Journal articles on the topic 'Admissible variation'
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Hu, Caiqi, Xiaoqi Hu, Jing Ji, Jude Liu, and Shengduo Li. "Dynamics Analysis on Piezoelectric Laminated Vibrator and Optimization of PZT Position." Shock and Vibration 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/8403829.
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Piezoelectric laminated structure is widely used as actuator’s drive part. The different position of PZT on a piezoelectric vibrator causes different incentive effects. Therefore, seeking an optimal PZT position is of great significance to improve actuator’s drive forces and electromechanical conversion efficiency. In this research, the optimization of PZT position was studied using the approximate solution of piezoelectric vibrator mode shape with mutation sections. The vibration mode function was expressed as a linear superposition of the admissible function according to Rayleigh Ritz method. Then solving of functional variation was converted into the solving of the coefficient matrix of the admissible function by Hamilton’s principle. Through analyzing the forms of admissible functions, the admissible functions that satisfied the boundary conditions of displacement were chosen. For a given vibrator, approximate function for natural frequency and vibration mode was calculated in given admissible functions. Calculated values and experimental results were compared. Results showed that the more items an admissible function sequence had the closer the calculated results were to the experimental values. The errors of calculations were analyzed based on the selection of admissible functions and electromechanical coupling effect. Optimization of PZT position was achieved by analyzing the mode forces of the piezoelectric laminated vibrator.
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Han, Yuecai, and Zheng Li. "Maximum Principle of Discrete Stochastic Control System Driven by Both Fractional Noise and White Noise." Discrete Dynamics in Nature and Society 2020 (June 5, 2020): 1–10. http://dx.doi.org/10.1155/2020/1959050.
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In this paper, we investigate the necessary optimality conditions of the discrete stochastic optimal control problems driven by both fractional noise and white noise. Here, the admissible control region is not necessarily convex. The corresponding variational inequalities are obtained by applying the classical variation method and Malliavin calculus. We also apply the stochastic maximum principle to a linear-quadratic optimal control problem to illustrate the main result.
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Liang, Feng, Xiao-Dong Yang, Ying-Jing Qian, and Wei Zhang. "Free Vibration Analysis of Pipes Conveying Fluid Based on Linear and Nonlinear Complex Modes Approach." International Journal of Applied Mechanics 09, no. 08 (December 2017): 1750112. http://dx.doi.org/10.1142/s1758825117501125.
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In this paper, linear and nonlinear complex modes are used to analyze the free vibration of pipes conveying fluid involving the gyroscopic properties of the system. The natural frequencies, complex mode functions and time domain responses of the admissible mode functions based on discretized model are obtained using the invariant manifold method and compared with those of the continuous model. A good agreement has been achieved if the admissible mode functions for the static beams are adopted. The energy contributions of different admissible modes to the modal motions are also studied which explores the gyroscopic coupling variation among the admissible modes for different fluid velocities. Nonlinear complex modes are constructed for the nonlinear case and the morphology of the modal motions is demonstrated for different initial energy to show the contribution of the nonlinear terms. ‘Traveling waves’ are found for the transverse vibrations of the pipes conveying fluid due to the gyroscopic effects, contrary to the “standing waves” found for the pipes without moving fluid.
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Burris, Stanley, and András Sárközy. "Fine Spectra and Limit Laws I. First-Order Laws." Canadian Journal of Mathematics 49, no. 3 (June 1, 1997): 468–98. http://dx.doi.org/10.4153/cjm-1997-022-4.
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AbstractUsing Feferman-Vaught techniques we show a certain property of the fine spectrumof an admissible class of structures leads to a first-order law. The condition presented is best possible in the sense that if it is violated then one can find an admissible class with the same fine spectrum which does not have a first-order law. We present three conditions for verifying that the above property actually holds.The first condition is that the count function of an admissible class has regular variation with a certain uniformity of convergence. This applies to a wide range of admissible classes, including those satisfying Knopfmacher's Axiom A, and those satisfying Bateman and Diamond's condition.The second condition is similar to the first condition, but designed to handle the discrete case, i.e., when the sizes of the structures in an admissible class K are all powers of a single integer. It applies when either the class of indecomposables or the whole class satisfies Knopfmacher's Axiom A#.The third condition is also for the discrete case, when there is a uniform bound on the number of K-indecomposables of any given size.
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Dafermos, Constantine M. "Asymptotic behavior of BV solutions to hyperbolic systems of balance laws with relaxation." Journal of Hyperbolic Differential Equations 12, no. 02 (June 2015): 277–92. http://dx.doi.org/10.1142/s0219891615500083.
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For hyperbolic systems of balance laws governing relaxation processes, in one space dimension, with source incurring nonnegative entropy production and satisfying a Kawashima-type condition, it is shown that when the initial data have small total variation on (-∞, ∞) and decay rapidly to zero, as |x| → ∞, then the Cauchy problem possesses a unique admissible BV solution, in the large, with total variation decaying to zero, as t → ∞.
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Brosnan, Patrick, Gregory Pearlstein, and Christian Schnell. "The locus of Hodge classes in an admissible variation of mixed Hodge structure." Comptes Rendus Mathematique 348, no. 11-12 (June 2010): 657–60. http://dx.doi.org/10.1016/j.crma.2010.04.002.
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Cianchi, Andrea. "A sharp trace inequality for functions of bounded variation in the ball." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 142, no. 6 (November 27, 2012): 1179–91. http://dx.doi.org/10.1017/s0308210511000758.
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The best constant in a mean-value trace inequality for functions of bounded variation on admissible domains Ω ⊂ ℝn is shown to agree with an isoperimetric constant associated with Ω. The existence and form of extremals is also discussed. This result is exploited to compute the best constant in the relevant trace inequality when Ω is a ball. The existence and the form of extremals in this special case turn out to depend on the dimension n. In particular, the best constant is not achieved when Ω is a disc in ℝ2.
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Díaz-Marín, Homero G. "A Poisson Algebra for Abelian Yang-Mills Fields on Riemannian Manifolds with Boundary." Symmetry 11, no. 7 (July 4, 2019): 880. http://dx.doi.org/10.3390/sym11070880.
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We define a family of observables for abelian Yang-Mills fields associated to compact regions U ⊆ M with smooth boundary in Riemannian manifolds. Each observable is parametrized by a first variation of solutions and arises as the integration of gauge invariant conserved current along admissible hypersurfaces contained in the region. The Poisson bracket uses the integration of a canonical multisymplectic current.
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Agamaliyeva, A. I. "Investigation of discrete analogue of one boundary problem of optimal control." Applied Mathematics and Control Sciences, no. 3 (December 15, 2022): 9–25. http://dx.doi.org/10.15593/2499-9873/2022.03.01.
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In the paper, one boundary value problem of optimal control for discrete two-parameter systems with discrete time is investigated. Such problems are discrete analogues of optimal control problems described by integro-differential partial differential equations of the first order. The initial function is controllable and is defined as the solution of the Cauchy problem for nonlinear ordinary difference equation, the right part of which includes concentrated control. The quality functional presents the sum of two different terms and is a Boltz type functional for the optimal control problem under consideration. The cases of arbitrary, convex and open control area defining the corresponding class of admissible controls are studied. Imposing various natural smoothness conditions on the right-hand sides of the two-dimensional and one-dimensional difference equations under consideration, assuming the convexity of the analogue of the set of admissible velocities of the system under consideration, a special increment of the quality criterion is calculated using a modified functional increment method and, based on its non-negativity along the optimal control, an analogue of the discrete Pontryagin maximum principle is proved. Assuming the convexity of the control area, by linearizing the terms in the functional increment formula and introducing a special variation of the admissible control, an analogue of the linearized maximum condition is proved. In contrast to the continuous case, the linearized maximum principle is not a consequence of the discrete maximum principle and has an independent value as a necessary condition for optimality. In the case of open control area, by introducing a classical variation of the control, the first variation (in the classical sense) of the functional is calculated and established that in the case of open control area, the first variation of the quality criterion equals zero, with its help, an analogue of the Euler equation for the optimal control problem under consideration is obtained. The scheme used in the work also makes it possible to further investigate some cases of degeneration of the obtained necessary conditions of optimality of the first order and to deduce new, constructive necessary conditions of optimality of the second order, allowing to narrow down the set of permissible controls suspicious of optimality.
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Carita, Graça, and Elvira Zappale. "Relaxation for an optimal design problem with linear growth and perimeter penalization." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 145, no. 2 (April 2015): 223–68. http://dx.doi.org/10.1017/s0308210513001479.
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This paper is devoted to the relaxation and integral representation in the space of functions of bounded variation for an integral energy arising from optimal design problems. The presence of a perimeter penalization is also considered in order to avoid non-existence of admissible solutions and, in addition, this leads to an interaction in the limit energy. More general models have also been taken into account.
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Зиннатуллин, Назиф, Nazif Zinnatullin, Булат Зиганшин, Bulat Ziganshin, Иршад Нафиков, Irshad Nafikov, Максим Лушнов, Maksim Lushnov, Гульнара Зиннатуллина, and Gul'nara Zinnatullina. "INJECTION MIXTURE OF SOLID, LOOSE MATERIALS." Vestnik of Kazan State Agrarian University 12, no. 3 (January 11, 2018): 68–71. http://dx.doi.org/10.12737/article_5a1d96936b0656.58609817.
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The injection pumps are used for stirring (mixing) of solid loose materials in gas and liquid media. An antilock brake device – spreader is used to unload the suction zone of the injector. The technological parameters of the process are defined: the limiting diameter of the arch of forming holes, the parameters of spreader, the speed of waving and entrainment, the criterion for estimating the homogeneity, the inhomogeneity coefficient, the coefficient of variation, the minimum admissible weight of sample.
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Jenssen, Helge Kristian, and Johanna Ridder. "On Φ-variation for 1-d scalar conservation laws." Journal of Hyperbolic Differential Equations 17, no. 04 (December 2020): 843–61. http://dx.doi.org/10.1142/s0219891620500277.
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Let [Formula: see text] be a convex function satisfying [Formula: see text], [Formula: see text] for [Formula: see text], and [Formula: see text]. Consider the unique entropy admissible (i.e. Kružkov) solution [Formula: see text] of the scalar, 1-d Cauchy problem [Formula: see text], [Formula: see text]. For compactly supported data [Formula: see text] with bounded [Formula: see text]-variation, we realize the solution [Formula: see text] as a limit of front-tracking approximations and show that the [Formula: see text]-variation of (the right continuous version of) [Formula: see text] is non-increasing in time. We also establish the natural time-continuity estimate [Formula: see text] for [Formula: see text], where [Formula: see text] depends on [Formula: see text]. Finally, according to a theorem of Goffman–Moran–Waterman, any regulated function of compact support has bounded [Formula: see text]-variation for some [Formula: see text]. As a corollary we thus have: if [Formula: see text] is a regulated function, so is [Formula: see text] for all [Formula: see text].
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Najafabadi, Seyed Ali Modarres, József Kövecses, and Jorge Angeles. "Energy Analysis and Decoupling in Three-Dimensional Impacts of Multibody Systems." Journal of Applied Mechanics 74, no. 5 (December 20, 2006): 845–51. http://dx.doi.org/10.1115/1.2712226.
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This paper discusses an exact decomposition of the kinetic energy to determine the energy content that influences the dynamics of unilateral contacts in multibody systems. This decomposition essentially divides the kinetic energy of the whole multibody system into two completely decoupled parts associated with the constrained and admissible directions of unilateral contacts. This will provide a picture of how the energy absorption/dissipation during impacts is related to the variation of the generalized velocities and the configuration of multibody systems. Potential applications of such a decoupling are highlighted.
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Cigan, Vesna. "Collocations and Term Variation in Mechanical Engineering Discourse." Fluminensia 30, no. 2 (2018): 99–120. http://dx.doi.org/10.31820/f.30.2.3.
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Terminological collocations1 are one of the most typical and very frequent units of representation of concepts in many disciplines. Although traditionally considered to be unwelcome in terminology, synonymy is amply present in specialized languages. Consequently, the same phenomenon is reflected in terminological collocations. This paper aims to investigate synonymous collocations extracted from mechanical engineering texts in terms of the most frequent and relevant types of denominative variation in the selected English collocations as well as of their equivalents in German and Croatian. The analysis of variations in terminological collocations gives insight into the (non)substitutability of collocation constituents as one of the major characteristics of collocations. Extracted collocations are analysed within a two-tier framework structured at a paradigmatic and a syntagmatic level, which allows for the identification of the three types of term variation: morphological, syntagmatic and semantic. Focusing on the collocations with the structure noun + noun and adjective + noun the results show that constituents of both syntactic structures allow substitution. The denominative variants are prevalent in adjective + noun collocations in which synonymous lexical elements functioning as collocates do not entail a concept change (admissible load ↔ allowable load). Lexeme substitutions are also annotated in noun + noun collocations expressing a slightly different dimension or facet of the concept (face gear vs. crown gear vs. crown wheel). The majority of German equivalents are nominal compounds that outnumber their morphological variants offering multiple equivalences.
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Darwish, Shaimaa. "Reflexives and Reciprocals in English and Modern Standard Arabic: An Investigation and a Comparison." Journal of Language Teaching and Research 12, no. 6 (November 2, 2021): 955–68. http://dx.doi.org/10.17507/jltr.1206.12.
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The aim of this paper is to investigate the typology of reflexives and reciprocals in English and MSA, which is a variety of standardized, literary Arabic used throughout Arab countries. It has shown that MSA morphologically encoded reflexives and reciprocals are in fact syntactically and semantically asymmetrical. It will be argued that morphologically encoded reflexives do not project an anaphor (an internal argument) syntactically and their morphological marker semantically serves as a reflexivizer, whereas morphologically encoded reciprocals do project an anaphor syntactically, realized either overtly or covertly. Concerning the distribution of such anaphor, the paper elucidates the admissible and in admissible environments. It is argued that MSA does not allow possessive reflexives, but allow possessive reciprocals such as the construct-state, whether it be a noun phrase or a locative prepositional phrase. This variation is accounted for by assuming that reciprocals occupy Spec of DP and therefore can be bound by an NP from a higher phase, whereas reflexives occupy a position lower than the D head and thus must be bound within their DP phase. Finally yet importantly, MSA override reflexives and reciprocals unlike their English counterparts, are always subject to the Principle A of the Binding Theory.
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Parvizi, Ali, and Karen Abrinia. "An Upper Bound Analysis of the Ring Rolling Process." Advanced Materials Research 383-390 (November 2011): 2819–26. http://dx.doi.org/10.4028/www.scientific.net/amr.383-390.2819.
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A generalized upper bound solution for the deformation of ring in the ring rolling process has been formulated. An admissible velocity field and strain rates are derived from the parametric definition of streamlines in the deformation zone. This new formulation was used to predict the upper bound on power. Minimizing the upper bound power with respect to neutral point position, the neutral point position and the rolling force were determined. Using the theory presented here, the variation of internal, shear, frictional and total powers with respect to ring revolution are discussed. Some of the results obtained from analysis were compared with experimental results.
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ZÄHLE, M. "LONG RANGE DEPENDENCE, NO ARBITRAGE AND THE BLACK–SCHOLES FORMULA." Stochastics and Dynamics 02, no. 02 (June 2002): 265–80. http://dx.doi.org/10.1142/s0219493702000406.
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A bond and stock model is considered where the driving process is the sum of a Wiener process W and a continuous process Z with zero generalized quadratic variation. By means of forward integrals a hedge against Markov-type claims is constructed. If Z is independent of W under some natural assumptions on Z and the admissible portfolio processes the model is shown to be arbitrage free. The fair price of the above claims agrees with that in the classical case Z ≡ 0. In particular, the Black–Scholes formula remains valid for non-semimartingale models with long range dependence.
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Chraptovič, Ela, and Juozas Atkočiūnas. "ROLE OF KUHN-TUCKER CONDITIONS IN ELASTICITY EQUATIONS IN TERMS OF STRESSES." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 6, no. 2 (April 30, 2000): 104–12. http://dx.doi.org/10.3846/13921525.2000.10531573.
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Solution of the elasticity problem in terms of stresses leads to the stress vector six components, satisfying the Beltrami compatibility eqns and boundary conditions, evaluation. A direct integration of the nine differential eqns system in respect of the six stress components is difficult to realise practically. This is the reason why often the Casigliano variation principle to solve the boundary elasticity problem in terms of stresses is applied. An application of the above-mentioned principle ensures the satisfaction of all the six Saint-Venant strain compatibility eqns (see the works of Southwell, Kliushnikov, a.o.). Castigliano variation principle does not define the number of independent strain compatibility eqns. Thus, it is not clear whether the elasticity problem eqns system in terms of stresses is over-defined or not. The strain compatibility eqns for an ideal elastic body is investigated in the article by means of the mathematical programming theory. A mathematical model to evaluate the statically admissible stresses is formulated on the basis of complementary energy minimum principle. It is proved that the strain compatibility eqns mean the Kuhn-Tucker optimality conditions of the mathematical programming problem. The method to formulate the strain compatibility eqns in respect of the statically admissible stresses defining eqns formulation technique is revealed. The proposed method is illustrated to achieve the six component stresses vector in functional space for the three-dimension problem: usually the solution of the elasticity problem in terms of the stresses is realised via the nine eqns system integration. The Kuhn-Tucker conditions allowed to confirm an original but not usually applied Washizu conclusion about Cauchy geometrical compatibility eqns.
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Dikariev, Ilya, Fabiola Angulo, and David Angulo-Garcia. "Single-Switching Reachable Operation Points in a DC-DC Buck Converter: An Approximation from Time Optimal Control." Micromachines 11, no. 9 (August 31, 2020): 834. http://dx.doi.org/10.3390/mi11090834.
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In this paper, we study the time optimal control problem in a DC-DC buck converter in the underdamped oscillatory regime. In particular, we derive analytic expressions for the admissible regions in the state space, satisfying the condition that every point within the region is reachable in optimal time with a single switching action. We then make use of the general result to establish the minimum and maximum variation allowed to the load in two predefined design set-ups that fulfills the time optimal single switching criteria. Finally, we make use of numerical simulations to show the performance of the proposed control under changes in the reference voltage and load resistance.
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Massa, Enrico, Danilo Bruno, Gianvittorio Luria, and Enrico Pagani. "Geometric constrained variational calculus I: Piecewise smooth extremals." International Journal of Geometric Methods in Modern Physics 12, no. 05 (May 2015): 1550061. http://dx.doi.org/10.1142/s0219887815500619.
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A geometric setup for constrained variational calculus is presented. The analysis deals with the study of the extremals of an action functional defined on piecewise differentiable curves, subject to differentiable, non-holonomic constraints. Special attention is paid to the tensorial aspects of the theory. As far as the kinematical foundations are concerned, a fully covariant scheme is developed through the introduction of the concept of infinitesimal control. The standard classification of the extremals into normal and abnormal ones is discussed, pointing out the existence of an algebraic algorithm assigning to each admissible curve a corresponding abnormality index, related to the co-rank of a suitable linear map. Attention is then shifted to the study of the first variation of the action functional. The analysis includes a revisitation of Pontryagin's equations and of the Lagrange multipliers method, as well as a reformulation of Pontryagin's algorithm in Hamiltonian terms. The analysis is completed by a general result, concerning the existence of finite deformations with fixed endpoints.
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Nurislamova, Liana F., Olga P. Stoyanovskaya, Olga A. Stadnichenko, Irek M. Gubaidullin, Valeriy N. Snytnikov, and Anastasia V. Novichkova. "Few-Step Kinetic Model of Gaseous Autocatalytic Ethane Pyrolysis and Its Evaluation by Means of Uncertainty and Sensitivity Analysis." Chemical Product and Process Modeling 9, no. 2 (December 1, 2014): 143–54. http://dx.doi.org/10.1515/cppm-2014-0008.
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Abstract A kinetic scheme of radical chain reactions in autocatalytic pyrolysis of ethane was studied using a sensitivity analysis method, bringing in the experimental data. In the gas-phase kinetic experiments, ethane pyrolysis was carried out in laboratory reactors with the reaction mixture heated by CO2 laser irradiation. It was shown that the scheme with autocatalytic routes includes as few steps as possible and adequately describes the ethane pyrolysis with high ethylene yield at 900–1,150 K. Admissible variation ranges of preexponential factors and activation energies for the kinetic model of the reactions were found using the Monte Carlo statistical method. Reducibility of the scheme was examined by means of the Sobol’s variance based strategy applied for the sensitivity analysis evaluation.
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Zdorovtsov, I. A., V. Yu Korolev, A. G. Surkov, and V. V. Shmytinskij. "Boundary Identification for Admissible Variation of External and Internal Factors Affecting Robustness of Fiber-Optic Communication Systems on Rail Transport*." Journal of Mathematical Sciences 189, no. 6 (February 28, 2013): 940–49. http://dx.doi.org/10.1007/s10958-013-1235-7.
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Noh, T. S., and D. Y. Yang. "A General Formulation for Hydroforming of Arbitrarily-Shaped Boxes and Its Application to Hydroforming of an Elliptic-Circular Box." Journal of Manufacturing Science and Engineering 120, no. 3 (August 1, 1998): 481–88. http://dx.doi.org/10.1115/1.2830150.
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A general kinematically admissible velocity field is suggested for the upper-bound solution of hydroforming of arbitrarily-shaped boxes. The suggested formulation is then applied to hydroforming of an elliptic-circular box. From the proposed velocity field, the fluid pressure vs. punch stroke relationship to render uniform thickness and the deformed configuration are determined by minimizing the total power consumption with respect to some chosen parameters. Experiments are carried out in the hydroforming press according to the computed pressure vs. punch stroke curve. The assumption of uniform wall thickness is confirmed by measuring the thickness variation. The effects of various process parameters including blank size, work-hardening exponent and frictional coefficient on the pressure curve are analyzed and discussed. It is thus shown that the proposed method of analysis in the present study can be effectively used for hydroforming of arbitrarily shaped boxes.
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Wang, Hui. "Some control problems with random intervention times." Advances in Applied Probability 33, no. 2 (June 2001): 404–22. http://dx.doi.org/10.1017/s0001867800010867.
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We consider the problem of optimally tracking a Brownian motion by a sequence of impulse controls, in such a way as to minimize the total expected cost that consists of a quadratic deviation cost and a proportional control cost. The main feature of our model is that the control can only be exerted at the arrival times of an exogenous uncontrolled Poisson process (signal). In other words, the set of possible intervention times are discrete, random and determined by the signal process (not by the decision maker). We discuss both the discounted problem and the ergodic problem, where explicit solutions can be found. We also derive the asymptotic behavior of the optimal control policies and the value functions as the intensity of the Poisson process goes to infinity, or roughly speaking, as the set of admissible controls goes from the discrete-time impulse control to the continuous-time bounded variation control.
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Stagnaro, Mattia, Arianna Cauteruccio, Luca G. Lanza, and Pak-Wai Chan. "On the Use of Dynamic Calibration to Correct Drop Counter Rain Gauge Measurements." Sensors 21, no. 18 (September 21, 2021): 6321. http://dx.doi.org/10.3390/s21186321.
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Dynamic calibration was performed in the laboratory on two catching-type drop counter rain gauges manufactured as high-sensitivity and fast response instruments by Ogawa Seiki Co. Ltd. (Japan) and the Chilbolton Rutherford Appleton Laboratory (UK). Adjustment procedures were developed to meet the recommendations of the World Meteorological Organization (WMO) for rainfall intensity measurements at the one-minute time resolution. A dynamic calibration curve was derived for each instrument to provide the drop volume variation as a function of the measured drop releasing frequency. The trueness of measurements was improved using a post-processing adjustment algorithm and made compatible with the WMO recommended maximum admissible error. The impact of dynamic calibration on the rainfall amount measured in the field at the annual and the event scale was calculated for instruments operating at two experimental sites. The rainfall climatology at the site is found to be crucial in determining the magnitude of the measurement bias, with a predominant overestimation at the low to intermediate rainfall intensity range.
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Zadeh, Mohammad Naghavi, Iman Dayyani, and Mehdi Yasaee. "Fish Cells, a new zero Poisson’s ratio metamaterial—part II: Elastic properties." Journal of Intelligent Material Systems and Structures 31, no. 19 (July 27, 2020): 2196–210. http://dx.doi.org/10.1177/1045389x20942576.
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Fish Cells as a new metamaterial with zero Poisson’s ratio in two planar directions is introduced with application in morphing aircraft skin. In order to tailor the design of this metamaterial for arbitrary loadings, equivalent elastic properties of the Fish Cells metamaterial are derived and analyzed using analytical and numerical methods. The admissible range of geometric parameters is presented and variation of elastic properties with parameters is studied. The effective elastic modulus of the metamaterial is derived analytically and verified with finite element models. The in-plane and transverse shear modulus of the metamaterial are evaluated using finite element analysis where accurate periodic boundary conditions for in-plane shear loading are investigated. The lower and upper bounds of the transverse shear modulus are derived based on strain and complementary energy relations which are verified with finite element results. As zero Poisson’s ratio behavior of the Fish Cells topology is proved, derivative geometries from this topology with zero Poisson’s ratio behavior are also presented.
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Rachid, El Kaak, El Bikri Khalid, and Benamar Rhali. "Geometrically Nonlinear Free Axisymmetric Vibrations Analysis of Thin Circular Functionally Graded Plates." Advanced Materials Research 971-973 (June 2014): 489–506. http://dx.doi.org/10.4028/www.scientific.net/amr.971-973.489.
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This paper deals with nonlinear free axisymmetric vibrations of functionally graded thin circular plates whose properties vary through its thickness. The inhomogeneity of the plate is characterized by a power law variation of the Young’s modulus and mass density of the material along the thickness direction, whereas Poisson’s ratio is assumed to be constant. The theoretical model is based on Hamilton’s principle and spectral analysis using a basis of admissible Bessel’s functions to yield the frequencies of the circular plates under clamped boundary conditions on the basis of the classical plate theory. The large vibration amplitudes problem, reduced to a set of non-linear algebraic equations, is solved numerically. The non-linear to linear frequency ratios are presented for various values of the volume fraction index n showing hardening type non-linearity. The distribution of the radial bending stress associated to the non-linear mode shape is also given for various vibration amplitudes, and is compared with those predicted by the linear theory.
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Movchan, Alexander B., and Leonid I. Slepyan. "Band gap Green's functions and localized oscillations." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2086 (July 31, 2007): 2709–27. http://dx.doi.org/10.1098/rspa.2007.0007.
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We consider some typical continuous and discrete models of structures possessing band gaps, and analyse the localized oscillation modes. General considerations show that such modes can exist at any frequency within the band gap provided an admissible local mass variation is made. In particular, we show that the upper bound of the sinusoidal wave frequency exists in a non-local interaction homogeneous waveguide, and we construct a localized mode existing there at high frequencies. The localized modes are introduced via the Green's functions for the corresponding uniform systems. We construct such functions and, in particular, present asymptotic expressions of the band gap anisotropic Green's function for the two-dimensional square lattice. The emphasis is made on the notion of the depth of band gap and evaluation of the rate of localization of the vibration modes. Detailed analysis of the extremal localization is conducted. In particular, this concerns an algorithm of a ‘neutral’ perturbation where the total mass of a complex central cell is not changed
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Pagliari, Valerio. "Halfspaces minimise nonlocal perimeter: a proof via calibrations." Annali di Matematica Pura ed Applicata (1923 -) 199, no. 4 (December 21, 2019): 1685–96. http://dx.doi.org/10.1007/s10231-019-00937-7.
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AbstractWe consider a nonlocal functional $$J_K$$ J K that may be regarded as a nonlocal version of the total variation. More precisely, for any measurable function $$u:\mathbb {R}^d\rightarrow \mathbb {R}$$ u : R d → R , we define $$J_K(u)$$ J K ( u ) as the integral of weighted differences of u. The weight is encoded by a positive kernel K, possibly singular in the origin. We study the minimisation of this energy under prescribed boundary conditions, and we introduce a notion of calibration suited for this nonlocal problem. Our first result shows that the existence of a calibration is a sufficient condition for a function to be a minimiser. As an application of this criterion, we prove that halfspaces are the unique minimisers of $$J_K$$ J K in a ball, provided they are admissible competitors. Finally, we outline how to exploit the optimality of hyperplanes to recover a $$\varGamma $$ Γ -convergence result concerning the scaling limit of $$J_K$$ J K .
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Livanov, N. D., and V. I. Ukhobotov. "ON ONE PROBLEM OF CONTROL OF VOLTAGE DURING SIGNAL TRANSMISSION IN A LONG LINE." Bulletin of the South Ural State University. Ser. Computer Technologies, Automatic Control & Radioelectronics 21, no. 3 (August 2021): 59–65. http://dx.doi.org/10.14529/ctcr210306.
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This article discusses the problem of controlling the process of electromagnetic oscillations in a long-distance transmission line. A long line is understood as an electrical line formed, in the sim-plest case, by two parallel current conductors, the length of which exceeds the wavelength of the transmitted electromagnetic waves, and the distance between the conductors is much less than the wavelength. Such a line is characterized by four distributed parameters, namely the ohmic re-sistance of the conductor, inductance, electrical capacity and leakage coefficient. A signal generator is connected to the left end of the line, and the right is grounded, but not of high quality. When transmitting a signal, the current and voltage make small oscillation. The control is the voltage at the left end of the long line, and the disturbance voltage at the right end, the values of which are li-mited. The boundaries of their permissible values are set. The magnitude of the aggregate of exter-nal disturbances acting on the conductor is not known exactly, but only its variation limits are given. Aim. The purpose of the control process is that at a given moment in time, the average value of the voltage value is in a given interval. This average is calculated using the specified function. Materials and methods. To solve the problem, the method of optimizing the guaranteed result was applied. Results. A transition was made to a new one-dimensional variable, with the help of which the considered problem was reduced to a control problem of the same type in the presence of inter-ference. This made it possible to find the necessary and sufficient conditions under which it is pos-sible to achieve the set goals with any admissible set of external forces and interference at the right end. A corresponding algorithm for constructing the law of voltage change at the left end of the conductor is proposed. An example is analyzed that clearly shows how management is built that guarantees the achievement of the set goal. Conclusion. If the found necessary and sufficient con-ditions are fulfilled, then it is always possible to construct such a law of voltage variation at the left end, which will lead to the achievement of the goal for any admissible interference.
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Segura, Rocio, Jamie Padgett, and Patrick Paultre. "Expected seismic performance of gravity dams using machine learning techniques." Bulletin of the New Zealand Society for Earthquake Engineering 54, no. 2 (June 1, 2021): 58–68. http://dx.doi.org/10.5459/bnzsee.54.2.58-68.
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Methods for the seismic analysis of dams have improved extensively in the last several decades. Advanced numerical models have become more feasible and constitute the basis of improved procedures for design and assessment. A probabilistic framework is required to manage the various sources of uncertainty that may impact system performance and fragility analysis is a promising approach for depicting conditional probabilities of limit state exceedance under such uncertainties. However, the effect of model parameter variation on the seismic fragility analysis of structures with complex numerical models, such as dams, is frequently overlooked due to the costly and time-consuming revaluation of the numerical model. To improve the seismic assessment of such structures by jointly reducing the computational burden, this study proposes the implementation of a polynomial response surface metamodel to emulate the response of the system. The latter will be computationally and visually validated and used to predict the continuous relative maximum base sliding of the dam in order to build fragility functions and show the effect of modelling parameter variation. The resulting fragility functions are used to assess the seismic performance of the dam and formulate recommendations with respect to the model parameters. To establish admissible ranges of the model parameters in line with the current guidelines for seismic safety, load cases corresponding to return periods for the dam classification are used to attain target performance limit states.
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Arguchintsev, A. V., and V. P. Poplevko. "An Optimal Control Problem by a Hyperbolic System with Boundary Delay." Bulletin of Irkutsk State University. Series Mathematics 35 (2021): 3–17. http://dx.doi.org/10.26516/1997-7670.2021.35.3.
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The paper deals with an optimal control problem by a system of semilinear hyperbolic equations with boundary differential conditions with delay. This problem is considered for smooth controls. Because this requirement it is impossible to prove optimality conditions of Pontryagin maximum principle type and classic optimality conditions of gradient type. Problems of this kind arise when modeling the dynamics of non-interacting age-structured populations. Independent variables in this case are the age of the individuals and the time during which the process is considered. The functions of the process state describe the age-related population density. The goal of the control problem may be to achieve the specified population densities at the end of the process.The problem of identifying the functional parameters of models can also be considered as the optimal control problem with a quadratic cost functional. For the problem we obtain a non-classic necessary optimality condition which is based on using a special control variation that provides smoothness of controls. An iterative method for improving admissible controls is developed. An illustrative example demonstrates the effectiveness of the proposed approach.
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MALLE, PIERRE, and MARTINE POUMEYROL. "A New Chemical Criterion for the Quality Control of Fish: Trimethylamine/Total Volatile Basic Nitrogen (%)." Journal of Food Protection 52, no. 6 (June 1, 1989): 419–23. http://dx.doi.org/10.4315/0362-028x-52.6.419.
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Trimethylamine (TMA) and the total volatile basic nitrogen (TVBN) were determined in 169 samples of sea-fish (herring, cod, whiting, and mackerel) at all stages of decomposition. The comparison of these two parameters with the ratio P=TVBN/TMA (%) showed that P provides a useful index of freshness. It is relatively constant between species, its dispersion is less than that of TMA and it increases more rapidly than TVBN at the start of decomposition. Statistical analysis of the experimental results showed that there is a non-linear correlation between P and the decomposition index (i). The comparison of the line-equations defining log P as a function of i for different species of marine Teleostei led us to show that there is little or no intraspace variation of this correlation under determined conservation conditions. It is noted that for a given species, this correlation is temperature-dependant. Statistical exploitation of these results permit us to determine the maximal admissible values for P which can be used as a support for the development of new standards.
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Eitzinger, B. "A Simulation Study of Self-Extinguishing Cigarettes." Beiträge zur Tabakforschung International/Contributions to Tobacco Research 22, no. 2 (July 1, 2006): 79–87. http://dx.doi.org/10.2478/cttr-2013-0819.
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AbstractIn some parts of the USA and in Canada smouldering cigarettes are required to extinguish if placed on a certain number of layers of filter paper. This is usually achieved by the use of bands on the cigarette paper, which reduce oxygen diffusion into the cigarette. From a smoker's perspective, however, it is desirable that a cigarette does not extinguish if left to smoulder, for example, in an ash tray. To facilitate the design of papers for such cigarettes the influence of various cigarette parameters on self-extinguishment is investigated by numerical simulation of a one-dimensional cigarette model, which describes the main thermodynamic behaviour of smouldering cigarettes. The tobacco density, the tobacco heat capacity, the width of the bands on the cigarette paper and the heat released during combustion are chosen as parameters whose influence on the required oxygen diffusion constant of the bands on the cigarette paper is investigated. As these parameters are subject to a certain variation, it is assumed that the parameters are independently normally distributed. Based on this assumption the probability that a cigarette with given mean parameter values will extinguish, is calculated numerically.The results show that the admissible range of diffusion constants for the bands on the cigarette paper is in general quite small and it is reduced even further if statistical variations of the cigarette parameters are considered.The results provide guidelines for the appropriate choice of the diffusion constant of the bands on the cigarette paper such that the cigarettes comply with legal requirements and do not extinguish during normal smoking.
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Rachid, El Kaak, Khalid El Bikri, and Benamar Rhali. "A Semi-Analytical Study of Geometrically Nonlinear Free Axisymmetric Vibrations of Thin Circular Functionally Graded Plates Using Iterative and Explicit Analytical Solution." Applied Mechanics and Materials 704 (December 2014): 131–36. http://dx.doi.org/10.4028/www.scientific.net/amm.704.131.
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. This paper deals with nonlinear free axisymmetric vibrations of functionally graded thin circular plates (FGCP) whose properties vary through its thickness. The inhomogeneity of the plate is characterized by a power law variation of the Young’s modulus and mass density of the material along the thickness direction, whereas Poisson’s ratio is assumed to be constant. The theoretical model is based on Hamilton’s principle and spectral analysis using a basis of admissible Bessel’s functions to yield the frequencies of the circular plates under clamped boundary conditions on the basis of the classical plate theory. The large vibration amplitudes problem, reduced to a set of non-linear algebraic equations, is solved numerically. The non-linear to linear frequency ratios are presented. Then, explicit analytical solutions are presented, based on the semi-analytical model previously developed by EL Kadiri et al. [1-2] for beams and rectangular plates, which allow direct and easy calculation for the first non-linear axisymmetric mode shape, with their associated non-linear frequencies of FG circular plates and which are expected to be very useful in engineering applications and in further analytical developments. An excellent agreement is found with the results obtained by the iterative method.
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Ren, Bingxuan, Tangwen Yin, and Shan Fu. "On Cognitive Searching Optimization in Semi-Markov Jump Decision Using Multistep Transition and Mental Rehearsal." Complexity 2021 (October 6, 2021): 1–20. http://dx.doi.org/10.1155/2021/3343494.
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Cognitive searching optimization is a subconscious mental phenomenon in decision making. Aroused by exploiting accessible human action, alleviating inefficient decision and shrinking searching space remain challenges for optimizing the solution space. Multiple decision estimation and the jumpy decision transition interval are two of the cross-impact factors resulting in variation of decision paths. To optimize the searching process of decision solution space, we propose a semi-Markov jump cognitive decision method in which a searching contraction index bridges correlation from the time dimension and depth dimension. With the change state and transition interval, the semi-Markov property can obtain the action by limiting the decision solution to the specified range. From the decision depth, bootstrap re-sampling utilizes mental rehearsal iteration to update the transition probability. In addition, dynamical decision boundary by the interaction process limits the admissible decisions. Through the flight simulation, we show that proposed index and reward vary with the transition decision steps and mental rehearsal frequencies. In conclusion, this decision-making method integrates the multistep transition and mental rehearsal on semi-Markov jump decision process, opening a route to the multiple dimension optimization of cognitive interaction.
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Wang, Hong-Tao, Ping Liu, Chi Liu, Xin Zhang, Yong Yang, and Lu-Yao Liu. "Three-Dimensional Upper Bound Limit Analysis on the Collapse of Shallow Soil Tunnels considering Roof Stratification and Pore Water Pressure." Mathematical Problems in Engineering 2019 (November 11, 2019): 1–15. http://dx.doi.org/10.1155/2019/8164702.
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Based on the plastic upper bound theorem, a three-dimensional kinematically admissible velocity field is constructed for the collapse of the soil masses above a shallow tunnel. In this field, this paper considers the influences of the roof stratification, pore water pressure, ground overload, and support pressure. This study deduced the upper bound solutions of the weight of the collapsed soil masses and the corresponding collapse surfaces by utilizing the nonlinear failure criterion, associated flow rule, and variation principle. Furthermore, we verified the validity of the proposed method in this paper by comparing this research with the existing work and numerical simulation results. This study obtains the influence laws of varying parameters on the area and weight of the collapsed soil masses. The results reveal that the area and weight of the collapsed soil masses increase with increasing support pressure and soil cohesion, but decrease with increasing thickness of the upper soil layer, nonlinear coefficient, pore water pressure, and ground overload. Among them, the roof stratification, pore water pressure, soil cohesion, and nonlinear coefficient have a significant influence on tunnel collapse, which should be given special consideration in engineering design.
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Kotov, V. L. "MAPPROXIMATING STRESSES IN THE VICINITY OF A CAVITY EXPANDING AT A CONSTANT VELOCITY IN A MEDIUM WITH THE MOHR - COULOMB PLASTICITY CONDITION." Problems of strenght and plasticity 81, no. 2 (2019): 177–90. http://dx.doi.org/10.32326/1814-9146-2019-81-2-177-190.
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A one-dimensional problem of a spherical cavity expanding at a constant velocity from a point in an infinite elastoplastic medium is considered. The problem has a first-kind self-similar solution. Elastoplastic deformation of the soil is described based on Hooke's law and the Mohr-Coulomb yield criterion. An analytical solution of the problem in the elastic region contacting with the plastic yield region has been obtained. To determine stress and velocity fields in the plastic region, a known algorithm, based on the shooting method, of analyzing a boundary-value problem for a system of two first-order ordinary differential equations, including the fourth-order Runge - Kutta method, has been realized. An effective algorithm of numerically analyzing an expanding cavity problem, earlier proposed in the works by М. Forrestal et al., makes it possible to solve the problem accurately enough for practical applications. A formula for determining the critical pressure - the minimal pressure required for the nucleation, accounting for internal pressure of a cavity in the framework of the Mohr - Coulomb yield criterion, has been derived, which is a generalization of the earlier published solution for an elastic ideally plastic medium with Tresca's criterion. The obtained critical value was compared with a numerical solution in a full formulation at the cavity expansion velocities close to zero in a wide range of variation of the parameters of the Mohr - Coulomb yield criterion. It is shown that the inaccuracy of the approximation of the proposed formula does not exceed 6% for the variation of the internal friction coefficient all over the admissible range, and for the initial value of the yield strength increasing by three orders of magnitude.
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Yudin, E. V., G. A. Piotrovskiy, O. A. Kolyuk, N. A. Smirnov, I. M. Galyautdinov, A. A. Sagirov, and I. A. Lomukhin. "OPERATIONAL FEATURES AND METHODS FOR DETERMINING THE OPTIMAL OPERATION PARAMETERS IN FRACTURED RESERVOIRS WITH A GAS CAP: OIL RIMS OF ORENBURG OGCF CASE STUDY." Энергия: экономика, техника, экология, no. 3 (2020): 26–32. http://dx.doi.org/10.7868/s2587739920030039.
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The paper deals with the features of well operation at the Eastern part of Orenburg oil and gas condensate field (OGCF). We propose a complex approach to determining the parameters of the fractured formation: based on the mathematical model of Warren–Root fracture reservoir, we find the dependence of the well flow rate on time and parameters of fracture under conditions of maintaining constant bottomhole pressure. Next stage is an extrapolation of this problem for the case of arbitrary dynamics of flow rates and pressures based on the deconvolution theory. The search of parameters of double fracture formation is carried out by their variation in the corridor of admissible values in order to minimize the deviation of the calculated flow rate relative to the true one. To identify possible reasons for the decline in well productivity with a decrease in bottomhole pressure, numerical experiments were performed on synthetic hydrodynamic models to determine the main influencing factors that can lead to an observed decrease in well productivity with increasing depression. Based on the information received, multivariate calculations of sector models of the EP OGCF were carried out in order to determine the optimal operating parameters to maximize oil production or minimize specific operating costs, taking into account the identified complicating factors.
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Ukhobotov, V. I., and N. D. Livanov. "ON A PROBLEM OF CONTROLLING A MOVING CART WITH ELASTIC ROD." Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics" 13, no. 1 (2021): 22–28. http://dx.doi.org/10.14529/mmph210103.
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This article discusses the problem of controlling the process of longitudinal oscillations of an elastic homogeneous rod of uniform cross section. A rod is understood as a body, the length of which significantly exceeds its cross dimensions. The rod is on a moving cart, the right end of which is rigidly fixed, and the left end is not fixed. There is no friction between the rod and the cart surface in the problem under consideration. When the cart moves, the rod performs constrained longitudinal oscillations in a noninertial frame of reference associated with the cart. The control is the acceleration of the cart, the magnitude of which is limited. The boundaries of its accepted values are set. The value of the combined external forces acting on the rod is not known exactly, but only its limits of variation are given. The purpose of the control process is to ensure that at a given moment in time, the average value of the stretch of the rod is within a given interval. This average is calculated using the specified function. In order to solve the problem, the method of optimizing a guaranteed result is applied. A transition to a new one-dimensional variable is made, with the help of which the considered problem of control of the longitudinal oscillations of a rod is reduced to a similar control problem in the presence of noise. The necessary and sufficient conditions are found, under which it is possible to accomplish the set goal for any admissible external forces, the total value of which satisfies the given constraints. A corresponding algorithm for constructing the law of variation of the cart acceleration is proposed. An example that clearly shows how to build the cart control, which will guarantee the achievement of the set goal, has been analyzed.
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Sharipov, V. M., Yu S. Shchetinin, and M. I. Dmitriev. "Kinematic analysis of double-flow hydromechanical transmissions." Traktory i sel hozmashiny 83, no. 12 (December 15, 2016): 10–15. http://dx.doi.org/10.17816/0321-4443-66243.
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Double-flow hydromechanical transmissions become more and more widely used in designs of modern tractors and automobiles. Double-flow hydromechanical transmission includes a torque converter or a complex hydrodynamic transmission and a differential unit made in form of three-link differential device. The article discusses all of the 12 possible schemes of double-flow hydromechanical transmissions with a differential unit at the input and at the output with mixed type of gear engagement, and also presents the results of their kinematic analysis. For all of the 12 possible schemes, the expressions are given for determining the angular velocity of links of three-link differential device, depending on the gear ratio of double-flow hydromechanical transmission and the characteristics of planetary gear set. The calculation results with the use of these expressions are presented as curves. It is found that in 4 of the 12 schemes, it is very likely that the angular velocity of either sun gear or satellites will exceed the limits admissible for rolling bearings. There is no such problem for other 4 schemes. The other schemes are applicable to a limited range of characteristics of the planetary gear set. It is found that for 6 schemes there is a possibility that when transmission is functioning in the range of variation of gear ratio from infinity to 1, the torque converter can be operated in modes not typical for its normal operation (the turbine wheel rotates faster than the pump wheel; the turbine wheel rotates counter to the rotation of pump wheel; pump wheel rotates in the opposite direction in relation to the reactor). The triggering conditions of such modes are established and variation limits of gear ratio of torque converter are determined for them.
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Skaržauskas, Valentinas, Dovilė Merkevičiūtė, and Juozas Atkočiūnas. "LOAD OPTIMIZATION OF ELASTIC-PLASTIC FRAMES AT SHAKEDOWN/PRISITAIKANČIŲ TAMPRIAI PLASTIŠKŲ RĖMŲ APKROVOS OPTIMIZACIJA." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 7, no. 6 (December 31, 2001): 433–40. http://dx.doi.org/10.3846/13921525.2001.10531769.
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In this article the theory of mathematical programming is used, composing improved mathematical models of nonlinear problems of frame loading optimization at shakedown and performing its numerical experiment. An elastic perfectly-plastic frame is considered. Frame geometry, material, load application places are considered known. Time independent load variation bounds are variable (history of loading is unknown). Mathematical model of load variation bounds optimization problem includes strength and stiffness constrains. The mentioned optimization load combines two problems. First problem is connected with the distribution of statically admissible moments at shakedown. This is a problem of residual bending moments analysis which is presented in two ways. In the first case it is formulated as a quadratic programming problem, where the objective function is non-linear, but the objective function of load optimization problem remains linear. The problem is solved by iterations, influential matrixes of residual displacements, and stresses are used. In next case, the equations of problem analysis and dependences are presented according to complete equation system of plasticity theory. Then the objective function of optimization problem becomes non-linear and it is solved in single stage. Solving the second problem, we check if it is possible to satisfy frame rigidity constrains, which are inferior or superior limits of residual displacement. This is considered as a linear programming problem. Mathematical model of frame load optimization problem at shakedown was made with the help of non-linear mathematical programming theory. Numerical experiment was realized with Rozen's gradients projecting method and using the penalty function techniques. Mathematical programming complementarity conditions prohibit taking into account the dechargable phenomena in some cross-sections, therefore analysis of residual deformation compatibility equations are performed, using linear mathematical programming.
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Kozlov, V. V. "Modeling Non-Stationary Processes of Diffusion of Solute Substances in the Near-Bottom Layer ofWater Reservoirs: Variation of the Direction of Flows and Assessment of Admissible Biogenic Load." Mathematical Modelling of Natural Phenomena 4, no. 5 (2009): 100–113. http://dx.doi.org/10.1051/mmnp/20094507.
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Lohmann, Gerrit. "Temperatures from energy balance models: the effective heat capacity matters." Earth System Dynamics 11, no. 4 (December 16, 2020): 1195–208. http://dx.doi.org/10.5194/esd-11-1195-2020.
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Abstract. Energy balance models (EBMs) are highly simplified models of the climate system, providing admissible conceptual tools for understanding climate changes. The global temperature is calculated by the radiation budget through the incoming energy from the Sun and the outgoing energy from the Earth. The argument that the temperature can be calculated by this simple radiation budget is revisited. The underlying assumption for a realistic temperature distribution is explored: one has to assume a moderate diurnal cycle due to the large heat capacity and the fast rotation of the Earth. Interestingly, the global mean in the revised EBM is very close to the originally proposed value. The main point is that the effective heat capacity and its temporal variation over the daily and seasonal cycle needs to be taken into account when estimating surface temperature from the energy budget. Furthermore, the time-dependent EBM predicts a flat meridional temperature gradient for large heat capacities, reducing the seasonal cycle and the outgoing radiation and increasing global temperature. Motivated by this finding, a sensitivity experiment with a complex model is performed where the vertical diffusion in the ocean has been increased. The resulting temperature gradient, reduced seasonal cycle, and global warming is also found in climate reconstructions, providing a possible mechanism for past climate changes prior to 3 million years ago.
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Rezapour, Shahram, Sina Etemad, İbrahim Avcı, Hijaz Ahmad, and Azhar Hussain. "A Study on the Fractal-Fractional Epidemic Probability-Based Model of SARS-CoV-2 Virus along with the Taylor Operational Matrix Method for Its Caputo Version." Journal of Function Spaces 2022 (September 1, 2022): 1–33. http://dx.doi.org/10.1155/2022/2388557.
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SARS-CoV-2 is a strain of the large coronavirus family that has led to COVID-19 disease. The virus has been one of the deadliest known viruses in the world to date. Rapid mutations and the creation of new strains cause researchers to focus on the dynamic behaviors of the virus and to analyze it accurately through clinical research and mathematical models. In this paper, from the point of view of mathematical modeling, we intend to focus on the dynamic behavior of the system and examine its analytical and numerical aspects in two different structures. In other words, by recalling newly formulated hybrid fractional-fractal operators, we present a fractal-fractional probability-based model of SARS-CoV-2 virus for the first time and extract its equivalent compact fractal-fractional IVP to investigate its existence and stability criteria. A type of special admissible contractions will help us in this regard. Moreover, based on the source data, we simulate our system according to algorithms derived by Adams-Bashforth method and explain the effects of variation of the dimension of fractal and fractional order on dynamics of solutions. Finally, we transform our fractal-fractional model into a Caputo probability-based model of SARS-CoV-2 to derive solutions via the operational matrix method under Taylor’s basis. The numerical simulations show close behaviors for both of models.
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Szeptyński, Paweł, Matija Gams, and Arkadiusz Kwiecień. "Modelling of Flexible Adhesives in Simple Mechanical States with the Use of the Darijani–Naghdabadi Strain Tensors and Kirchhoff–de Saint-Venant Elastic Potential." Polymers 13, no. 10 (May 18, 2021): 1639. http://dx.doi.org/10.3390/polym13101639.
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Practical aspects of modelling of flexible adhesives with the energy conjugate measures of stress and strain of the Darijani–Naghdabadi (D-N) family are discussed. A possibility of description of materials exhibiting non-linear physical characteristics with the use of non-linear geometric relationships and linear elastic constitutive law is considered. Nominal stress vs. stretch relations are specified in cases of simple tension and simple shear with the use of the Kirchhoff–de Saint-Venant elastic potential and D-N energy conjugate stress and strain measures. Obtained theoretical estimates were compared with experimental results of simple tension and simple shear tests performed on Sika PM polyurethane (Cracow, Sika Poland). The deformation rate was fixed in order to minimize the influence of viscosity. Values of parameters α,β in the definition of the D-N strain tensor were optimized in order to provide good agreement between model predictions and experimental results. Observed discrepancies indicate that the proposed approach is not appropriate for constitutive modelling of the PM polymer. The presented approach is proposed to be used as a simple design model providing practical formulas describing the behavior of materials of non-linear characteristics in chosen mechanical states. Admissible values of exponents α,β are discussed regarding its bijectivity in a limited range of variation of principal stretches.
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Ko, Soo-Min, and Jae-Hoon Kang. "Vibration of Hemispherical-Cylindrical-Hemispherical Shells and Complete Hollow Spherical Shells with Variable Thickness." International Journal of Structural Stability and Dynamics 19, no. 03 (March 2019): 1950018. http://dx.doi.org/10.1142/s0219455419500184.
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The natural frequencies and mode shapes of enclosed shell typed structures with variable thickness (hemispherical-cylindrical-hemispherical shells and complete hollow spherical shells) are determined by the Ritz method using a three-dimensional (3D) analysis. However, in the conventional shell analysis, mathematically two-dimensional (2D) thin shell theories or higher order thick shell theories are often employed, which adopt limiting assumptions about the displacement variation through the shell thickness. While most researchers have adopted the 3D shell coordinates that are normal and tangential to the shell mid-surface, the present analysis is based upon the circular cylindrical coordinates. By the Ritz method, the Legendre polynomials, which are mathematically orthonormal and minimal, are used as the admissible functions, instead of the ordinary algebraic polynomials. The strain and kinetic energies of the combined shell structures are formulated, and upper bound solutions of the frequencies are obtained by minimizing the solution for frequencies. As the degree of the Legendre polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies. The frequencies from the present 3D method are compared with those from other 3D approach and 2D thin and thick shell theories existing in the literature. The present 3D analysis is applicable to both very thick shells and very thin shells.
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Kumar, Pramod, and S. K. Tiwari. "Eigen Value Analysis of Glass Fiber Reinforced Composite Plate." Advanced Materials Research 488-489 (March 2012): 676–80. http://dx.doi.org/10.4028/www.scientific.net/amr.488-489.676.
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Finite element analysis has been used to find out eigen values and mode shape for fiber reinforced composite plates. FRC plates are important structural elements in modern engineering structures. Vibrations of laminated composite plates have been the subject of significant research activities in recent years. Last two decades have witnessed continued development of advanced composite and other high performance aerospace materials with increased specific strength and modulus, longer fatigue life, higher combat survivability etc. Advanced composite laminates extend the possibility of optimal design through the variation of stacking sequence and fiber orientation, known as composite tailoring. The benefits that accrue from this are not attainable without solving the complexities that are introduced by various coupling effects, such as bending–stretching and bending-twisting. Even, as the matrix material is of relatively low shearing stiffness as compared to the fibers, a reliable prediction of frequency response of laminated plates must account for transverse shear deformation. A four noded quadrilateral finite element is considered for the study of frequency response of composite plate. An analytical solution to the boundary value problem of free vibration response of arbitrarily laminated plates subjected to an admissible boundary condition is presented. A rectangular fiber reinforced composite plate is modeled in FEM software (NISA 15) and natural frequencies, mode shapes are obtained and are compared with the available analytical solutions.
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Shawki, T. G. "An Energy Criterion for the Onset of Shear Localization in Thermal Viscoplastic Materials, Part I: Necessary and Sufficient Initiation Conditions." Journal of Applied Mechanics 61, no. 3 (September 1, 1994): 530–37. http://dx.doi.org/10.1115/1.2901492.
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Necessary and/or sufficient conditions for the onset of shear flow localization in thermal viscoplastic materials are derived. Initiation of shear band formation is examined through the analysis of a one-dimensional model of dynamic simple shear with velocity-controlled boundaries. An exact energy estimate is derived for the fully nonlinear initial boundary value problem which illustrates the weak effect of elasticity as regards the onset of localization. The existence, uniqueness and well-posedness properties of a spatially homogeneous solution are also examined. A unique homogeneous solution is shown to exist for the dynamic simple shear problem with velocity controlled and thermally insulated boundaries. The former solution is also shown to be the unique static solution of the simple shear problem, with no elastic or heat conduction effects, consistent with the foregoing boundary conditions. A linear system of equations is derived for the perturbations superposed on the reference, time-dependent homogeneous (static) solution. A discussion regarding the notions of instability and localization motivates the introduction of a novel localization criterion, based on an appropriately selected energy norm, that takes full account of the time variation of the homogeneous solution. Taking advantage of the admissible spatial form of the perturbations together with the foregoing criterion allows for the association of the positive rate of change of the total kinetic energy of the absolute perturbations with the onset of shear strain localization.
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Snoussi, Jamila, Seifeddine Ben Elghali, Mohamed Benbouzid, and Mohamed Mimouni. "Auto-Adaptive Filtering-Based Energy Management Strategy for Fuel Cell Hybrid Electric Vehicles." Energies 11, no. 8 (August 14, 2018): 2118. http://dx.doi.org/10.3390/en11082118.
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The global need to solve pollution problems has conducted automotive engineers to promote the development and the use of electric vehicle technologies. This paper focuses on the fuel cell hybrid electric vehicle which uses a proton exchange membrane fuel cell as a main source associated to hybrid storage device: lithium ion battery and ultracapacitors. A common interest in such technology is to spread out the energy flow between its different sources in order to satisfy the power demand for any requested mission. However, the challenging task stills the optimization of this split to reduce hydrogen consumption and respect, at the same time, the system limitations such as admissible limits of storage system capacities and battery current variation. An adaptive filtering-based energy management strategy is proposed in this paper to ensure an optimum distribution of the energy between the sources taking into account dynamic and energetic constraints of each device. For more performance, a fuzzy logic system is used to adapt the frequency of separation with the system state evolution. A sliding mode control is applied to control electric characteristics (voltage and currents) in the considered hybrid power supply. Simulation results, obtained under MATLAB®/SimPowerSystems® for four driving cycles are presented. The proposed strategy achieved good performances by respecting the ultracapacitors state of charge while preserving the battery lifetime under various driving missions.