Boundary Rotation Research Articles

Simulations of the Rotor-Stator-Cavity Flow in Liquid-Floating Rotor Micro Gyroscope

When rotating at a high speed in a microscale flow field in confined spaces, rotors are subject to a complex flow due to the joint effect of the centrifugal force, hindering of the stationary cavity and the scale effect. In this paper, a rotor-stator-cavity (RSC) microscale flow field simulation model of liquid-floating rotor micro gyroscopes is built, which can be used to study the flow characteristics of fluids in confined spaces with different Reynolds numbers (Re) and gap-to-diameter ratios. The Reynolds stress model (RSM) is applied to solve the Reynolds averaged Navier–Stokes equation for the distribution laws of the mean flow, turbulence statistics and frictional resistance under different working conditions. The results show that as the Re increases, the rotational boundary layer gradually separates from the stationary boundary layer, and the local Re mainly affects the distribution of velocity at the stationary boundary, while the gap-to-diameter ratio mainly affects the distribution of velocity at the rotational boundary. The Reynolds stress is mainly distributed in boundary layers, and the Reynolds normal stress is slightly greater than the Reynolds shear stress. The turbulence is in the state of plane-strain limit. As the Re increases, the frictional resistance coefficient increases. When Re is within 104, the frictional resistance coefficient increases as the gap-to-diameter ratio decreases, while the frictional resistance coefficient drops to the minimum when the Re exceeds 105 and the gap-to-diameter ratio is 0.027. This study can enable a better understanding of the flow characteristics of microscale RSCs under different working conditions.

Deformation-induced grain rotation and grain boundary formation achieved through dislocation-disclination reactions in polycrystalline hexagonal close-packed metals

Grain boundary mediated plasticity (e.g., grain rotation and grain boundary sliding) plays a critical role in determining the deformation behavior of polycrystals, which is especially important for nanocrystalline metals or plastic deformation at elevated temperatures. However, due to the lack of a theoretical framework, the mechanism of deformation-induced grain rotation has not been well understood. By introducing a disclination-based description, we show that crystal rotation can be captured conveniently through the characteristic rotational vector of a disclination (i.e., the Frank vector). Under the framework of topological defect theory, grain boundary mediated plasticity can be treated as topological reactions between dislocations and disclinations, leading to rigorous predictions of grain/subgrain rotation through a pseudo-inverse solution for the reformulated Frank-Bilby equation. Systematic classifications of grain/subgrain rotation and grain boundary formation are raised for hexagonal close-packed (HCP) metals, which has been validated by Electron-Backscattered Diffraction characterizations in Mg alloys. Our work not only suggests a theoretical approach to investigate grain/subgrain rotation based on the topological correlation between dislocations and disclinations, but also provides a new insight into the plastic behaviors of polycrystalline HCP metals.

Analysis of the Tensile Deformation Behaviors and Microstructure Characterization under Various Temperatures of MarBN Steel by EBSD

The uniaxial tensile behavior of MarBN steel with a constant strain rate of 5 × 10-5 s-1 under various temperatures ranging from room temperature to 630 °C was analyzed. This study aimed to identify the effect of the temperature on the tensile behavior and to understand the microstructure deformation by electron backscatter diffraction. The tensile results showed that the yield and ultimate tensile strength decreased with increasing temperature. Serrated flow was observed from 430 °C to 630 °C. The electron backscatter diffraction analysis showed that the low-angle grain boundaries decreased at the medium deformation and increased at the maximum deformation. In contrast, they decreased with increasing temperatures. In addition, the number of voids increased with the increasing plastic strain. As the strain increased, the voids joined together, and the tiny cracks became larger and failed. Three mechanisms were responsible for the tensile deformation failure at various temperatures: grain rotation, the formation and rearrangement of low angle grain boundaries, and void nucleation and propagation. Finally, the formation of the low-angle grain boundaries and voids under different degrees of deformation is discussed.

Particle Collision Study Based on a Rotational Boundary Condition

The main engineering machinery for the hydrodynamic lifting of seafloor mineral particles is rotor machinery with rotating impeller motion. It is important to study the rebound mechanism of collisions between particles and rotating walls to improve the accuracy of numerical simulation of rotor machinery. In this study, the law of motion change after collisions between particles and rotating walls is investigated using an experimental research method. The results show that the deflection angle of the particles after collision decreases with increases in the rotational speed of the wall, and the spin angular velocity increases with increases in the rotational speed of the wall. The normal velocity coefficient of restitution under the rotating wall is not affected by the rotational speed of the wall. The tangential coefficient of restitution under rotational boundary condition is smaller than the tangential coefficient of restitution under the stationary wall, and the higher the rotational speed, the closer it is to the coefficient of restitution under the stationary wall. During collision in the experiment, the main mode of contact between the particle and the rotating wall is sliding contact. Sliding friction between the particle and the rotating wall results in energy loss in the tangential velocity of the particle, and also provides energy for deflection of the particle’s trajectory and increased kinetic energy from the spin angular velocity; sliding friction loss is affected by the speed of the wall.

Development of the Median Tectonic Line-related shear zone, southwest Japan: An analysis of strain localization processes

The development of a mylonite zone along the Median Tectonic Line (MTL), southwest Japan, which developed in the Cretaceous granitic rocks, was examined to understand strain localization during cooling. The mylonites are E-W trending, north-dipping, and represent the hanging wall of the MTL. The mylonite zone includes both protomylonite and mylonite, which were derived from two distinct protoliths: tonalite (protomylonite) and granite (mylonite) and occur at distances of c. 0–300 m and 300–700 m from the MTL, respectively. We used quartz microstructures and crystallographic preferred orientations (CPOs) and two-feldspar thermometry to infer the spatiotemporal development of deformation conditions in the MTL mylonite zone. The mylonitic granite is sub-divided into southern and northern mylonite zones, which exhibit A- and B-type quartz microstructure formed by subgrain rotation and grain boundary migration recrystallization, respectively. In both the mylonitic granite and protomylonitic tonalite, quartz c-axis CPOs primarily display a moderate-temperature Y-maximum pattern, as well as a less common low-temperature type-I crossed-girdle pattern. In the northern zone, quartz deformation initially occurred at moderate temperatures of 435 °C–490 °C, forming mylonitic granite with B-type quartz microstructure. As temperature decreased to 355 °C–435 °C, the strain localized into the southern zone to form A-type quartz microstructure. The protomylonitic tonalite formed under similar temperature conditions. At temperatures below 355 °C, ductile deformation ceased in the majority of the granite and tonalite, with only a narrow zone of ultramylonite up to 50 m wide, deforming adjacent to the MTL at conditions approximating the brittle–ductile transition in quartz (c. 300 °C). Strain localization did not occur within a single shear zone, but in several deforming strands that formed in distinct protoliths, one of which developed into the narrow ultramylonite zone reworked as the brittle MTL, likely controlled by cooling.

Significance of Darcy–Forchheimer Law, Activation Energy, and Brownian Motion of Tiny Particles on the Dynamics of Rotating MHD Micropolar Nanofluid

The time-independent performance of a micropolar nanofluid under the influence of magneto hydrodynamics and the existence of a porous medium on a stretching sheet has been investigated. Nano-sized particles were incorporated in the base fluid because of their properties such as their extraordinary heat-enhancing ability, which plays a very important role in modern nanotechnology, cooling electronic devices, various types of heat exchangers, etc. The effects of Brownian motion and thermophoresis are accounted for in this comprehensive study. Using similarity conversion, the leading equations based on conservation principles are non-dimensionalized with various parameters yielding a set of ODEs. The numerical approach boundary value problem fourth-order method (bvp4c) was implemented as listed in the MATLAB computational tool. The purpose of this examination was to study and analyze the influence of different parameters on velocity, micro-rotation, concentration, and temperature profiles. The primary and secondary velocities reduced against the higher inputs of boundary concentration, rotation, porosity, and magnetic parameters, however, the base fluid temperature distribution grows with the increasing values of these parameters. The micro-rotation distribution increased against the rising strength of the Lorentz force and a decline is reported against the growing values of the micropolar material and rotational parameters.

Study of Generalized q -Close-to-Convex Functions Related to Parabolic Domain

The concepts of bounded boundary rotation and parabolic domain are used to define certain new classes of analytic functions such as V 1 , q m , g , R 1 , q m , g , T 1 , q m , g , and Q 1 , q γ m , g , a . The difference of coefficients, necessary conditions, distortion bounds, radius problem, and several other interesting properties of these newly defined classes are also studied.

Initial coefficient bounds for certain new subclasses of bi-univalent functions with bounded boundary rotation

<abstract><p>In the current article, we introduced new subclasses of bi-univalent functions associated with bounded boundary rotation. For these new classes, the authors first obtained two initial coefficient bounds. They also verified the special cases where the familiar Brannan and Clunie's conjecture were satisfied. Furthermore, the famous Fekete-Szegö inequality was obtained for the newly defined subclasses of bi-univalent functions, and some of the results improved the earlier results available in the literature.</p></abstract>

Problems concerning sharp coefficient functionals of bounded turning functions

<abstract><p>The work presented in this article has been motivated by the recent research going on the Hankel determinant bounds and their related consequences, as well as the techniques used previously by many different authors. We aim to establish a new subfamily of holomorphic functions connected with the hyperbolic tangent function with bounded boundary rotation. We investigate the sharp estimate of the third Hankel determinant for this newly defined family of functions. Moreover, for the defined functions family, the Krushkal inequality, the first four initial sharp bounds of the logarithmic coefficients and the sharp second Hankel determinant of the logarithmic coefficients are given.</p></abstract>

An Exploration of Brannan’s Coefficient Conjecture

Complex analysis of a single variable is a type of mathematical analysis that observe properties for holomorphic functions. Over decades of development, complex analysis nowadays has played a more and more important role in algebraic geometry, fluid dynamics, quantum mechanics, and so on. This paper is to elaborate the Brannan’s coefficient conjecture, which was first proposed by D.A Brannan, J.G. Clunie, and W.E Kirwam in their paper on the coefficient problem for functions of bounded boundary rotation in 1973. The purpose of this paper is to give a detailed review and exploration of complicated but elegant proofs by D. Aharonov and S. Friedland. This paper mainly focuses on proving the inequality for p > 0 |α| = 1 within condition n ≥ 1, which was derived from Brannan’s coefficient conjecture. The proof of the inequality is done by dividing the techniques of complex numbers, trigonometric functions, binomial expansions, and other mathematical formulas into three different cases.

A dynamic stiffness formulation for the vibration analysis of rotating cross-ply laminated coupled conical–cylindrical–conical shells

In this paper, a dynamic stiffness formulation is reported to analyze the free vibration characteristics of a rotating cross-ply laminated coupled conical–cylindrical–conical shell. In order to ensure the stability of the numerical results, the whole system is firstly divided into substructures, and each substructure is divided into several segments. The theoretical formulation of the rotating shell segment is derived by the first-order shear deformation theory and Hamilton’s principle. The effects of centrifugal force and Coriolis acceleration on the initial hoop tension are considered in the formulation. The dynamic stiffness matrix of the shell segment is derived from the relationship between the state vector and its derivative, where the state vector consists of the resultant force and displacement components of the shell segment. The dynamic stiffness matrix of the whole system is assembled by the displacement coordination relationship. After the number of segments is determined by the convergence analysis, it is compared with the results of the existing literature and finite element software to ensure the accuracy of the dynamic stiffness formulation. Based on this, the effects of rotational speed, geometry and boundary conditions on the structure are studied.

Comprehensive study of hot compression behaviors and microstructure evolution of solutionized 6082 aluminum alloy extruded bar

Recently, an efficient integrated forging process has been proposed in which solutionized aluminum alloy extruded bars are directly hot forged and quenched. In this study, the hot deformation behaviors and microstructure evolution of 6082 aluminum alloy extruded bar was investigated via isothermal compression tests under the temperature range of 400–535 ℃ and strain rates range of 0.1–10 s−1 with different strains. The deformation behaviors were described by the established strain-compensated constitutive model and processing maps. The microstructure evolution of the deformed specimens was revealed by electron back scattered diffraction (EBSD) and transmission electron microscopy (TEM). It was found that the Zener-Hollomon (Z) parameter, which involved temperature and strain rate, exerted a considerable influence on the deformation behaviors and microstructure evolution. Deformation-induced extensive dislocations were pinned by the dispersoids and generated cellular substructures under high ln Z (i.e. low temperature or high strain rate), potentially triggering dynamic instability. The tangled dislocations pinned by the insoluble dispersoids continued to overcome the pinning points as ln Z decreased, while the dislocations were consumed by the rotation of subgrain boundaries. As a result, the geometrically necessary dislocation (GND) was decreased with the significant increase of the fraction of high angle grain boundaries (HAGBs). In addition, the stable-end orientations, namely, Brass {011}< 211 > and Goss {011}< 001 > texture components with high Schmid Factors (SFs) are generated during compression, facilitating the dislocation movement and thus promoting the fraction of recrystallization. The above findings demonstrate the foundation for improving forming performance and optimizing the processing parameters for the integrated forging process.

Coefficients estimates of a new class of analytic bi-univalent functions with bounded boundary rotation

In this paper, we introduce a new subclass of analytic bi-univalent functions defined by using $q$-derivative operator. Further, we obtain both some initial and general coefficient bounds, and also Fekete-Szegö inequalities for bi-univalent functions that belong to this class. Our results extend and improve some known results as special cases.

An inverse coefficient problem of identifying the flexural rigidity in damped Euler-Bernoulli beam from measured boundary rotation.

We present a new mathematical model and method for identifying the unknown flexural rigidity [Formula: see text] in the damped Euler-Bernoulli beam equation [Formula: see text] [Formula: see text], subject to the simply supported boundary conditions [Formula: see text], [Formula: see text], from the available measured boundary rotation [Formula: see text]. We prove the existence of a quasi-solution and derive an explicit gradient formula for the Fréchet derivative of the Tikhonov functional [Formula: see text]. The results obtained here also form the basis of gradient-based computational methods for solving this class of inverse coefficient problems. This article is part of the theme issue 'Non-smooth variational problems and applications'.

Intermetallic particle heterogeneity controls shear localization in high-strength nanostructured Al alloys

The mechanical behavior of two nanocrystalline Al alloys, Al-Mg-Y and Al-Fe-Y, is investigated with in-situ micropillar compression testing. Both alloys were strengthened by a hierarchical microstructure including grain boundary segregation, nanometer-thick amorphous complexions, carbide nanorod precipitates with sizes of a few nanometers, and submicron-scale intermetallic particles. The maximum yield strength of the Al-Mg-Y system was measured to be 950 MPa, exceeding that of the Al-Fe-Y system (680 MPa), primarily due to a combination of more carbide nanorods and more amorphous complexions. Both alloys exhibited yield strengths much higher than those of commercial Al alloys, and therefore have great potential for structural applications. However, some micropillar specimens were observed to plastically soften through shear banding. Post-mortem investigation revealed that intermetallic-free deformation pathways of a few micrometers in length were responsible for this failure. Further characterization showed significant grain growth within the shear band. The coarsened grains maintained the same orientation with each other, pointing to grain boundary mechanisms for plastic flow, specifically grain rotation and/or grain boundary migration. The presence of intermetallic particles made it difficult for both matrix and intermetallic grains to rotate into the same orientation due to the different lattice parameters and slip systems. Therefore, we are able to conclude that a uniform distribution of intermetallic particles with an average spacing less than the percolation length of shear localization can effectively prevent the maturation of shear bands, offering a design strategy for high-strength nanocrystalline Al alloys with both high strength and stable plastic flow.

Teğet Sınır Şartlarının Ortasından Tekil Yüklü Katmanlı Kompozit Silindirik Panellerin Nonlineer Davranışlarına Etkisi

In this study, the influence of straight edge tangential restraints on the nonlinear response of symmetrically laminated and balanced composite cylindrical panels subject to a pinching force is investigated. An 8-node degenerated nonlinear shell element, formulation of which is based on the Total Lagrangian Formulation, is employed for geometrically nonlinear analysis and the Arc-Length Method is used to trace the nonlinear path. First, the element is validated for geometrically non-linear analysis by solving two verification problems. Then, numerical results for different rotational boundary conditions are presented for two different stacking sequences, and thickness values. The numerical results presented show that there is no significant difference between the tangentially unrestrained and restrained clamped panels when only one edge is tangentially unrestrained. However, it is observed that the simply supported panels demonstrate a much less stiff behavior when one of the straight edges is tangentially unrestrained.

A cell-based smoothed radial point interpolation method applied to kinematic limit analysis of thin plates

The cell-based smoothed radial point interpolation method in conjunction with a second order cone programming is proposed for kinematic limit analysis of rigid-perfectly plastic thin plates in this paper. The transverse displacement field is interpolated by the radial point interpolation method (RPIM) and no rotational degrees of freedom are involved. The gradient smoothing technique is utilized to construct smoothed curvature field in every smoothing domain and there is no need to compute the second derivatives of shape functions. The rotational boundary conditions are satisfied in the process of curvature smoothing and the translational boundary conditions can be directly enforced without any special treatment. The limit analysis problem of thin plates is formulated by minimizing the dissipation power subject to a set of equality constraints and this minimization problem can be expressed easily as a standard second order cone programming. It is testified from the computational results that the proposed procedure can provide reasonable and satisfactory upper bound limit load multipliers for thin plates.

Characterization of various interfaces in a TiAl-based alloy

As for a two phase TiAl-based alloy, γ/α2 lamellar structure has been studied, where, various atomic microstructures for interfaces generated by phase transformation and recrystallization upon high-temperature compression have been studied. As expected, mixed interfaces including phase boundary (PB), true twin (TT), pseudo-twin (PT), 120° rotational boundary (RB) and large angle grain boundary (LAGB) can be observed in the as-formed structure. A detailed characterization using high resolution electron microscopy has been performed, which helps to obtaining the optimum microstructure and the corresponding excellent mechanical properties of the TiAl alloy.

Modeling method for analyzing veering and nonlinear vibration of rotating hard-coated drum-disk structures considering the strain-amplitude dependency

This paper proposes a modeling method of rotating hard-coated drum-disk structures considering the strain-amplitude dependency of coatings and studies the veering of frequency curves and nonlinear coupled vibration. Firstly, Sanders’ shell theory and Kirchhoff's plate theory are used to derive the energy expressions of the hard-coated drum and hard-coated disk, respectively. The arbitrary multi-arc joints between disk and drum and arbitrary boundaries are presented based on the artificial spring. Furthermore, the displacements of the drum and disk are expanded by using the orthogonal polynomials, and Lagrange's equations are employed to derive the linear semi-analytical model. Secondly, the multi-domain dividing approach is used to develop a general method considering the strain-amplitude dependency in the rotation state, and the nonlinear semi-analytical model of rotating hard-coated drum-disk structures is created and further solved by an efficient algorithm proposed in the present work. The convergence and validation of the semi-analytical model are verified. Finally, the veering of frequency curves caused by the variations in rotation speeds, connection and boundary conditions, and thickness of coatings and substrates is revealed. The variation law and mechanism of nonlinear coupled vibration during veering are also investigated. The proposed modeling method can provide helpful references for the modeling and vibration analysis of multi-stage hard-coated drum-disk structures in aero-engine and other rotating hard-coated structures.

A consistent finite-strain plate model for wrinkling of stretched anisotropic hyperelastic films

Stretch-induced wrinkles usually occur in a thin, clamped–clamped, hyperelastic film and eventually disappear upon excess stretching, with wrinkling direction being perpendicular to the stretching direction within isotropic elasticity framework. Here, we consider in-plane anisotropy induced by infilling fibers in thin films, which significantly affects the orientation and amplitude of wrinkles. To precisely predict the isola-center bifurcation (“birth” and “death” of wrinkles) and to capture wrinkling morphology evolution under large in-plane anisotropic deformations, we develop a consistent finite-strain plate model by accounting for anisotropic hyperelastic constitutive laws. Advantages of this plate model lie in its asymptotic consistency with the 3D field equations and its applicability to large deformations. A new type of rotational symmetric boundary conditions is proposed to reduce the computational cost and to achieve robust convergence. We reveal that the fiber orientation plays a critical role in the wrinkling and restabilization behavior of stretched films. The fibers parallel or perpendicular to the stretching direction can resist the appearance of wrinkles, while the oblique fiber orientation (15°∼75°) can advance wrinkle formation. Besides, oblique wrinkling patterns can be regulated by fiber/matrix shear modulus ratio, and we draw phase diagrams on stability boundary to demonstrate the interactive parametric effects. Our results could provide quantitative guidance to design wrinkle-tunable surfaces for fiber-composite or biomimetic films.