Search results for: stability theory

Authors: Mojtaba Hakimi-Moghaddam

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Routh-Hurwitz stability criterion is a powerful approach to determine stability of linear time invariant systems. On the other hand, applying this criterion to characteristic equation of a system, whose stability or marginal stability can be determined. Although the command roots (.) of MATLAB software can be easily used to determine the roots of a polynomial, the characteristic equation of closed loop system usually includes parameters, so software cannot handle it; however, Routh-Hurwitz stability criterion results the region of parameter changes where the stability is guaranteed. Moreover, this criterion has been extended to characterize the stability of interval polynomials as well as fractional-order polynomials. Furthermore, it can help us to design stable and minimum-phase controllers. In this paper, theory and application of this criterion will be reviewed. Also, several illustrative examples are given.

Keywords: Hurwitz polynomials, Routh-Hurwitz stability criterion, continued fraction expansion, pure imaginary roots

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Authors: Safia Hocine, Zina Benouaret, Djamil A¨ıssani

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In this paper, we study the performance of the strong stability method of the univariate classical risk model. We interest to the stability bounds established using two approaches. The first based on the strong stability method developed for a general Markov chains. The second approach based on the regenerative processes theory . By adopting an algorithmic procedure, we study the performance of the stability method in the case of exponential distribution claim amounts. After presenting numerically and graphically the stability bounds, an interpretation and comparison of the results have been done.

Keywords: Marcov chain, regenerative process, risk model, ruin probability, strong stability

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Authors: Arcady Ponosov, Ramazan Kadiev

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Input-to-State Stability (ISS) is widely used in deterministic control theory but less known in the stochastic case. Roughly speaking, the theory explains when small perturbations of the right-hand sides of the system on the entire semiaxis cause only small changes in the solutions of the system, again on the entire semiaxis. This property is crucial in many applications. In the report, we explain how to define and study ISS for systems of linear stochastic differential equations with or without delays. The central result connects ISS with the property of Lyapunov stability. This relationship is well-known in the deterministic setting, but its stochastic version is new. As an application, a method of studying asymptotic Lyapunov stability for stochastic delay equations is described and justified. Several examples are provided that confirm the efficiency and simplicity of the framework.

Keywords: asymptotic stability, delay equations, operator methods, stochastic perturbations

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Authors: Boualem Chetti

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The dynamic characteristics of a three-lobe journal bearing lubricated with micropolar fluids are determined by the linear stability theory. Lubricating oil containing additives and contaminants is modeled as micropolar fluid. The modified Reynolds equation is obtained using the micropolar lubrication theory and the finite difference technique has been used to solve it. The dynamic characteristics in terms of stiffness, damping coefficients, the critical mass and whirl ratio are determined for various values of size of material characteristic length and the coupling number. The computed results show compared with Newtonian fluids, that micropolar fluid exhibits better stability.

Keywords: three-lobe bearings, micropolar fluid, dynamic characteristics, stability analysis

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Authors: Arcady Ponosov., Ramazan Kadiev

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The work studies the global moment stability of solutions of systems of nonlinear differential Itô equations with delays. A modified regularization method (W-method) for the analysis of various types of stability of such systems, based on the choice of the auxiliaryequations and applications of the theory of positive invertible matrices, is proposed and justified. Development of this method for deterministic functional differential equations is due to N.V. Azbelev and his students. Sufficient conditions for the moment stability of solutions in terms of the coefficients for sufficiently general as well as specific classes of Itô equations are given.

Keywords: asymptotic stability, delay equations, operator methods, stochastic noise

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Authors: V. Sankaranarayanan, V. Amrita Sundari, Sunit P. Gopal

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This paper presents the design and implementation of a nonlinear controller for the point to point control of a mobile inverted pendulum (MIP). The controller is designed based on the kinematic model of the MIP to stabilize all the four coordinates. The stability of the closed-loop system is proved using Lyapunov stability theory. The proposed controller is validated through numerical simulations and also implemented in a laboratory prototype. The results are presented to evaluate the performance of the proposed closed loop system.

Keywords: mobile inverted pendulum, switched control, nonlinear systems, lyapunov stability

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Authors: Swati Tyagi, Syed Abbas

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Fractional-order Hopfield neural networks are generally used to model the information processing among the interacting neurons. To show the constancy of the processed information, it is required to analyze the stability of these systems. In this work, we perform Mittag-Leffler stability for the corresponding Caputo fractional-order bidirectional associative memory (BAM) neural networks with various time-delays. We derive sufficient conditions to ensure the existence and uniqueness of the equilibrium point by using the theory of topological degree theory. By applying the fractional Lyapunov method and Mittag-Leffler functions, we derive sufficient conditions for the global Mittag-Leffler stability, which further imply the global asymptotic stability of the network equilibrium. Finally, we present two suitable examples to show the effectiveness of the obtained results.

Keywords: bidirectional associative memory neural network, existence and uniqueness, fractional-order, Lyapunov function, Mittag-Leffler stability

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Authors: Ramazan Kadiev, Arkadi Ponossov

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Semidiscrete systems contain both continuous and discrete components. This means that the dynamics is mostly continuous, but at certain instants, it is exposed to abrupt influences. Such systems naturally appear in applications, for example, in biological and ecological models as well as in the control theory. Therefore, the study of semidiscrete systems has recently attracted the attention of many specialists. Stochastic effects are an important part of any realistic approach to modeling. For example, stochasticity arises in the population dynamics, demographic and ecological due to a change in time of factors external to the system affecting the survival of the population. In control theory, random coefficients can simulate inaccuracies in measurements. It will be shown in the presentation how to incorporate such effects into semidiscrete systems. Stability analysis is an essential part of modeling real-world problems. In the presentation, it will be explained how sufficient conditions for the moment stability of solutions in terms of the coefficients for linear semidiscrete stochastic equations can be derived using non-Lyapunov technique.

Keywords: abrupt changes, exponential stability, regularization, stochastic noises

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Authors: Péter Restás, Andrea Czibor, Zsolt Péter Szabó

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Purpose: This article aims to rethink the phenomena of employee behavior as a product of a system. Both organizational culture and Complex Adaptive Systems (CAS) theory emphasize that individual behavior depends on the specific system and the unique organizational culture. These two major theories are both represented in the field of organizational studies; however, they are rarely used together for the comprehensive understanding of workplace behavior. Methodology: By reviewing the literature we use key concepts stemming from organizational culture and CAS theory in order to show the similarities between these theories and create an enriched understanding of employee behavior. Findings: a) Workplace behavior is defined here as social cognition issue. b) Organizations are discussed here as complex systems, and cultures which drive and dictate the cognitive processes of agents in the system. c) Culture gives CAS theory a context which lets us see organizations not just as ever-changing and unpredictable, but as such systems that aim to create and maintain stability by recurring behavior. Conclusion: Applying the knowledge from culture and CAS theory sheds light on our present understanding of employee behavior, also emphasizes the importance of novel ways in organizational research and management.

Keywords: complex adaptive systems theory, employee behavior, organizational culture, stability

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Authors: Mohd Salmi Md Noorani, Ghada Al-Mahbashi, Sakhinah Abu Bakar

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This paper investigates projective lag synchronization (PLS) behavior in drive response dynamical networks (DRDNs) model with identical nodes. A hybrid feedback control method is designed to achieve the PLS with mismatch and without mismatch terms. The stability of the error dynamics is proven theoretically using the Lyapunov stability theory. Finally, analytical results show that the states of the dynamical network with non-delayed coupling can be asymptotically synchronized onto a desired scaling factor under the designed controller. Moreover, the numerical simulations results demonstrate the validity of the proposed method.

Keywords: drive-response dynamical network, projective lag synchronization, hybrid feedback control, stability theory

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Authors: Manuel A. Guzman, Davide Forcellini, Ricardo Moreno, Diego H. Giraldo

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Elastomeric bearings (EB) are used in many applications, such as base isolation of bridges, seismic protection and vibration control of other structures and machinery. Their versatility is due to their particular behavior since they have different stiffness in the vertical and horizontal directions, allowing to sustain vertical loads and at the same time horizontal displacements. Therefore, vertical, horizontal and bending stiffnesses are important parameters to take into account in the design of EB. In order to acquire a proper design methodology of EB all three, theoretical, finite element analysis and experimental, approaches should be taken into account to assess stability due to different loading states, predict their behavior and consequently their effects on the dynamic response of structures, and understand complex behavior and properties of rubber-like materials respectively. In particular, the recent large-displacement theory on the stability of EB formulated by Forcellini and Kelly is validated with both numerical simulations using the finite element method, and experimental results set at the University of Antioquia in Medellin, Colombia. In this regard, this study reproduces the behavior of EB under compression loads and investigates the stability behavior with the three mentioned points of view.

Keywords: elastomeric bearings, experimental tests, numerical simulations, stability, large-displacement theory

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Authors: R. Bennai, M. Nebab, H. Ait Atmane, B. Ayache, H. Fourn

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In this work, a study of the stability of a functionally graduated sandwiches beam using a refined theory of hyperbolic shear deformation of a beam was developed. The effects of transverse shear strains and the transverse normal deformation are considered. The constituent materials of the beam are supposed gradually variable depending on the height direction based on a simple power distribution law in terms of the volume fractions of the constituents; the two materials with which we worked are metals and ceramics. In order to examine the present model, illustrative examples are presented to show the effects of changes in different parameters such as the material graduation, the stretching effect of the thickness and thickness ratio –length on the buckling of FGM sandwich beams.

Keywords: FGM materials, refined shear deformation theory, stretching effect, buckling, boundary conditions

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Authors: Sabri Arik

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In this paper, we study the global asymptotic robust stability of delayed neural networks with norm-bounded uncertainties. By employing the Lyapunov stability theory and Homeomorphic mapping theorem, we derive some new types of sufficient conditions ensuring the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete time delays under parameter uncertainties and with respect to continuous and slopebounded activation functions. An important aspect of our results is their low computational complexity as the reported results can be verified by checking some properties symmetric matrices associated with the uncertainty sets of network parameters. The obtained results are shown to be generalization of some of the previously published corresponding results. Some comparative numerical examples are also constructed to compare our results with some closely related existing literature results.

Keywords: neural networks, delayed systems, lyapunov functionals, stability analysis

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Authors: F. Rahimi Dehgolan, S. E. Khadem, S. Bab, M. Najafee

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Nowadays, using rotating systems like shafts and disks in industrial machines have been increased constantly. Dynamic stability is one of the most important factors in designing rotating systems. In this study, linear frequencies and stability of a coupled continuous flexible rotor-disk-blades system are studied. The Euler-Bernoulli beam theory is utilized to model the blade and shaft. The equations of motion are extracted using the extended Hamilton principle. The equations of motion have been simplified using the Coleman and complex transformations method. The natural frequencies of the linear part of the system are extracted, and the effects of various system parameters on the natural frequencies and decay rates (stability condition) are clarified. It can be seen that the centrifugal stiffening effect applied to the blades is the most important parameter for stability of the considered rotating system. This result highlights the importance of considering this stiffing effect in blades equation.

Keywords: rotating shaft, flexible blades, centrifugal stiffness, stability

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Authors: Soumya Kedia, Puja Agarwala, Mahesh Tirumkudulu

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Linear stability analysis is performed for a radially expanding liquid sheet in the presence of a gas medium. A liquid sheet can break up because of the aerodynamic effect as well as its thinning. However, the study of the aforementioned effects is usually done separately as the formulation becomes complicated and is difficult to solve. Present work combines both, aerodynamic effect and thinning effect, ignoring the non-linearity in the system. This is done by taking into account the formation of the gas boundary layer whilst neglecting viscosity in the liquid phase. Axisymmetric flow is assumed for simplicity. Base state analysis results in a Blasius-type system which can be solved numerically. Perturbation theory is then applied to study the stability of the liquid sheet, where the gas-liquid interface is subjected to small deformations. The linear model derived here can be applied to investigate the instability for sinuous as well as varicose modes, where the former represents displacement in the centerline of the sheet and the latter represents modulation in sheet thickness. Temporal instability analysis is performed for sinuous modes, which are significantly more unstable than varicose modes, for a fixed radial distance implying local stability analysis. The growth rates, measured for fixed wavenumbers, predicated by the present model are significantly lower than those obtained by the inviscid Kelvin-Helmholtz instability and compare better with experimental results. Thus, the present theory gives better insight into understanding the stability of a thin liquid sheet.

Keywords: boundary layer, gas-liquid interface, linear stability, thin liquid sheet

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Authors: Gholamreza Koochaki

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This paper presents the buckling analysis of functionally graded beams with various boundary conditions. The first order shear deformation beam theory (Timoshenko beam theory) and the classical theory (Euler-Bernoulli beam theory) of Reddy have been applied to the functionally graded beams buckling analysis The material property gradient is assumed to be in thickness direction. The equilibrium and stability equations are derived using the total potential energy equations, classical theory and first order shear deformation theory assumption. The temperature difference and applied voltage are assumed to be constant. The critical buckling temperature of FG beams are upper than the isotropic ones. Also, the critical temperature is different for various boundary conditions.

Keywords: buckling, functionally graded beams, Hamilton's principle, Euler-Bernoulli beam

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Authors: Jignesh Patel, Satish K. Joshi

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This paper presents the literature review on the works done so far in the area of stability of power system with high penetration of Wind Power with other conventional power sources. Out of many problems, the voltage and frequency stability is of prime concern as it is directly related with the stable operation of power system. In this paper, different aspects of stability of power system, particularly voltage and frequency, Optimization of FACTS-Energy Storage devices is discussed.

Keywords: small singal stability, voltage stability, frequency stability, LVRT, wind power, FACTS

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Authors: Mustafa Bayram Gücen, Coşkun Yakar

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In this study, we have investigated the strict stability of fuzzy differential systems and we compare the classical notion of strict stability criteria of ordinary differential equations and the notion of strict stability of fuzzy differential systems. In addition that, we present definitions of stability and strict stability of fuzzy differential equations and also we have some theorems and comparison results. Strict Stability is a different stability definition and this stability type can give us an information about the rate of decay of the solutions. Lyapunov’s second method is a standard technique used in the study of the qualitative behavior of fuzzy differential systems along with a comparison result that allows the prediction of behavior of a fuzzy differential system when the behavior of the null solution of a fuzzy comparison system is known. This method is a usefull for investigating strict stability of fuzzy systems. First of all, we present definitions and necessary background material. Secondly, we discuss and compare the differences between the classical notion of stability and the recent notion of strict stability. And then, we have a comparison result in which the stability properties of the null solution of the comparison system imply the corresponding stability properties of the fuzzy differential system. Consequently, we give the strict stability results and a comparison theorem. We have used Lyapunov second method and we have proved a comparison result with scalar differential equations.

Keywords: fuzzy systems, fuzzy differential equations, fuzzy stability, strict stability

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Authors: Chang-Ho Lee, Seung-Hoon Lee, Myeong-Jin Park, Oh-Min Kwon

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This paper investigates improved stability criteria for sampled-data control of linear systems with disturbances and time-varying delays. Based on Lyapunov-Krasovskii stability theory, delay-dependent conditions sufficient to ensure H∞ stability for the system are derived in the form of linear matrix inequalities(LMI). The effectiveness of the proposed method will be shown in numerical examples.

Keywords: sampled-data control system, Lyapunov-Krasovskii functional, time delay-dependent, LMI, H∞ control

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Authors: Jitendra Singh, Vivek Kumar

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In this paper, a susceptible infective susceptible mathematical model is proposed and analyzed where the migration of human population is given by migration function. It is assumed that the disease is transmitted by direct contact of susceptible and infective populations with constant contact rate. The equilibria and their stability are studied by using the stability theory of ordinary differential equations and computer simulation. The model analysis shows that the spread of infectious disease increases when human population immigration increases in the habitat but it decreases if emigration increases.

Keywords: SIS (Susceptible Infective Susceptible) model, migration function, susceptible, stability

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Authors: Ali Kargar, Kamyar Mansour

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In this paper, experimental results of using hot wire anemometer and smoke visualization are presented. The results obtained on the hot wire anemometer for critical Reynolds number and transitional Reynolds number are compared by previous results. Excellent agreement is found for the transitional Reynolds number. The results for the transitional Reynolds number are also compared by previous linear stability results. The results of the smoke visualization clearly show the cross flow vortices which arise in the transition process from a laminar to a turbulent flow. A non-zero angle of attack is also considered. We compare our results by linear stability theory which was done by Garret et. Al (2007). We just emphasis, Also the visualization and hot wire anemometer results have been compared graphically. The goal in this paper is to check reliability of using hot wire anemometer and smoke visualization in transition problems and check reliability of linear stability theory for this case and compare our results with some trusty experimental works.

Keywords: transitional reynolds number, wind tunnel, rotating cone, smoke visualization

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Authors: Shittu Akinpelu, Issac Popoola

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The compound NbRhGe has been predicted to be a semiconductor with excellent mechanical properties. It is an indirect band gap material. The potential of NbRhGe for non-volatile data storage via element addition is being studied using the Density Functional Theory (DFT). Preliminary results on the electronic and magnetic properties are suggestive for their application in spintronic.

Keywords: half-metals, Heusler compound, semiconductor, spintronic

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Authors: Safia Hocine, Djamil Aïssani

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Risk models, recently studied in the literature, are becoming increasingly complex. It is rare to find explicit analytical relations to calculate the ruin probability. Indeed, the stability issue occurs naturally in ruin theory, when parameters in risk cannot be estimated than with uncertainty. However, in most cases, there are no explicit formulas for the ruin probability. Hence, the interest to obtain explicit stability bounds for these probabilities in different risk models. In this paper, we interest to the stability bounds of the univariate classical risk model established using the regenerative processes approach. By adopting an algorithmic approach, we implement this approximation and determine numerically the bounds of ruin probability in the case of large claims (heavy-tailed distribution).

Keywords: heavy-tailed distribution, large claims, regenerative process, risk model, ruin probability, stability

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Authors: J. Ritonja, R. Brezovnik, M. Petrun, B. Polajžer

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Many modern synchronous generators in power systems are extremely weakly damped. The reasons are cost optimization of the machine building and introduction of the additional control equipment into power systems. Oscillations of the synchronous generators and related stability problems of the power systems are harmful and can lead to failures in operation and to damages. The only useful solution to increase damping of the unwanted oscillations represents the implementation of the power system stabilizers. Power system stabilizers generate the additional control signal which changes synchronous generator field excitation voltage. Modern power system stabilizers are integrated into static excitation systems of the synchronous generators. Available commercial power system stabilizers are based on linear control theory. Due to the nonlinear dynamics of the synchronous generator, current stabilizers do not assure optimal damping of the synchronous generator’s oscillations in the entire operating range. For that reason the use of the robust power system stabilizers which are convenient for the entire operating range is reasonable. There are numerous robust techniques applicable for the power system stabilizers. In this paper the use of sliding mode control for synchronous generator stability improvement is studied. On the basis of the sliding mode theory, the robust power system stabilizer was developed. The main advantages of the sliding mode controller are simple realization of the control algorithm, robustness to parameter variations and elimination of disturbances. The advantage of the proposed sliding mode controller against conventional linear controller was tested for damping of the synchronous generator oscillations in the entire operating range. Obtained results show the improved damping in the entire operating range of the synchronous generator and the increase of the power system stability. The proposed study contributes to the progress in the development of the advanced stabilizer, which will replace conventional linear stabilizers and improve damping of the synchronous generators.

Keywords: control theory, power system stabilizer, robust control, sliding mode control, stability, synchronous generator

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Authors: Daniel Nkrumah

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The Magic Bullet theory was a popular media effect theory that defined the power of the mass media in altering beliefs and perceptions of its audiences. However, following the People's Choice study, the theory was said to have been disproved and was supplanted by the Two-Step Flow Theory. This paper examines the relevance of the Magic Bullet theory in Africa and establishes whether it is still relevant in Africa's media spaces and societies. Using selected cases on the continent, it adopts a grounded theory approach and explores a new theoretical model that attempts to enforce an argument that the Two-Step Flow theory though important and valid, was ill-conceived as a direct replacement to the Magic Bullet theory.

Keywords: magic bullet theory, two-step flow theory, media effects, african media

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Authors: Hamed Khani Arani, Mohammad Shariyat, Armaghan Mohammadian

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In this research, the free vibration of a rectangular sandwich nano-plate (SNP) made of three smart layers in the visco Pasternak foundation is studied. The core of the sandwich is a piezo magnetic nano-plate integrated with two layers of piezoelectric materials. First-order shear deformation plate theory is utilized to derive the motion equations by using Hamilton’s principle, piezoelectricity, and modified couple stress theory. Elastic medium is modeled by visco Pasternak foundation, where the damping coefficient effect is investigated on the stability of sandwich nano-plate. These equations are solved by the differential quadrature method (DQM), considering different boundary conditions. Results indicate the effect of various parameters such as aspect ratio, thickness ratio, shear correction factor, damping coefficient, and boundary conditions on the dimensionless frequency of sandwich nano-plate. The results are also compared by those available in the literature, and these findings can be used for automotive industry, communications equipment, active noise, stability, and vibration cancellation systems and utilized for designing the magnetostrictive actuator, motor, transducer and sensors in nano and micro smart structures.

Keywords: free vibration, modified couple stress theory, sandwich nano-plate, visco Pasternak foundation

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Authors: Davide Forcellini, James Marshal Kelly

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Seismic isolation using multi-layer elastomeric isolators has been used in the United States for more than 20 years. Although isolation bearings normally have a large factor of safety against buckling due to low shear stiffness, this phenomenon has been widely studied. In particular, the linearly elastic theory adopted to study this phenomenon is relatively accurate and adequate for most design purposes. Unfortunately it cannot consider the large deformation response of a bearing when buckling occurs and the unresolved behaviour of the stability of the post-buckled state. The study conducted in this paper may be viewed as a development of the linear theory of multi-layered elastomeric bearing, simply replacing the differential equations by algebraic equations, showing how it is possible to evaluate the post-buckling behaviour and the interactions at large deformations.

Keywords: multi-layer elastomeric isolators, large deformation, compressive load, tensile load, post-buckling behaviour

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Authors: M. Madigoe, R. Modiba

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High alloyed beta (β) phase-stabilized titanium alloys are known to have a low elastic modulus comparable to that of the human bone (≈30 GPa). The β phase in titanium alloys exhibits an elastic Young’s modulus of about 60-80 GPa, which is nearly half that of α-phase (100-120 GPa). In this work, a theoretical investigation of structural stability and thermodynamic stability, as well as the elastic properties of a quaternary Ti-Nb-Ta-Zr alloy, will be presented with an attempt to lower Young’s modulus. The structural stability and elastic properties of the alloy were evaluated using the first-principles approach within the density functional theory (DFT) framework implemented in the CASTEP code. The elastic properties include bulk modulus B, elastic Young’s modulus E, shear modulus cʹ and Poisson’s ratio v. Thermodynamic stability, as well as the fraction of β phase in the alloy, was evaluated using the Thermo-Calc software package. Thermodynamic properties such as Gibbs free energy (Δ?⁰?) and enthalpy of formation will be presented in addition to phase proportion diagrams. The stoichiometric compositions of the alloy is Ti-Nbx-Ta5-Zr5 (x = 5, 10, 20, 30, 40 at.%). An optimum alloy composition must satisfy the Born stability criteria and also possess low elastic Young’s modulus. In addition, the alloy must be thermodynamically stable, i.e., Δ?⁰? < 0.

Keywords: elastic modulus, phase proportion diagram, thermo-calc, titanium alloys

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Authors: Arne Fagerstrom, Gary Cunningham, Fredrik Hartwig

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In this paper, a theory of sustainable enterprises, sustainable enterprise theory (SET), is developed. The sustainable enterprise theory can only be a valid theory if knowledge about life and nature is complete. Knowledge limitations should not stop enterprises from doing business with a goal of better long-term life on earth. Life demands stewardship of the resources used during one’s lifetime. This paper develops a model influenced by (the classical) enterprise theory and resource theory that includes more than money in the business activities of an enterprise. The sustainable enterprise theory is then used in an analysis of accountability and in discussions about sustainable businesses.

Keywords: sustainable business, sustainability reporting, sustainable values, theory of the firm

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Authors: Rami Georg Johann

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Against the background of the current geopolitical constellations, the author looks at various empire models, which are discussed and compared with each other with regard to their stability and functioning. The focus is on the fifth concept as a possible new world order in the 21st century. These will be discussed and compared to one another according to their stability and functioning. All empires to be designed will be conceptualised based on one, two, three, four, and five worlds. All worlds are made up of a different constellation of states and relating coalitions. All systems will be discussed in detail. The one-world-system, the“Western Empire,” will be presented as a possible solution to a new world order in the 21st century (fifth concept). The term “Western” in “Western Empire” describes the Western concept after World War II. This Western concept was the result of two horrible world wars in the 20th century.” With this in mind, the fifth concept forms a stable empire system, the “Western Empire,” by political measures tied to two issues. Thus, this world order provides a significantly higher long-term stability in contrast to all other empire models (comprising five, four, three, or two worlds). Confrontations and threats of war are reduced to a minimum. The two issues mentioned are “merger” and “competition.” These are the main differences in forming an empire compared to all empires and realms in the history of mankind. The fifth concept of this theory, the “Western Empire,” acts explicitly as a counter model. The Western Empire (fifth concept) is formed by the merger of world powers without war. Thus, a world order without competition is created. This merged entity secures long-term peace, stability, democratic values, freedom, human rights, equality, and justice in the new world order.

Keywords: empire formation, theory of international relations, Western Empire, world order

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