Rotational Degrees Of Freedom Research Articles

Generalized macroscale model for Cosserat elasticity using Generalized Multiscale Finite Element Method

In this paper, we develop a multiscale computational approach for heterogeneous Cosserat media without scale separation and high contrast. Cosserat medium has been used in many applications to describe materials whose particles possess rotational degrees of freedom. Many previous findings investigate Cosserat medium in the presence of heterogeneities. Approaches that include homogenization and numerical homogenization have been developed for problems with scale separation, such as periodicity. In these approaches, macroscopic models are derived that show the resulting equations can be Cauchy medium or Cosserat medium depending on the Cosserat intrinsic length scale. In our paper, we consider computational macroscopic models for Cosserat medium without scale separation. We use Generalized Multiscale Finite Element Method (GMsFEM) to derive a macroscopic model on a coarse computational grid, that does not resolve the small scales and the contrast. In this approach, multiple macroscopic basis functions are used to describe the small scales. The resulting macroscopic model is similar to multicontinua model as it contains multiple macroscopic parameters at each macroscopic point (or grid). We present numerical results for different heterogeneous media types. Our numerical results show that using a few multiscale basis functions (i.e., macroscopic parameters), we can achieve a good accuracy.

A comprehensive investigation of vortex-induced vibrations and flow-induced rotation of an elliptic cylinder

This work finds its motivation in heat exchanger design and flow control. Flow-induced vibration is studied numerically for combined vortex-induced vibrations and vortex-induced rotations of a horizontally positioned elliptic cylinder. The aspect ratio is taken as 2, and the value of reduced velocities (Ured) considered for the present simulation is between 2 and 12. The body can have to and fro motions in a transverse (y) direction, in-line (x) direction as well as in azimuthal (θ) direction, which provides three degrees of freedom (DOF) to the body. It is found that for one-DOF (y-direction only) and two-DOF (y and x directions) cases, lock-in regions are the same while it is wider for the case of the three-DOF system. With the rotational DOF, y-directional motion is amplified and when it is compared with the one-DOF and two-DOF cases, difference in peak amplitude is about 30%. The rotational response reaches a maximum value within the synchronization regime, and the frequency behavior of rotational and transverse oscillations is showing the same characteristics. The phase difference is plotted to check their synchronization with respective forces and moments. For all DOFs and Ured, synchronized or desynchronized regions, 2S mode of vortex shedding was observed. For one-DOF and two-DOF cases, the transverse vibrational frequency ratio (fy/fn) becomes equal to unity for the range 3.75≤Ured≤5. For three-DOF, fy/fn and rotational frequency ratio (fR/fn) become close to the unity for 3.75≤Ured≤6. The three-DOF system shows smaller wake width and vortex formation length whereas the vortex strength is maximum.

Competing ionization and dissociation in the H$$_{2}$$ gerade system

A numerically solvable two-dimensional (2D) model, employed by the authors to study the dissociative recombination of H$_2^+$ in the ungerade symmetry [Phys. Rev. A $\mathbf{98}$, 062706 (2018)], is extended to describe the collision process in the gerade symmetry of H$_2$. In this symmetry the ionization and dissociation processes are driven primarily by the direct, curve-crossing mechanism. The model is represented by a set of three coupled electronic channels in 2D, in the space of $s,p,d$ partial waves of the colliding electron. We demonstrate that the Born-Oppenheimer properties of the H$_2$ molecule in the relevant range of internuclear distances can be described by such a model. The molecular rotational degrees of freedom are accounted for by the rotational frame transformation. The numerical solution of the model is discussed and the resulting rovibrationally inelastic and dissociative recombination cross sections are compared with the available data.

Highly stretchable van der Waals thin films for adaptable and breathable electronic membranes.

The conformal integration of electronic systems with irregular, soft objects is essential for many emerging technologies. We report the design of van der Waals thin films consisting of staggered two-dimensional nanosheets with bond-free van der Waals interfaces. The films feature sliding and rotation degrees of freedom among the staggered nanosheets to ensure mechanical stretchability and malleability, as well as a percolating network of nanochannels to endow permeability and breathability. With an excellent mechanical match to soft biological tissues, the freestanding films can naturally adapt to local surface topographies and seamlessly merge with living organisms with highly conformal interfaces, rendering living organisms with electronic functions, including leaf-gate and skin-gate transistors. On-skin transistors allow high-fidelity monitoring and local amplification of skin potentials and electrophysiological signals.

Quadrilateral scaled boundary spectral shell elements for static and dynamic analyses of functionally graded plates and shells

This paper presents new shell elements for static and dynamic analyses of functionally graded plates and shells with the material properties varying through the thickness according to a power-law distribution in terms of the volume fractions of the constituents. In the formulation, a shell element is treated as a three-dimensional linear elastic body and its middle surface is represented with a quadrilateral spectral element. Along the thickness direction, the shell geometry is described by scaling the middle surface while the displacements are approximated by interpolating the displacements on the top, middle and bottom surfaces using quadratic Lagrange shape functions. The assumed natural strain method is applied to eliminate transverse shear locking, membrane locking and curvature thickness locking. The developed shell elements are featured by requiring only the shell mid-surface to be discretized, containing no rotational degree of freedom, adopting the full three-dimensional constitutive law and involving only the in-plane numerical integration. The validity and performance of the formulation are demonstrated through benchmark examples covering plates, cylindrical shells and spherical shells with varying span-to-thickness ratio and material gradation index. Static solutions of two functionally graded shell problems under gravity loads are also provided.

Characterization of void space, large-scale structure, and transport properties of maximally random jammed packings of superballs

Dense, disordered packings of particles are useful models of low-temperature amorphous phases of matter, biological systems, granular media, and colloidal systems. The study of dense packings of nonspherical particles enables one to ascertain how rotational degrees of freedom affect packing behavior. Here, we study superballs, a large family of deformations of the sphere, defined in three dimensions by $|{x}_{1}{|}^{2p}+|{x}_{2}{|}^{2p}+{|{x}_{3}|}^{2p}\ensuremath{\le}1$, where $p\ensuremath{\in}(0,\ensuremath{\infty})$ is a deformation parameter indicating to what extent the shape deviates from a sphere. As $p$ increases from the sphere point ($p=1$), the superball tends to a cuboidal shape and approaches a cube in the $p\ensuremath{\rightarrow}\ensuremath{\infty}$ limit. As $p\ensuremath{\rightarrow}0.5$, it approaches an octahedron, becomes a concave body with octahedral symmetry for $p<0.5$, and approaches a three-dimensional cross in the limit $p\ensuremath{\rightarrow}0$. Previous characterization of superball packings has shown that they have a maximally random jammed (MRJ) state, whose properties (e.g., packing fraction $\ensuremath{\phi}$, average contact number $\overline{Z}$) vary nonanalytically as $p$ diverges from unity. Here, we use an event-driven molecular dynamics algorithm to produce MRJ superball packings with $0.85\ensuremath{\le}p\ensuremath{\le}1.50$. To supplement the previous work on such packings, we characterize their large-scale structure by examining the behaviors of their structure factors $S(Q)$ and spectral densities ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\chi}}}_{{}_{V}}(Q)$, as the wave number $Q$ tends to zero, and find that these packings are effectively hyperuniform for all values of $p$ examined. We show that the mean width $\overline{w}$ is a useful length scale to make distances dimensionless in order to compare systematically superballs of different shape. Moreover, we compute the complementary cumulative pore-size distribution $F(\ensuremath{\delta})$ and find that the pore sizes tend to decrease as $|1\ensuremath{-}p|$ increases. From $F(\ensuremath{\delta})$, we estimate how the fluid permeability, mean survival time, and principal diffusion relaxation time vary as a function of $p$. Additionally, we compute the diffusion ``spreadability'' $\mathcal{S}(t)$ [Torquato, Phys. Rev. E 104, 054102 (2021)] of these packings and find that the long-time power-law scaling indicates these packings are hyperuniform with a small-$Q$ power law scaling of the spectral density ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\chi}}}_{{}_{V}}(Q)\ensuremath{\sim}{Q}^{\ensuremath{\alpha}}$ with an exponent $\ensuremath{\alpha}$ that ranges from 0.64 at the sphere point to 0.32 at $p=1.50$, and decreases as $|1\ensuremath{-}p|$ increases. Each of the structural characteristics computed here exhibits an extremum at the sphere point and varies nonanalytically as $p$ departs the sphere point. We find the nonanalytic behavior in $\ensuremath{\phi}$ on either side of the sphere point is nearly linear, and determine that the rattler fraction ${\ensuremath{\phi}}_{R}$ decreases rapidly as $|1\ensuremath{-}p|$ increases. Our results can be used to help inform the design of colloidal or granular materials with targeted densities and transport properties.

Research into the kinematic singularity problem of an all-attitude simulator and its control

All-attitude flight simulators can simulate flight attitude through three rotational degrees of freedom. In this paper, the inverse kinematics and singularity of the all-attitude simulator are analyzed. Because a singularity will reduce the fidelity of the flight attitude simulation, we investigated ways to resolve this problem. An approximate method for quickly quantifying singularities is proposed. Static damping and dynamic damping are designed to optimize the singularity of the all-attitude simulator and improve the fidelity of flight attitude simulation. Attitude data of typical flight movements, whose inverse kinematics has an obvious singular position, are used to test the two methods. The results of the simulation show that the two methods are feasible and effective, and that dynamic damping has better control over singular excesses than static damping.

The frequency spectrum of rotobreathers with many degrees of freedom

A rotobreather in a lattice of coupled particles with rotational degrees of freedom is a dynamical regime when one particle rotates and the other particles vibrate with amplitudes exponentially decaying with distance from the rotating particle. In addition to rotational, particles can have internal degrees of freedom. Here, the influence of internal degrees of freedom on the possible rotational frequencies of rotobreathers is discussed for two models: a chain of coupled elastic rotators and a molecular crystal of carbon nanotubes (CNTs). It is shown that additional degrees of freedom create forbidden frequency bands for rotobreathers. In the case of a CNT crystal, due to resonances with many internal degrees of freedom, the frequency spectrum of a rotobreather has a complex structure resembling a Cantor set.

Extended micropolar approach within the framework of 3M theories and variations thereof

As part of his groundbreaking work on generalized continuum mechanics, Eringen proposed what he called 3M theories, namely the concept of micromorphic, microstretch, and micropolar materials modeling. The micromorphic approach provides the most general framework for a continuum with translational and (internal) rotational degrees of freedom (DOF), whilst the rotational DOFs of micromorphic and micropolar continua are subjected to more and more constraints. More recently, an “extended” micropolar theory has been presented by one of the authors: Eringen’s 3M theories were children of solid mechanics based on the concept of the indestructible material particle. Extended micropolar theory was formulated both ways for material systems as well as in spatial description, which is useful when describing fluid matter. The latter opens the possibility to model situations and materials with a continuum point that on the microscale consists no longer of the same elementary units during a physical process. The difference culminates in an equation for the microinertia tensor, which is no longer a kinematic identity. Rather it contains a new continuum field, namely an independent production term and, consequently, establishes a new constitutive quantity. This makes it possible to describe processes of structural change, which are difficult if not impossible to be captured within the material particle model. This paper compares the various theories and points out their communalities as well as their differences.

A Geometric Model in 3+1D Space-Time for Electrodynamic Phenomena

With the idea to find geometric formulations of particle physics we investigate the predictions of a three-dimensional generalization of the Sine-Gordon model, very close to the Skyrme model and to the Wu-Yang description of Dirac monopoles. With three rotational degrees of freedom of spatial Dreibeins, we formulate a Lagrangian and confront the predictions to electromagnetic phenomena. Stable solitonic excitations we compare with the lightest fundamental electric charges, electrons, and positrons. Two Goldstone bosons we relate to the properties of photons. These particles are characterized by three topological quantum numbers, which we compare to charge, spin, and photon numbers. Finally, we conjecture some ideas for further comparisons with experiments.

Membrane fiber element for reinforced concrete walls – the benefits of macro and micro modeling approaches

A novel element that mixes the formulation and versatility of microscopic models, and the mesh refinement of macroscopic models, was developed to predict the nonlinear response of reinforced concrete walls. The element, named as Membrane Fiber Element (MEFI), is described by four nodes, each containing three degrees of freedom (DOFs), two translations, and one in-plane rotation (drilling) DOF, which incorporates a blended interpolation function for the displacements over the element. The element formulation accommodates the quadrature points and weights of the classical finite element formulation of membrane elements to resemble strips (fibers), similarly to macroscopic elements. In this modeling approach, a RC panel element that follows a fixed-angle approach was used. The element was validated against five RC wall specimen tests with rectangular cross-sections and different aspect ratios reported in the literature. Also, the element was validated for walls with discontinuities using data from an experimental program of walls with openings. Comparisons of model predictions and experimental results, reveal that the MEFI element is reliable to predict the nonlinear response of reinforced concrete walls with different aspect ratios and properties, requiring less mesh refinement, and therefore less running time, for an accurate response estimation compared to finite element models.

A 3D HIGHER-ORDER GRADIENT MODEL FOR A HALF-SPACE GEOMEDIUM

In this paper, a structural model of a geomedium (a soil) is proposed in the form of a simple cubic lattice of spherical particles (blocks) possessing three translational and three rotational degrees of freedom. The force and couple interactions between the particles are modeled by elastic springs of five types. A long-wavelength continuum mathematical model of the soil has been elaborated by the method of structural modeling. An analytical relationship between its macroconstants and microstructure parameters has been found. It is shown that the obtained model differs from the model of the reduced Cosserat medium, which is often employed to describe granular media. In the low-frequency approximation, it can be reduced to the equations of the higher-order gradient theory of elasticity, which are similar to the Cosserat continuum equations with constrained rotation of particles. These equations contain both terms with mixed derivatives with respect to time and coordinate that take into account the inertia of particles rotation in the medium and lead to the wave dispersion, and terms proportional to the spatial derivatives of the fourth order, which describe the contribution of stresses caused by bending of the medium to the potential energy. In the framework of the higher-order gradient model, expressions for the classical and couple stresses in the considered geomedium are found. Boundary conditions are set that consist in the absence of normal and shear stresses on the upper platform of a half-space medium. A condition for the microstructure parameters has been revealed, under which the couple stresses can be neglected. The proposed here higher-order gradient model with given boundary conditions can be used to investigate the propagation and interaction of elastic waves in a semi-infinite geomedium, which are generated by the high-speed movement of trains, as well as to identify and study potentially dangerous effects caused by such movement.

Control of an Orbital Manipulator with Reaction Wheels for On-orbit Servicing

In on-orbit servicing missions, a spacecraft equipped with a manipulator arm grasps a client satellite. Afterwards, the momentum-dumping phase follows and the manipulator can be utilized for servicing tasks. Once the momentum has been dumped, a desired manipulator configuration and base attitude may be needed for initializing a servicing phase such as berthing. The proposed approach prioritizes the attitude maintenance of the servicer spacecraft, and reconfigures the manipulator arm with the grasped client satellite in the nullspace of the servicer's attitude. The approach utilizes the redundancy in rotational degrees of freedom, provided by reaction wheels, to decouple the manipulator reconfiguration task from the attitude of the servicer-base. The proposed controller shows convergence of the attitude and joint-level task, independent of kinematic singularities of the manipulator arm. Additionally, the problem of speed saturation of the reaction wheels is tackled by increasing the damping torques as a function of the wheel speed. Simulation results verify the effectiveness of the proposed control approach.

Research on solid shell element based on penalty method

Since the angle degrees of freedom do not have the vector property, it is critical to handle this for nonlinear geometrical behavior. To simulate the nonlinear geometrical behavior of shell structure efficiently, we developed a solid‐shell element type without drilling degrees of freedom. In this paper, the element satisfies the assumption of the straight normal of the shell and we established penalty functions in the thickness direction of the shell. The formulations of equivalent node force and tangent stiffness obtained by 3D isoparametric element theory can be expressed by matrix forms clearly. The constitutive relationship in the global system is derived from the local constitutive matrix according to the tensor coordinate transform. Finally, taking a series of classic flat plate problems and curved shell problems as examples, the solid shell element using the penalty method is compared with the solid shell element using the artificial stiffness method and other shell elements. The results show that the solid element proposed in this paper can effectively eliminate shear self-locking after using the reduced integral scheme and obtain satisfactory accuracy for thin shells and medium-thickness•A type of solid shell element without rotational degrees of freedom is introduced using the penalty method.•A suitable penalty factor of this element is determined through numerical experiments.•This element is more efficient than the traditional shell elements and can be programmed with less time.

Circularly polarized light-induced potentials and the demise of excited states.

In the presence of strong electric fields, the excited states of single-electron molecules and molecules with large transient dipoles become unstable because of anti-alignment, the rotation of the molecular axis perpendicular to the field vector, where bond hardening is not possible. We show how to overcome this problem by using circularly polarized electromagnetic fields. Using a full quantum description of the electronic, vibrational, and rotational degrees of freedom, we characterize the excited electronic state dressed by the field and analyze its dependence on the bond length and angle and the stability of its vibro-rotational eigenstates. Although the dynamics is metastable, most of the population remains trapped in this excited state for hundreds of femtoseconds, allowing quantum control. Contrary to what happens with linearly polarized fields, the photodissociation occurs along the initial molecular axis, not perpendicular to it.

Atroposelective construction of axially chiral enamides via N-allylic alkylation.

Herein, we report the catalytic asymmetric synthesis of a unique family of axially chiral enamides in good yields with excellent enantioselectivities under mild conditions. These new axially chiral compounds feature a flexible skeleton and a high degree of rotational freedom, which raises difficulties for enantiocontrol. A mechanism model is proposed to interpret the stereoselectivity, in which both the steric difference of the ortho substituents and the π-π stacking interaction may contribute to the stereo-control.

Active depletion torque between two passive rods.

The active depletion torque experienced by two anisotropic objects in an active bath is a conceptional generalization of the equilibrium entropic torque. Using Brownian dynamics simulations, we compute the active depletion torque suffered by two passive rods immersed in an ensemble of active Brownian particles. Our results demonstrate that the active depletion torque is qualitatively different from its passive counterpart. Interestingly, we find that the active depletion torque can be greatly affected by the external constraint applied on the rotational degree of freedom of the rods, and even the direction may be changed with the orientational constraint, which is in contrast to the equilibrium depletion torque. The main reason for the remarkable features of the active depletion torque is that the active particles can significantly accumulate in the vicinity of the rods due to persistent self-propulsion, which is sensitively dependent on the constraint strength and the rod configurations. Our findings could be relevant for understanding the self-assembly and dynamics of anisotropic macromolecules in living environments.

Многокритериальная оптимизация конструкции дельта-робота с четырьмя степенями свободы

A delta robot with three degrees of freedom, having been well studied over the past 40 years, is one of the most popular parallel mechanisms. Nowadays, an urgent task is to study the properties of various modifications of this mechanism. The article considers a delta robot with four degrees of freedom, in which one of the kinematic chains with a parallelogram is divided into two, allowing the output link to have an additional rotational degree of freedom. To maximize the working area and minimize the cost of modification the optimization of the robot design was performed. The problem of maximizing a cubic workspace has been solved.

Numerical investigation on VIV energy harvesting enhancement with adding eccentricity to a circular cylinder

In recent years, energy harvesting from vortex-induced vibration (VIV) of a cylinder as a renewable source of energy has been increased. The main goal is to enhance the harnessed hydrokinetic energy of the VIV converters. In this work, the effect of adding a rotational degree of freedom by giving eccentricity to the circular cylinder is investigated on vibration and rotational response as well as hydrokinetic energy conversion. Simulations are done at the Reynolds number ranging from 2×10^3 to 13×10^3. Twodimensional unsteady Reynolds-averaged Navier–Stokes equations (URANS), supplemented with SST turbulence models, are solved on moving mesh, and arbitrary Lagrangian-Eulerian formulation is employed to accommodate the deforming boundaries. For the freely rotating and vibrating cylinder, results demonstrate that increasing the inlet velocity increases the vibration amplitude, and the cylinder experiences complete rotation in some of the flow times. Moreover, adding a rotational degree of freedom causes hydrodynamic instability, in which the location of separation points changes and makes a wide wake pattern with unstable vortexes behind the cylinder. As a result, the harnessed power and energy conversion efficiency of the system is increased. The freely vibrating-rotating system generates a maximum power of 0.024 (W), and the energy conversion efficiency increases and fluctuates around 11.2%.

A quadrilateral flat-shell element for the static and dynamic analysis of composite and sandwich cylindrical, spherical and conical shell panels

Abstract A quadrilateral flat-shell element is developed for analysing the deflections, stresses and natural frequencies along with their allied mode shapes of cylindrical, spherical, and conical shell panels made up of layered composite and sandwich material. The developed element (DKZigTS1) is based on zigzag theory and has seven local as well as global DOF per node. The concept of obtaining transformation matrix is used for transforming actions and reactions from local to global direction to convert the plate bending into a flat-shell element. The two separate coordinate systems are used to transform rotational and translational degrees-of-freedom (DOF), from local to global direction. The local translational DOF are transformed to global Cartesian coordinates (x, y, z) and the local rotational DOF are transformed to the surface coordinate system (ξ 1, ξ 2, ξ 3), in which ξ 3 is perpendicular to the surface. The DKZigTS1 element gives fairly accurate results that align with the 2D analytical and the 3D elasticity solutions, reported in the literature for moderately thick and thick shell panel. The present results are also in good agreement with the 3D finite element solutions for shallow and deep shell panels having various material properties, boundary restrained environments, and geometrical shapes considered in this study.