Analytical modeling of the binary dynamic circuit motion

The binary dynamic circuit, which can be a design scheme for a number of technical systems is considered in the paper. The dynamic circuit is characterized by the kinetic energy of the translational motion of two masses, the potential energy of these masses’ elastic interaction and the dissipative function of energy dissipation during their motion. The free motion of a binary dynamic circuit is found according to a given initial phase state. A mathematical model of the binary dynamic circuit motion in the canonical form and the corresponding characteristic equation of the fourth degree are compiled. Analytical modeling of the binary dynamic circuit is carried out on the basis of the proposed particular solution of the complete algebraic equation of the fourth degree. A homogeneous dynamic circuit is considered and the reduced coefficients of elasticity and damping are introduced. The dependence of the reduced coefficients of elasticity and damping is established, which provides the required class of solutions to the characteristic equation. An ordered form of the analytical representation of a dynamic process is proposed in symmetric determinants, which is distinguished by the conservatism of notation with respect to the roots of the characteristic equation and phase coordinates.

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Dependence of trehalose protective action on the initial phase state of dipalmitoylphosphatidylcholine bilayers

Cryobiology ◽

10.1016/0011-2240(88)90033-8 ◽

1988 ◽

Vol 25 (3) ◽

pp. 256-263 ◽

Cited By ~ 21

Author(s):

N. Tsvetkova ◽

B. Tenchov ◽

L. Tsonev ◽

Ts. Tsvetkov

Keyword(s):

Initial Phase ◽

Phase State ◽

Protective Action

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On the Universal Regularity of the Numbers of Generalized Recurrence Sequence and Solutions to Its Characteristic Equation of Second Order

10.23939/cds2019.01.027 ◽

2020 ◽

pp. 27-33

Author(s):

P. Kosobutskyy

Keyword(s):

Characteristic Equation ◽

Quadratic Equation ◽

Second Order ◽

Recurrence Sequence ◽

Phase Coordinates ◽

Fibonacci Sequences

In this work shows that the classical oscillations of the ratio of neighboring members of the Fibonacci sequences are valid for arbitrary directions on the plane of the phase coordinates, approaching, to a maximum, the solutions to the characteristic quadratic equation at a given point. The values of the solutions to the characteristic equation along the satellites are asymptotically close to their integer values of the corresponding root lines.

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DCDR Spectroscopy as Efficient Tool for Liposome Studies: Aspect of Preparation Procedure Parameters

Spectroscopy An International Journal ◽

10.1155/2012/182720 ◽

2012 ◽

Vol 27 ◽

pp. 349-353 ◽

Cited By ~ 4

Author(s):

E. Kočišová ◽

A. Vodáková ◽

M. Procházka

Keyword(s):

Lipid Composition ◽

Phosphate Buffer ◽

Initial Phase ◽

Liquid Crystalline ◽

Phase State ◽

Hydrophobic Surface ◽

Drying Process ◽

Lipid Concentration ◽

Efficient Tool ◽

Coating Deposition

Drop-coating deposition Raman (DCDR) spectroscopy was employed to study liposome suspensions. The method is based on a specific drying process on the hydrophobic surface that efficiently accumulates the macromolecular sample in a ring of the edge of the dried drop. We studied liposome suspensions purchased from two sources (Avanti Polar Lipids, Inc. and Sigma-Aldrich, Co.) and prepared under different conditions. Structure of the dried drop substantially depends on the lipid concentration, lipid composition of the sample, and used solvent. Optimal lipid concentration is about 0.3 mg/ml in all cases, asolectin and DSPC suspensions form compact dried drops when dissolved in water and phosphate buffer, respectively. Drying process of the sample drop does not influence the initial phase state (gel or liquid-crystalline) of the studied liposomes excepting DSPC from Sigma-Aldrich, Co.

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Analytical Modeling of Bolted Flange Joints With Full Face Gaskets

2004 International Pipeline Conference, Volumes 1, 2, and 3 ◽

10.1115/ipc2004-0663 ◽

2004 ◽

Author(s):

Hichem Galai ◽

Abdel-Hakim Bouzid

Keyword(s):

Contact Stress ◽

Analytical Modeling ◽

Elastic Interaction ◽

Bolted Joints ◽

Low Leakage ◽

Proposed Model ◽

Asme Code ◽

The Many ◽

Full Face ◽

Bolted Flange

Following the low leakage performance of flat face flanges, neither Appendix 2 nor Appendix Y of the ASME code which describes the design rules of flanges, are reliable to assess load changes when full face gaskets are used. The prediction of the tightness of these connections relies very much on the level of precision of the gasket contact stress during operation. However, determining this stress is complex, due to the many geometric and material parameters involved. This paper analyses the behaviour of bolted joints with full face gaskets. It presents an analytical approach to evaluate the operating flange rotation, gasket load and contact stress that may be used for leak prediction. The method is based on the gasket-bolt-flange elastic interaction, including flange rotational flexibility. The proposed model is supported by comparison with numerical FEA of different size flanges.

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Effect of the initial phase state of DT-matter on the compression of inertial fusion targets

Journal of Russian Laser Research ◽

10.1007/s10946-011-9251-x ◽

2011 ◽

Vol 32 (6) ◽

pp. 596-603 ◽

Cited By ~ 5

Author(s):

Sergey Yu. Gus’kov ◽

Nikolay V. Zmitrenko ◽

Vladislav B. Rozanov

Keyword(s):

Initial Phase ◽

Phase State ◽

Inertial Fusion

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A bistable kinetic system with oscillations on the thermodynamic and flow-through branches

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19872365 ◽

1987 ◽

Vol 52 (10) ◽

pp. 2365-2374 ◽

Cited By ~ 1

Author(s):

Antonín Tockstein

Keyword(s):

Characteristic Equation ◽

Parameter Dependence ◽

Fourth Degree ◽

Stationary Concentration ◽

Competitive Reactions ◽

Stirred Reactor ◽

Kinetic System ◽

Oscillatory Character ◽

Flow Through ◽

Parallel Reactions

A model of a flow-through perfectly stirred reactor comprising three consecutive competitive reactions with parallel reactions of some intermediates and exhibiting bistable behaviour and possessing regions with an oscillatory character on the thermodynamic branch is treated. The stationary concentration vs parameter dependence is of the fourth degree and the characteristic equation, of the fifth degree.

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Analytical Modeling of Flat Face Flanges With Metal-to-Metal Contact Beyond the Bolt Circle

Volume 5: High Pressure Technology; Nondestructive Evaluation Division; Student Paper Competition ◽

10.1115/pvp2009-77207 ◽

2009 ◽

Author(s):

Hichem Galai ◽

Abdel-Hakim Bouzid

Keyword(s):

Analytical Modeling ◽

Plate Theory ◽

Beam Theory ◽

Elastic Interaction ◽

Bolted Joints ◽

Metal Contact ◽

Design Rules ◽

Load Change ◽

Asme Code ◽

Analytical Approaches

Design rules for flat face flanges with metal-to-metal contact beyond the bolt circle are covered by Appendix Y of the ASME Code. These design rules are based on Schneider’s work [1]. The prediction of tightness of these bolted joints relies very much on the level of precision of the O-ring gasket compression during operation. The evaluation of this compression requires a rigorous flexibility analysis of the joint including bolt-flange elastic interaction. This paper analyses flange separation and the bolt load change in flat face bolted joints. It proposes two different analytical approaches capable of predicting flange rotation and bolt load change during operation. The first method is based on beam theory applied to a continuous flange sector. This approach is an improvement of the discrete beam theory used by Schneider [1]. The second method is based on circular plate theory and is developed for the purpose of a more accurate assessment of the load changes. As in the Taylor Forge method, this approach is in general better suited than the beam theory for flat face flanges in particular when the flange width is small. The proposed models are compared to the discrete beam theory and validated using numerical FEA on different flange sizes.

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On the subject of influence of dissipative and permanent momentums on stability of uniform rotations of two elastically connected free gyroscopes of Lagrange

Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine ◽

10.37069/1683-4720-2019-33-11 ◽

2019 ◽

Vol 33 ◽

pp. 132-141

Author(s):

Yuri Kononov ◽

Yaroslav Sviatenko

Keyword(s):

Asymptotic Stability ◽

Characteristic Equation ◽

Joint Stiffness ◽

Quadratic Equation ◽

Stability Conditions ◽

Spherical Joint ◽

Fourth Degree ◽

Left Hand ◽

Resisting Medium ◽

Complex Coefficients

In many works, there are studies of the asymptotic stability of rotation of a free Lagrange gyroscope in a resisting medium. This article generalizes this problem to the case of uniform rotations of two free Lagrange gyroscopes connected by an elastic restoring spherical hinge. The rotation of each gyroscope is maintained by a constant moment in an inertial coordinate system. The characteristic equation of the perturbed motion is presented in the form of an algebraic equation of the fourth degree with complex coefficients. Based on the innor approach, conditions of asymptotic stability are obtained in the form of a system of three inequalities. The left-hand side of these inequalities is represented, respectively, in the form of determinants of the third, fifth, and seventh orders. Up to first-order values of smallness, relative to the reciprocal of the stiffness coefficient, a study is made of the effect of the joint stiffness on stability conditions. From the conditions of positivity of the highest coefficients in three inequalities, it is shown that for a sufficiently large rigidity, the stability conditions are determined by only one inequality. Cases of degeneration of an elastic spherical joint into a spherical inelastic, cylindrical, and universal elastic joint (Hooke's joint) are considered. In the case of an inelastic spherical joint, the system of three inequalities is slightly simplified. The greatest simplification arises in the case of a cylindrical hinge. In this case, the characteristic equation is represented as a quadratic equation with complex coefficients. According to the innoric approach, the conditions of asymptotic stability are written in the form of a single inequality, the left side of which is presented in the form of third-order determinants. It is shown that this inequality coincides with the inequality obtained earlier for the case of a sufficiently large rigidity of the hinge. If the angular velocities of the proper rotations of the gyroscopes coincide, the inequality obtained for the cylindrical hinge coincides with the well-known inequality for one gyroscope. In the case of a universal elastic hinge (Hooke's hinge), the first inequality is represented as a square inequality with respect to the angular velocity of proper rotation.

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