Critical Angular Velocity Research Articles

Application of Lateral Overturning and Backward Rollover Analysis in a Multi-Purpose Agricultural Machine Developed in South Korea

This study analyzed the lateral overturning and backward rollover characteristics of a multi-purpose agricultural machine recently developed in South Korea. Free body diagrams for theoretical analysis and a three-dimensional model for dynamic simulation were created by reflecting the actual dimensions and material properties of the multi-purpose agricultural machine. The simulation model was verified using the minimum turning radius and angle of static falling down sidelong derived through the certified performance test. The lateral overturning and backward rollover characteristics of the multi-purpose agricultural machine were analyzed using a verified simulation model and theoretical equations derived through literature review. In the lateral overturning analysis, the critical traveling speed at which lateral overturning occurs was derived according to the inner steering angle of the front wheels under steady-state turning conditions. In the backward rollover analysis, the critical angular velocity and theoretical traveling speed of the main body at which backward rollover occurs were derived according to lifting angle of the front wheels. There was no significant difference between the theoretical analysis and simulation results at 5% significance level, and we derived the appropriate traveling speed conditions of the multi-purpose agricultural machine that do not cause lateral overturning and backward rollover.

Size-dependent frequency analysis of the magneto-electro-elastic rotary microdisk by incorporating modified couple stress and higher-order shear deformation theories

In this research, critical angular velocity and frequency of a magneto-electro-elastic (MEE) rotary microdisk using modified couple stress theory (MCST) is presented. The computational formulations of the MEE microdisk are obtained by mixing the strain terms of MCST to the microsystem's strain energy. Fore modeling the current microstructure's displacement field, higher-order shear deformation theory (HSDT) is presented. Consequently, for obtaining the microsystem's critical angular velocity and frequency information, the size-dependent governing equations are solved using the generalized differential quadrature method (GDQM). Afterward, a parametric study is done to present the impacts of the applied ampere, length scale factor, applied voltage, and radius ratio on the frequency responses and critical rotating speed of the MEE rotary microdisk by considering MCST. The results show that the impact of length scale on the system dynamics is considerable than the effect of applied ampere and the mentioned issue is more clear for simply boundary conditions. Finally, in plane ( ), we can find a triangular surface in which applied ampere and length scale do not have any effect on the frequency of the rotary system, and the triangular surface becomes smaller due to changing boundary conditions from simply-simply to clamped-clamped.

Frequency and critical angular velocity characteristics of rotary laminated cantilever microdisk via two-dimensional analysis

In this article, amplitude, and vibrational characteristics of a rotating laminated cantilever microdisk are presented. The centrifugal and Coriolis effects due to the rotation are considered. The strain and stress relations can be determined via the higher-order shear deformable theory (HSDT). For accessing to size-effects, the nonlocal strain gradient theory (NSGT) is used for obtaining the correct results. The boundary conditions are derived through governing equations of the laminated rotating microdisk using an energy method known as Hamilton's principle and finally are solved using generalized differential quadrature method (GDQM). Vibration characteristics of the spinning microdisk with various boundary conditions are described based on the curves drawn by Matlab software. Also, the simply-supported conditions are applied to edges θ=π/2, and θ=3π/2, and, cantilever (clamped–free) boundary conditions are investigated in R = Ri, and R0, respectively. Apart from the numerical solution, a 3-D finite element model using ABAQUS software is presented using the finite element package to simulate the response of the laminated cantilever disk. The results created from a finite element simulation illustrates a close agreement with the semi-numerical method results. The outcomes show that the number of layers, angle of ply, angular velocity speed, length scale, and nonlocal parameters, and geometrically properties of microdisk have a considerable impact on the amplitude, and vibration behavior of a rotating laminated cantilever microdisk. As an applicable result in related industries, if the structure is made of an even number of layers, the frequency response of the system would be better, especially at the smaller values of the radius ratio.

Quantized vortices in dipolar supersolid Bose-Einstein-condensed gases

We investigate the properties of quantized vortices in a dipolar Bose-Einstein condensed gas by means of a generalized Gross-Pitaevskii equation. The size of the vortex core hugely increases by increasing the weight of the dipolar interaction, approaching the transition to the supersolid phase. The critical angular velocity for the existence of an energetically stable vortex decreases in the supersolid, due to the reduced value of the density in the interdroplet region. The angular momentum per particle associated with the vortex line is shown to be smaller than $\ensuremath{\hbar}$, reflecting the reduction of the global superfluidity. The real-time vortex nucleation in a rotating trap is shown to be triggered, as for a standard condensate, by the softening of the quadrupole mode. For large angular velocities, when the distance between vortices becomes comparable to the interdroplet distance, the vortices are arranged into a honeycomb structure, which coexists with the triangular geometry of the supersolid lattice and persists during the free expansion of the atomic cloud.

Topological term, QCD anomaly, and the \u03b7\u2032 chiral soliton lattice in rotating baryonic matter

We study the ground states of low-density hadronic matter and high-density color-flavor locked color superconducting phase in three-flavor QCD at finite baryon chemical potential under rotation. We find that, in both cases under sufficiently fast rotation, the combination of the rotation-induced topological term for the η′ meson and the QCD anomaly leads to an inhomogeneous condensate of the η′ meson, known as the chiral soliton lattice (CSL). We find that, when baryon chemical potential is much larger than isospin chemical potential, the critical angular velocity for the realization of the η′ CSL is much smaller than that for the π0 CSL found previously. We also argue that the η′ CSL states in flavor-symmetric QCD at low density and high density should be continuously connected, extending the quark-hadron continuity conjecture in the presence of the rotation.

A Molecular Dynamics Study on Rotational Nanofluid and Its Application to Desalination.

In this work, we systematically study a rotational nanofluidic device for reverse osmosis (RO) desalination by using large scale molecular dynamics modeling and simulation. Moreover, we have compared Molecular Dynamics simulation with fluid mechanics modeling. We have found that the pressure generated by the centrifugal motion of nanofluids can counterbalance the osmosis pressure developed from the concentration gradient, and hence provide a driving force to filtrate fresh water from salt water. Molecular Dynamics modeling of two different types of designs are performed and compared. Results indicate that this novel nanofluidic device is not only able to alleviate the fouling problem significantly, but it is also capable of maintaining high membrane permeability and energy efficiency. The angular velocity of the nanofluids within the device is investigated, and the critical angular velocity needed for the fluids to overcome the osmotic pressure is derived. Meanwhile, a maximal angular velocity value is also identified to avoid Taylor-Couette instability. The MD simulation results agree well with continuum modeling results obtained from fluid hydrodynamics theory, which provides a theoretical foundation for scaling up the proposed rotational osmosis device. Successful fabrication of such rotational RO membrane centrifuge may potentially revolutionize the membrane desalination technology by providing a fundamental solution to the water resource problem.

Ground state properties of trapped boson system with finite-range Gaussian repulsion: exact diagonalization study

We use exact diagonalization to study an interacting system of N spinless bosons with finite-range Gaussian repulsion, confined in a quasi-two-dimensional harmonic trap with and without an introduced rotation. The diagonalization of the Hamiltonian matrix using Davidson algorithm in subspaces of quantized total angular momentum Lz is carried out to obtain the N-body lowest eigenenergy and eigenstate. To bring out the effect of quantum (Bose) statistics and consequent phase stiffness (rigidity) of the variationally obtained many-body wavefunction on various physical quantities, our study spans from few-body (N = 2) to many-body (N = 16) systems. Further, to examine the finite-range effect of the repulsive Gaussian potential on many-body ground state properties of the Bose-condensate, we obtain the lowest eigenstate, the critical angular velocity of single vortex state and the quantum correlation (measured) in terms of von Neumann entanglement entropy and degree of condensation. It is found that for small values of the range (measured by the parameter σ) of Gaussian potential, the ground state energy increases for few-boson (2 ⩽ N ⩽ 8) systems but decreases for many-boson (N > 8) systems. On the other hand for relatively large values of the range of Gaussian potential, the ground state energy exhibits a monotonic decrease, regardless of the number of bosons N. For a given N, there is found an optimal value of the range of Gaussian potential for which the first vortex (with Lz = N) nucleates at a lower value of the rotational angular velocity Ωc1 compared to the zero-range (δ-function) potential. Further, we observe that the inter-particle interaction and the introduced rotation are competing effects with latter being dominant over the former. With increase in the range of Gaussian potential, the value of von Neumann entropy decreases and the degree of condensation increases implying an enhanced quantum correlation and phase rigidity.

Movement initiation of millimeter particles on a rotating rough surface: The role of adhesion

We performed experiments to determine the critical moment for movement initiation of a millimeter bead on a rotating rough surface. The corresponding critical angular velocities were measured for glass and stainless-steel ball bearings over two different rough surfaces with glued glass beads. A basic theoretical analysis was developed to explain the observed results. Although the expectation of a simple approach with the presence of the obstacles offered by a rough surface could be sufficient to describe the problem, we prove here that the sole consideration of these obstacles, and even friction, are insufficient to explain the results in the range of a few-millimeter glass particles. Where the thermodynamic work of adhesion between surfaces is significant, the adhesion forces must be considered in the force balance for particle detachment. This effect is a determinant for describing theoretically and numerically the dynamics of millimeter particles.

Rotation induced charged pion condensation in a strong magnetic field: A Nambu–Jona-Lasino model study

We investigate the possibility of charged pion condensation in the presence of parallel rotation and magnetic field within the Nambu--Jona-Lasinio model with quarks as the fundamental degrees of freedom. Previous study based on non-interacting Klein-Gordon theory for pions showed that the charged pions will undergo Bose-Einstein condensation under this circumstance [Y. Liu and I. Zahed, Phys. Rev. Lett. ${\bf 120}$, 032001 (2018)]. In this work, we take into account the internal quark structures of charged pions self-consistently through quark polarization loops in an interacting theory, i.e., the Nambu--Jona-Lasino model. The stability of the system is explored against the formation of a nonzero expectation value of the composite charged pion field $\bar{u}i\gamma_5d$. We find that two competing effects are induced by the rotation: the isospin enhancement which favors charged pion condensation and the spin breaking which disfavors the condensation. For a strong magnetic field ($\sqrt{eB}\sim1{\rm GeV}$) and system size of a few fermi, the isospin enhancement effect is stronger than the spin breaking one, and the charged pion condensation becomes energetically favored beyond a critical angular velocity of a few MeV.

Viscoplastic Couette Flow in the Presence of Wall Slip with Non-Zero Slip Yield Stress.

The steady-state Couette flow of a yield-stress material obeying the Bingham-plastic constitutive equation is analyzed assuming that slip occurs when the wall shear stress exceeds a threshold value, the slip (or sliding) yield stress. The case of Navier slip (zero slip yield stress) is studied first in order to facilitate the analysis and the discussion of the results. The different flow regimes that arise depending on the relative values of the yield stress and the slip yield stress are identified and the various critical angular velocities defining those regimes are determined. Analytical solutions for all the regimes are presented and the implications for this important rheometric flow are discussed.

Nonlocal longitudinal, flapwise, and chordwise vibrations of rotary doubly coaxial/non-coaxial nanobeams as nanomotors

The advancement in both experiment and theory of rotating nanomotors provides a vital base for succeeding nano-electro-mechanical system technology. This paper deals with nonlocal dynamic modeling of double-nanobeam-systems with coaxial and non-coaxial patterns rotate with a rigid shaft accounting for longitudinal, flapwise, and chordwise vibrations. The full lateral interactions of doubly adjacent nanobeams due to three-dimensional vigorous van der Waals forces are considered in the framework of linear vibrations. Using Hamilton’s principle, the nonlocal equations of motion of the nanosystem are constructed by employing Rayleigh and Timoshenko beam theories. By exploiting the size-dependent mode shapes, the unknown deformation fields are appropriately discretized, the Galerkin approach is applied, and the natural frequencies associated with the longitudinal, in-plane, and out-of-plane motions are evaluated. The roles of various crucial factors, including geometrical properties of the nanosystem, nonlocality and shear effects, angular velocity, radius of the shaft, and intertube distance, in the free dynamic response of the rotating nanosystem are explained and discussed comprehensively. Further, the size-dependent critical angular velocity pertinent to the initial dynamic instability of the nanosystem is also introduced and the effects of influential parameters on this key factor are displayed.

Envelopes, foci, and maxima of special trajectories

Some special orbits are presented. The envelopes of the trajectories are presented, as are the loci of their maxima and their foci. Some of them have critical parameters for the envelope, such as a critical angle or a critical angular velocity.

Attitude recovery scheme of magnetically controlled satellite with constant thrust

When the constant thrust is acting directly on the bias momentum satellite, one component of the angular velocity vector would increment gradually to a larger one or even to infinite, which beyond the controllable region corresponding to B-dot algorithm. And in the following rate damping control process, the corresponding control effort would lead to attitude instability. In this study, under the constant thrust, the satellite's attitude evolution laws is researched and, under the control effort corresponding to B-dot damping algorithm, the satellite's tumbling mechanism is analyzed. Two critical angular velocities, respectively corresponding to the watershed value and the saddle point value, are determined according to the details of attitude control systems, including attitude control cycle and the corresponding time sequence. Theoretical analysis results show that, when the angular velocity is larger than the first critical angular velocity corresponding to the controllable region of B-dot algorithm, the B-dot damping algorithm would fail to de-tumble the satellite. On the contrary, the corresponding control effort would drive the angular velocity to another critical angular velocity, which is the saddle point for B-dot algorithm. Finally, a series of simulation examples are presented to verify the proposed conclusions.

Critical angular velocity and anisotropic mass loss of rotating stars with radiation-driven winds

Context. The understanding of the evolution of early-type stars is tightly related to that of the effects of rapid rotation. For massive stars, rapid rotation combines with their strong radiation-driven wind. Aims. The aim of this paper is to investigate two questions that are prerequisite to the study of the evolution of massive rapidly rotating stars: (i) What is the critical angular velocity of a star when radiative acceleration is significant in its atmosphere? (ii) How do mass and angular momentum loss depend on the rotation rate? Methods. To investigate fast rotation, which makes stars oblate, we used the 2D ESTER models and a simplified approach, the ω-model, which gives the latitudinal dependence of the radiative flux in a centrifugally flattened radiative envelope. Results. We find that radiative acceleration only mildly influences the critical angular velocity, at least for stars with masses lower than 40 M⊙. For instance, a 15 M⊙ star on the zero-age main sequence would reach criticality at a rotation rate equal to 0.997 the Keplerian equatorial rotation rate. We explain this mild reduction of the critical angular velocity compared to the classical Keplerian angular velocity by the combined effects of gravity darkening and a reduced equatorial opacity that is due to the centrifugal acceleration. To answer the second question, we first devised a model of the local surface mass flux, which we calibrated with previously developed 1D models. The discontinuity (the so-called bi-stability jump) included in the Ṁ − Teff relation of 1D models means that the mass flux of a fast-rotating star is controlled by either a single wind or a two-wind regime. Mass and angular momentum losses are strong around the equator if the star is in the two-wind regime. We also show that the difficulty of selecting massive stars that are viewed pole-on makes detecting the discontinuity in the relation between mass loss and effective temperature also quite challenging.

Synchronization transition in Sakaguchi-Kuramoto model on complex networks with partial degree-frequency correlation.

We investigate transition to synchronization in the Sakaguchi-Kuramoto (SK) model on complex networks analytically as well as numerically. Natural frequencies of a percentage (f) of higher degree nodes of the network are assumed to be correlated with their degrees and that of the remaining nodes are drawn from some standard distribution, namely, Lorentz distribution. The effects of variation of f and phase frustration parameter α on transition to synchronization are investigated in detail. Self-consistent equations involving critical coupling strength (λc) and group angular velocity (Ωc) at the onset of synchronization have been derived analytically in the thermodynamic limit. For the detailed investigation, we considered the SK model on scale-free (SF) as well as Erdős-Rényi (ER) networks. Interestingly, explosive synchronization (ES) has been observed in both networks for different ranges of values of α and f. For SF networks, as the value of f is set within 10%≤f≤70%, the range of the values of α for existence of the ES is greatly enhanced compared to the fully degree-frequency correlated case when scaling exponent γ<3. ES is also observed in SF networks with γ>3, which is never observed in fully degree-frequency correlated environment. On the other hand, for random networks, ES observed is in a narrow window of α when the value of f is taken within 30%≤f≤50%. In all the cases, critical coupling strengths for transition to synchronization computed from the analytically derived self-consistent equations show a very good agreement with the numerical results. Finally, we observe ES in the metabolic network of the roundworm Caenorhabditis elegans in partially degree-frequency correlated environment.

Three-dimensional dynamics of beam-like nanorotors on the basis of newly developed nonlocal shear deformable mode shapes

The longitudinal, chordwise, and flapwise vibrations of nanorotors are going to be examined via nonlocal Euler-Bernoulli and Timoshenko beam models. By exploiting Hamilton’s principle on the basis of the nonlocal constitutive relations, the novel-nonlocal equations of motion that display three-dimensional vibrations of the beam-like nanorotors are constructed and solved for natural frequencies using the Galerkin-based assumed mode methodology. For capturing the frequencies more accurately, the newly developed-size-dependent mode shapes are employed in which the true nonlocal boundary conditions at the free end are satisfied exactly. Accounting for dynamic couplings of the longitudinal and chordwise vibrations, the roles of the angular velocity, nonlocality, length of the nanorotor, and radius of the nanoshaft on the longitudinal, chordwise, and flapwise frequencies are displayed and discussed. Further, the critical angular velocity of the nanorotor by considering the nonlocality is derived and its influential factors are displayed. The crucial role of the shear deformation on the obtained results is also explained methodically.

Thermal characterization of the end-forming process of PVC pipes: influence of the number of lamps on critical angular velocities

The end-forming, or belling, of plastic pipes allows them to be joined together to form longer ducts. The first stage of the process entails softening the pipe wall through heating, and defines the properties of the final product. Because of the very low value of thermal conductivity of plastics and to speed heating up, the pipes are placed in ovens whose walls are lined with infra-red short-wave (SW) lamps. The radiation emitted partly penetrates the pipe wall, quickening the process. The heating elements have a straight configuration, and can only be laid axially flush over the oven’s wall, the pipes, therefore, must rotate to obtain a circumferentially uniform heating and avoid damage. The threshold speed to avoid scorching while exceeding a desired temperature over the thickness of the pipe wall is defined as ”critical angular velocity” and is strictly dependent on pipe geometry and oven characteristics such as the number and layout of lamps. The Authors have already investigated the problem extensively, as is well documented in the literature, yet one aspect still remains to be studied, namely the influence of the number of lamps on the heat flux distribution over the pipe’s perimeter and on the critical velocity. In this work, the issue is investigated thoroughly using the same approach previously adopted and recalled in its main aspects in the paper. It is found that even a significant reduction in the number of lamps does not increase threshold velocities to technically unfeasible values. A non-negligible reduction in costs can therefore be achieved without significant impact on the process outcomes.

Buckling of a spinning elastic cylinder: linear, weakly nonlinear and post-buckling analyses

An elastic cylinder spinning about a rigid axis buckles beyond a critical angular velocity, by an instability driven by the centrifugal force. This instability and the competition between the different buckling modes are investigated using analytical calculations in the linear and weakly nonlinear regimes, complemented by numerical simulations in the fully post-buckled regime. The weakly nonlinear analysis is carried out for a generic incompressible hyperelastic material. The key role played by the quadratic term in the expansion of the strain energy density is pointed out: this term has a strong effect on both the nature of the bifurcation, which can switch from supercritical to subcritical, and the buckling amplitude. Given an arbitrary hyperelastic material, an equivalent shear modulus is proposed, allowing the main features of the instability to be captured by an equivalent neo-Hookean model.

On the inertio-elastic instability of variable-thickness functionally-graded disks

Instability is observed at certain speeds for rotating disks when the radial displacement in the centrifugal force is taken into consideration. The critical angular velocity values which cause unbounded displacement and stresses will be determined. Analysis of functionally-graded variable-thickness disks requires solving variable-coefficient governing differential equations. Analytical solutions of such equations can be obtained only for certain material grading functions and uniform thickness profiles. In the present study, disks with non-uniform thickness profiles and heterogeneous material properties graded in the radial direction are considered. Solution of the resulting variable-coefficient governing equation of displacement requires the implementation of numerical methods. To this end, a novel approach, Complementary Functions Method is employed as the solution scheme. Complementary Functions Method provides an accurate and efficient solution procedure by reducing the two-point boundary value problem to a system of initial value problems. It is applicable for any continuous material grading functions and thickness profiles. The presented method is validated using a benchmark disk problem with uniform-thickness and material properties graded by a simple power function. Also, the efficiency of the solution scheme is demonstrated by comparing the results with those of finite element method (ANSYS).

Free vibration of an ultra-fast-rotating-induced cylindrical nano-shell resting on a Winkler foundation under thermo-electro-magneto-elastic condition

Recently, ultra-fast-rotating-induced cylindrical nano-shells subjected to electro-magnetic fields are used as a water pump. An enormous centrifugal acceleration (up to 1011 g), which is surpassed by five orders of magnitude acceleration in the fastest centrifuges available today, on such nano-structure would have a considerable effect on the vibration and buckling behavior of the structure. In order to predict the first natural frequency and the critical angular velocity of a thermo-electro-magneto-elastic single-layer cylindrical nano-shell resting on a Winkler foundation, the governing equations of motion are derived based on the Hamiltonian Principle and by using first shear deformation theories in conjunction with modified couple stress theory. The effects of the centrifugal acceleration are considered in the formulation. For different boundary conditions, GDQ method is applied as a numerical solution and an analytical solution is presented for the simple-simple boundary conditions at the end of the nano-cylinder. The contributions of the centrifugal acceleration, angular velocities, electrical field, magnetic field, elastic foundation and boundary conditions are investigated. The convergency of the results as well as the verification of the solutions with available results in the literature are presented in details.