks, deformation bands and flow localization, as well as extremely uneven grain distribution and a low recrystallization volume fraction, and the stable zone mainly exhibited the phenomenon of DRX dominated recrystallization behavior improving microstructure homogenization. By comparing the specific hot processing map and microstructure evolution, the prediction ability for determining Murty instability criterion is stronger than Prasad for homogenized cast Al-Mg-Si alloy.

A study of mechanism of wellbore instability by means of strain energy density

The paper presents a new analytical method based on the strain energy density to investigate the mechanism of wellbore instability. To establish the method, pre- and post-drilling states of strain energy densities were first formulated, and then have been applied to the wellbore wall using the strain energy balance. This innovative approach differentiates the instability prone zones into two distinct parts; the compressive, and the tensile zones that also known as borehole breakout and drilling-induced fracture, respectively. These two types of instabilities are related to the restored strain energy density (RESED) and the released strain energy density (RLSED), accordingly. Among the two types of instabilities, the geometrical characteristics of the compressive instable prone zone, that is, width, 2 θ b , and length, L b , were further formulated, examined and proposed. The results of the presently developed method have been compared with those that obtained by using the existing borehole breakout’s geometry. In each case, good agreement was found between the results of this study and the conventional methods. This method has further been compared and verified by using the experimental data. Finally, it has been demonstrated that how this method helps to determine the optimal mud pressure for a safe wellbore design.

Investigation of the Hot Deformation Behavior of 22Cr‐25Ni Austenitic Heat‐Resistant Steel by Combining Constitutive Model and Processing Map

The hot deformation behavior of 22Cr‐25Ni austenitic heat‐resistant steel at the temperatures of 950–1150 °C and strain rates of 0.01–10 s−1 is studied by isothermal compression test. It is found that the dynamic recrystallization (DRX) degree of the steel increases with the increase of temperature. The DRX degree decreases with the increase of the strain rate from 0.01 to 1 s−1, whereas the DRX degree increases with the increase of the strain rate from 1 to 10 s−1. The hot deformation activation energy is as high as 624.25 kJ mol−1 due to the addition of a large number of alloying elements. The typical strain compensation Arrhenius constitutive model established can be used to roughly predict the hot flow behavior of the steel. Furthermore, a modified model considering the influence of strain rate and deformation heat on the deformation process is proposed and showed higher accuracy (statistical parameters r = 0.994 and average absolute relative error = 4.59%). The DRX zone of the steel is determined to be 1080–1150 °C/0.01–0.1 s−1 through processing map analysis, representing the appropriate hot working zone. The microstructure corresponding to the instability zone in the processing map exhibits deformation concentration bands or necklace structures.

Hot-working characteristics and microstructure analysis of Zr-Sn alloy at different temperatures and strain rates

In this work, the hot-working characteristics and microstructure evolution of Zr-Sn alloy at 600–900 °C/0.01–10 s−1 were investigated. The results indicate that the flow stress of Zr-Sn alloy decreases with the increase of compression temperature and increases with the increase of strain rate. An Arrhenius constitutive equation for the Zr-Sn alloy was established, the average deformation activation energy was calculated to be 278630.1 J/mol. The processing map of Zr-Sn alloy was obtained based on the flow stress curve, revealing that the instability zone was mainly concentrated in the low temperature zone and the medium-high strain rate zone in the high temperature zone. As the temperature increases, the proportion of dynamic recrystallization (DRX) grains increases gradually. With the increase of strain rate, the proportion of DRX grains gradually decreases. Three DRX mechanisms were observed: continuous DRX (CDRX), discontinuous DRX (DDRX), and twin induced DRX (TDRX). The secondary phase of the initial grains is mainly FeCr phase, which is not completely dissolved at 650–750°C/0.01–1 s−1.

Nonlinear stability of two superimposed electrified dusty fluids of type Rivlin-Ericksen: Non-perturbative approach

The nonlinear instability of a planar interface between two overlapping Rivlin-Ericksen viscoelastic liquids, in the occurrence of fine dust and vertical electric fields throughout permeable media, and the influence of surface tension is studied. The prototype structure is assumed to be a two-dimensional groundwork for the sake of simplicity. The growing approval of several disciplines of practical physics and technology serves as motivation for analyzing this problem. Using viscous potential theory, the mathematical procedure is condensed. To properly control electro convection in liquid crystals, which is widely used in various displays technologies, it was crucial to have a thorough comprehension of stability. Gaining understanding of the behavior of viscoelastic fluids at interfaces was crucial in polymer manufacturing industries. Employing the linear equations of movement with the suitable nonlinear bounder circumstances forms the basis of the considered nonlinear technique. A nonlinear partial differential equation that evaluates the interface movement is the objective of the process. Since linear stability has frequently been investigated, the present situation will be constructed only in the nonlinear sense, where a number of dimensionless physical numerals are achieved. The non-perturbative methodology is used to accomplish the nonlinear standards. The main idea behind the novel performance is to convert an ordinary nonlinear ordinary differential equation into a linear one. The new technique differs from the conventional perturbation methods in that it may be used to exactly and correctly analyze the behavior of the strong nonlinear aspects of the interface displacement. This innovative method is established by using He's frequency formula. Using the nonlinear distinguishing equation, the special situation of the real and the complex coefficients is accomplished. It was observed that the instability zone expands as the electric field, porosity of porous medium, and density ratio of two fluids rise. The stability configuration is enhanced by the viscoelasticity parameter, Bond number, and ratio of kinematic viscoelasticity.

Vibrational dynamics of a subjected system to external torque and excitation force

This work focuses on the dynamical response of a novel auto-parametric two-degrees-of-freedom (DOF) dynamical system when it is subjected to external torque and force. It consists of a forced oscillator with nonlinear stiffness that is connected to a linear spring. In accordance with the system’s DOF, an organizing system of equations of motion (EOM) is produced using Euler–Lagrange’s equations. To obtain the analytical approximate solutions (ASs) of the equations of this system, the multiple scales technique (MST) is employed. The provided solutions are being juxtaposed with the numerical solutions (NSs) for comparison to show how closely they agree, as well as the precision of the MST. In view of removing secular terms, the system’s solvability criteria are obtained. All arising resonance cases are classified, and two of them are then examined at once. The relevant system of modulation equations is solved numerically to illustrate the advantageous influence of diverse factors on the behavior of the modified phases and amplitudes. Based on the values of these parameters, the frequency response curves (FRCs) are drawn to explore different zones of stability and instability. A wide variety of values for the system’s parameters shows that its behavior is steady. The achieved outcomes are deemed novel, as the MST has been applied on a new dynamical model. The results have broad relevance and can be implemented in various engineering contexts, including the analysis of ship movements, in which nonlinear coupling between rolling and pitching motions can be found.

Enhancing the trustworthiness of chaos and synchronization of chaotic satellite model: a practice of discrete fractional-order approaches

Accurate development of satellite maneuvers necessitates a broad orbital dynamical system and efficient nonlinear control techniques. For achieving the intended formation, a framework of a discrete fractional difference satellite model is constructed by the use of commensurate and non-commensurate orders for the control and synchronization of fractional-order chaotic satellite system. The efficacy of the suggested framework is evaluated employing a numerical simulation of the concerning dynamic systems of motion while taking into account multiple considerations such as Lyapunov exponent research, phase images and bifurcation schematics. With the aid of discrete nabla operators, we monitor the qualitative behavioural patterns of satellite systems in order to provide justification for the structure’s chaos. We acquire the fixed points of the proposed trajectory. At each fixed point, we calculate the eigenvalue of the satellite system’s Jacobian matrix and check for zones of instability. The outcomes exhibit a wide range of multifaceted behaviours resulting from the interaction with various fractional-orders in the offered system. Additionally, the sample entropy evaluation is employed in the research to determine complexities and endorse the existence of chaos. To maintain stability and synchronize the system, nonlinear controllers are additionally provided. The study highlights the technique’s vulnerability to fractional-order factors, resulting in exclusive, changing trends and equilibrium frameworks. Because of its diverse and convoluted behaviour, the satellite chaotic model is an intriguing and crucial subject for research.

Microstructure Evolution, Hot Deformation Behavior and Processing Maps of an FeCrAl Alloy.

The deteriorated plasticity arising from the insoluble precipitates may lead to cracks during the rolling of FeCrAl alloys. The microstructure evolution and hot deformation behavior of an FeCrAl alloy were investigated in the temperature range of 750-1200 °C and strain rate range of 0.01-10 s-1. The flow stress of the FeCrAl alloy decreased with an increasing deformation temperature and decreased strain rate during hot working. The thermal deformation activation energy was determined to be 329.49 kJ/mol based on the compression test. Then, the optimal hot working range was given based on the established hot processing maps. The hot processing map revealed four small instability zones. The optimal working range for the material was identified as follows: at a true strain of 0.69, the deformation temperature should be 1050-1200 °C, and the strain rate should be 0.01-0.4 s-1. The observation of key samples of thermally simulated compression showed that discontinuous dynamic recrystallization started to occur with the temperate above 1000 °C, leading to bended grain boundaries. When the temperature was increased to 1150 °C, the dynamic recrystallization resulted in a microstructure composed of fine and equiaxed grains.

Dynamic response of existing embankment dams in specific geotechnical and seismological conditions: contemporary framework for Serbian national guidelines

We suggest a new approach for evaluating the dynamic response of existing embankment dams as a guideline for national engineering regulations in Serbia. This novel concept is applied to the case study of the existing embankment dam “Zavoj” (Serbia), built at the place of the previously formed natural dam (due to large landslide activity), and exposed to Mw7.4 Vrančea earthquake and under double impact of Kresna earthquake (Mw6.8 and Mw7.1). Results of transient FEM and direct dynamical analysis of the three-dimensional FEM model of the “Zavoj” dam indicate that the existing dam is stable in dynamic conditions, while the surrounding terrain is either on the verge of stability or becomes unstable, depending on the assumed geotechnical conditions and a relevant earthquake analyzed. As a result, we construct a landslide hazard map in dynamic conditions and the dam damage map, which enables the identification of unstable, damaged, or weak parts of the dam, its immediate surroundings, and the accumulation zone in general. The results indicate that direct dynamical analysis is obligatory when two succeeding earthquakes occur and temporal evolution of displacements in the model is required. Additionally, the application of the remaining bearing capacity criterion indicates a much larger zone of potential instability compared to the extent of equivalent plastic strain and the location of the old sliding surface. By following the proposed guidelines, one secures the inclusion of all the relevant influential factors in the comprehensive dynamic analysis of existing embankment dams, leading eventually to reliable decisions on further design, (re)construction, and/or monitoring activities.

The role of Germany as a NATO «framework nation»

Unlike its predecessors, Germany used its military potential not to solve exceptionally national issues, but to participate in the activities of multilateral military blocs. At the same time she maintained its ambitions as a power. The combination of two trends has conditioned the Bundeswehrʼs usage as a means that provided Germany with the opportunity to become a framework nation for different multinational military groupings. The article explores the cases of such a role of Germany in the instability zones in the Balkans in the 1990s, in Afghanistan, Lebanon and Mali in the XXI century. The constraints caused by the state of the Bundeswehr for the implementation of the tasks of the Federal Republic of Germany as a «framework nation» are considered. The cases of such Bundeswehr`s activity as NATO Response Force, enhanced and tailored Forward Presence during the confrontation between the West and Russia are considered. The political importance of each case for the change of Germany`s positions in Europe and in the world is presented.

Analysis of Edge Drop on Strip Due to Bending and Elastic Deformation of Back up Rolls in a Four-High Cold Mill

The superficial quality of the strip is a very important issue in steel production. Considering the dimensions, the thickness is one of the most important variables in the production of a strip. In the present study, the elastic curve of Back Up Rolls (BURs) is analyzed, considering them as simply supported beams as well as the effect of rolls on the profile of the strip, specifically in the strip edge producing edge drop. The analysis included theoretical and numerical measurements in the mill. The results showed that there is an instability zone of 76 mm in the strip edge, and this geometry is symmetrical in both ends of the strip. This study not only provides a theoretical basis for the edge drop, but also provides a basis for the understanding of deformation on rolls used in rolling mill processes and their effect on the thickness, profile, shape, and dimensional quality of strips. To reduce the edge drop and significantly improve the surface quality of the strip, it is suggested to complement the simulation by compensating for the elastic curve of BUR, in the process applying bending on Work Roll (WR) combined with the use of positive crowns on it.

Influence of the discrete lattice spacing on the formation of intrinsic localized structures in the Salerno model

We report in this paper the influence of the discrete lattice spacing on the formation of intrinsic localized structures in the Salerno model. Through the linear stability analysis, appearance criterions of the modulation instability (MI) are derived. We show via the growth rate that, the discrete lattice spacing and the nonlinearity term can affect significantly the formation of instability zones. We find that for large values of the discrete lattice spacing, the MI is developed to increase the number instability zones whereas for very low values of this parameter, the MI growth rate is arisen up to enlarge the bandwidth. The theoretical findings have been numerically tested via the discrete spatial Fourier transform method and the direct simulations, and have been found to be in full agreement with the analytical prediction. Moreover, it has been revealed that a higher modulation index can dramatically modify the shape and the amplitude of the modulated waves.

Hot deformation behavior and hot working window of a solid solution strengthened Ni–Cr–Fe-based superalloy

The hot deformation behavior of Ni–Cr–Fe-based ChS57 alloy was investigated by isothermal compression tests in the temperature range of 1000–1200 °C with strain rates covering 0.001–10 s−1. Based upon the hyperbolic sine function and dynamic material model, the constitutive model and processing maps of the alloy were established, the microstructure evolution was systematically analyzed and the optimization of the hot working window was completed. The results indicate that the flow stress increases remarkably with increasing strain rate and decreasing deformation temperature, while the amount of strain required to reach peak stress also gradually increases. The hot deformation process of this alloy is the result of the competition between dynamic softening and work hardening, with a deformation activation energy of 451.34 kJ/mol; dynamic recrystallization (DRX) is the main softening mechanism, while both continuous dynamic recrystallization (CDRX) and discontinuous dynamic recrystallization (DDRX) exist; the low temperatures and medium strain rates (1000–1025 °C, 0.045–0.37s−1) are the instability zone parameters of the alloy when flow localization and deformation bands are the microstructural manifestations of unstable hot working. The optimum hot working window for ChS57 alloy is the medium-low temperatures and low strain rates（1050–1100 °C, 0.001–0.003s−1）and the medium-high temperatures and high rates（1125–1175 °C, 1-10s−1 or 1100 °C/10s−1）, where the microstructure appears as randomly oriented and uniformly distributed full DRX grains.

Hot processing map and high temperature deformation behaviour of TB17 Ti alloy

The thermal compression experiments of TB17 titanium alloy under different thermal deformation process parameters were carried out using a thermal simulation compressor. The high-temperature plastic flow behaviour of the alloy was studied. It was found that with the decrease of the deforming temperature and the increase of the strain rate, the flow stress increased, and the discontinuous yield phenomenon occurred in hot deformation. The larger the strain rate, the more obvious the discontinuous yield phenomenon. The thermal activation energy Q decreased with the increase of strain, and the average value of activation energy Q is 209.54 KJ / mol. The constitutive equation of high-temperature plastic flow of TB17 titanium alloy was established. The predicted values of this equation are in good agreement with the experimental values. The average error is 3.987 %, and the correlation coefficient is 0.9972, which has high accuracy. Based on the Prasad criterion, the hot processing map of TB17 titanium alloy was constructed. It was found that the flow instability zone was mainly concentrated in the high strain rate region. The flow instability zone was determined to be 795 °C ~ 895 °C, 0.046s-1 ~ 1s-1, and the stable deformation zone was mainly located in the region with high temperature and low strain rate. The optimum processing parameter range is 860 °C ~ 895 °C, 0.001 s-1 ~ 0.025 s-1.