Rigid Body Rotation Research Articles

Digital volume correlation using a spherical shell template and cubic element for large rotation measurement.

The displacement hypothesis of eight-node cubic elements is selected as the shape function of digital volume correlation (DVC), and the Newton-Raphson iterative method is selected to solve the partial differential equation to measure the displacement field. In order to ensure that the DVC algorithm is usable under the large rotation condition, the spherical shell template matching technique is presented to perform the integer-voxel displacement searching for nodes, which can provide the optimal initial values for the Newton-Raphson iterative method due to the rotation and translation invariance of the spherical shell template. Simulated volume images are used to verify the reliability of the proposed method, and the results show that the proposed DVC method can be used to measure the deformation with an arbitrary rigid body rotation angle. This work is expected to be useful to measure deformation with large rotation of the internal structure of materials.

On the free rotations of rigid bodies with a liquid-filled gap

We consider the system constituted by a hollow rigid body whose cavity contains a homogeneous rigid ball, and let the gap between the solids be entirely filled by a viscous incompressible fluid. We investigate the free rotations of the whole system, i.e., motions driven only by the inertia of the fluid-solids system once an initial angular momentum is imparted on the whole system. We prove the existence of global weak solutions and local strong solutions to the equations of motion. In addition, we prove that the fluid velocity as well as the inner core angular velocity relative to the outer solid converge to zero as time approaches infinity.

An optical beam deflection based system for multi-axis out-of-plane motion measurement at multiple points

This note presents an optical beam deflection-based measurement system to make multi-axis out-of-plane motion measurement at multiple points on both micro- and macro-scale targets. A novel automated calibration stage has been designed to change the measurement locations on the target and to calibrate the sensitivity matrix of the measurement system at each location. The developed measurement system is validated by measuring the rigid body rotation of a target, after which its utility is demonstrated by performing dynamic characterization of a micro-electro-mechanical system micro-cantilever beam in order to obtain its first two mode shapes.

A high order spectral difference-based phase field lattice Boltzmann method for incompressible two-phase flows

In this paper, a high order spectral difference-based phase field lattice Boltzmann method (SD-PFLBM) is proposed for simulating incompressible two-phase flows. The spectral difference method (SDM) is used to discretize the convection term and the gradient term of the discrete Boltzmann equation for obtaining the flow field. Moreover, the SDM is also adopted to discretize the convection term and the high order partial derivative term of the Cahn–Hilliard equation for interface tracking. The proposed method can overcome the drawback of the standard LBM such as tie-up between the time step and the mesh spacing. Meanwhile, the present method still holds the locality of the standard LBM because each cell only needs its own information to complete the discretization. Numerical validations of the proposed method are implemented by simulating rigid-body rotation of Zalesak’s disk, layered Poiseuille flows, bubble deformation in shear flow, Rayleigh–Taylor instability, and bubble merging. More satisfactory interface shapes and flow properties can be achieved as compared with the published data in the literature. In addition, the convergence studies are also given, which prove that the current SD-PFLBM can achieve high order accuracy by increasing the order of cell local polynomials.

Phase-field lattice Boltzmann model for interface tracking of a binary fluid system based on the Allen-Cahn equation.

A lattice Boltzmann (LB) model is proposed to track the interface of binary fluid system based on the conservative-form Allen-Cahn (A-C) equation for phase field. Utilizing an equilibrium distribution function and a modified LB equation, this model is able to correctly recover the conservative A-C equation through the Chapman-Enskog analysis. A series of two-dimensional (2D) and three-dimensional (3D) phase-capturing benchmark tests have been conducted for validation, which include the diagonal translation of a circular interface, the rigid-body rotation of a Zalesak disk, and the deformation of 2D circular interface and 3D spherical interface in shear flows, all illustrating better accuracy and stability of the proposed model than the previous models tested. By coupling the incompressible hydrodynamic equation, a stationary droplet, a spinodal decomposition, and the Rayleigh-Taylor instability are simulated as well, showing the satisfying performance of the model in dealing with complex interfaces of binary fluid systems.

Probing the Dynamic Structure-Function and Structure-Free Energy Relationships of the Coronavirus Main Protease with Biodynamics Theory.

The SARS-CoV-2 main protease (Mpro) is of major interest as an antiviral drug target. Structure-based virtual screening efforts, fueled by a growing list of apo and inhibitor-bound SARS-CoV/CoV-2 Mpro crystal structures, are underway in many laboratories. However, little is known about the dynamic enzyme mechanism, which is needed to inform both assay development and structure-based inhibitor design. Here, we apply biodynamics theory to characterize the structural dynamics of substrate-induced Mpro activation under nonequilibrium conditions. The catalytic cycle is governed by concerted dynamic structural rearrangements of domain 3 and the m-shaped loop (residues 132–147) on which Cys145 (comprising the thiolate nucleophile and half of the oxyanion hole) and Gly143 (comprising the second half of the oxyanion hole) reside. In particular, we observed the following: (1) Domain 3 undergoes dynamic rigid-body rotation about the domain 2–3 linker, alternately visiting two primary conformational states (denoted as M1pro ↔ M2pro); (2) The Gly143-containing crest of the m-shaped loop undergoes up and down translations caused by conformational changes within the rising stem of the loop (Lys137–Asn142) in response to domain 3 rotation and dimerization (denoted as M1/downpro ↔ 2·M2/uppro) (noting that the Cys145-containing crest is fixed in the up position). We propose that substrates associate to the M1/downpro state, which promotes the M2/downpro state, dimerization (denoted as 2·M2/uppro–substrate), and catalysis. Here, we explore the state transitions of Mpro under nonequilibrium conditions, the mechanisms by which they are powered, and the implications thereof for efficacious inhibition under in vivo conditions.

A variational flexible multibody formulation for partitioned fluid–structure interaction: Application to bat-inspired drones and unmanned air-vehicles

We present a three-dimensional (3D) partitioned aeroelastic formulation for a flexible multibody system interacting with incompressible turbulent fluid flow. While the incompressible Navier–Stokes system is discretized using a stabilized Petrov–Galerkin procedure, the multibody structural system consists of a generic interaction of multiple components such as rigid body, beams and flexible thin shells along with various types of joints and connections among them. A co-rotational framework is utilized for the category of small strain problems where the displacement of the body is decomposed into a rigid body rotation and a small strain component. This assumption simplifies the structural equations and allows for the incorporation of multiple bodies (rigid as well as flexible) in the system. The displacement and rotation constraints at the joints are imposed by a Lagrange multiplier method. The equilibrium conditions at the fluid–structure interface are satisfied by the transfer of tractions and structural displacements via the radial basis function approach, a scattered data interpolation technique, which is globally conservative. For the coupled stability in low structure-to-fluid mass ratio regimes, a nonlinear iterative force correction scheme is employed in the partitioned staggered predictor–corrector scheme. The convergence and generality of the radial basis function mapping are analyzed by carrying out systematic error analysis of the transfer of fluid traction across the non-matching fluid–structure interface where a third-order of convergence is observed. The proposed aeroelastic framework is then validated by considering a flow across a flexible pitching plate configuration with serration at the trailing edge. Finally, we demonstrate the flow across a flexible flapping wing of a bat modeling the bone fingers as beams and the flexible membrane as thin shells in the multibody system along with the joints.

The Falling Rod Race

So many fundamental physics problems involve rigid body rotation that mastery of the subject is essential to many science and engineering undergraduate degrees. Rigid body rotation is typically taught in introductory mechanics courses and while students are generally comfortable with the corresponding kinematic equations, torques and moments of inertia are more difficult to conceptualize. This paper discusses a teaching approach we have developed that exploits the Falling Rod Race, in which the angular acceleration of rods with different weights attached are compared. We present the underlying theory for two different classes of weighted rods using torque, describe an adaptable classroom demonstration that highlights the essential physics, and produce a plug-and-play numerical code for instructor and student use.

Left ventricular rotational abnormalities in adult patients with corrected tetralogy of Fallot following different surgical procedures – a three-dimensional speckle-tracking echocardiographic study

Abstract Introduction Tetralogy of Fallot (TOF) is the most common cyanotic congenital heart disease. Abnormal aortic dimensions and elasticity parameters have been long described for corrected TOF (cTOF) together with left ventricular (LV) rotational abnormalities. The present study focuses on investigating LV rotational mechanics in cTOF, and possible correlation of these parameters with aortic elastic properties. It was also aimed to be examined whether different surgical strategies has any effect on the results. Methods The study involved 26 adult cTOF patients, from which 14 had palliative surgery first [Blaloc-Taussig (n=10), Waterstone-Cooley (n=2) shunts, or Brock procedure (n=2)] (mean age at the repair: 7.3±10.2 years) and a late total correction (mean age at the repair: 10.0±13.3 years) (pcTOF), while the early total correction was the treatment of choice in 12 patients (mean age at the repair: 4.2±3.2 years) (etrTOF). Their results were compared to that of 37 age- and gender-matched healthy adults. Routine transthoracic two-dimensional Doppler echocardiography extended with assessment of aortic elastic properties and three-dimensional speckle-tracking echocardiography (3DSTE) was performed in all cTOF patients and controls. Results Sixteen out of 26 cTOF patients showed normally directed LV rotational mechanics, while apical and basal LV rotations were in the same clockwise and counterclockwise directions in 7 and 3 cTOF cases, respectively (38%). This sort of LV movement is called as LV rigid body rotation (RBR). The ratio of LV-RBR between etrTOF and pcTOF patients did not differ significantly (33% vs. 43%, p=0.70). Significantly reduced LV apical rotation (5.2±3.7 degree vs. 10.2±4.5 degree, p<0.05) and twist (9.0±3.3 degree vs. 14.6±4.9 degree, p<0.05) could be demonstrated in cTOF patients with normally directed LV rotational mechanics with preserved LV basal rotation regardless of previous procedure. pcTOF patients showed significantly reduced LV apical rotation as compared to that of etrTOF cases (3.2±3.7 degree vs. 7.1±2.5 degree, p<0.05). From the 7 cTOF patients with clockwise LV-RBR, apical and basal LV rotation proved to be −6.8±5.4 degree and −4.9±2.4 degree, respectively with LV apico-basal gradient of 4.3±3.6 degree. The mean LV apical and basal LV rotation of 3 cTOF patients with counterclockwise LV-RBR prove to be −2.1±3.4 degree and 0.2±0.9 degree, respectively with LV apico-basal gradient of 2.5±2.4 degree. Significant correlations could be demonstrated between LV apical rotation and aortic stiffness index (r=−0.55, p=0.03) and aortic distensibility (r=0.52, p=0.04). Conclusions Significant LV rotational abnormalities could be demonstrated in cTOF with the high prevalence of LV-RBR. cTOF patients with early total reconstruction proved to have beneficial results. Abnormal physiologic response of LV rotational mechanics to increased aortic stiffness can be detected in cTOF patients without LV-RBR. Funding Acknowledgement Type of funding source: None

Differential rotation in cholesteric pillars under a temperature gradient

Steady rotation is induced in cholesteric droplets dispersed in a specific liquid solvent under a temperature gradient. In this phenomenon, two rotational modes have been considered: (1) collective rotation of the local director field and (2) rigid-body rotation of the whole droplet structure. However, here we present another rotational mode induced in a pillar-shaped cholesteric droplet confined between substrates under a temperature gradient, that is, a differential rotation where the angular velocity varies as a function of the radial coordinate in the pillar. A detailed flow field analysis revealed that every pillar under a temperature gradient involves a double convection roll. These results suggested that the differential rotation in the cholesteric pillars was driven by the inhomogeneous material flow induced by a temperature gradient. The present experimental study indicates that the coupling between the flow and the director motion plays a key role in the rotation of the cholesteric droplets under the temperature gradient.

Supersonic Aeroelasticity and Dynamic Instability of Functionally Graded Porous Cylindrical Shells Using a Unified Solution Formulation

This study provides an overview on the effect of porosity on free vibrations and more importantly aeroelastic stability margins of cylindrical shells. A general formulation for cylindrical shells is first developed including the effects of shear deformation and rotary inertia along with Sander’s rigid body rotation modification. Two porosity distributions of even and uneven are considered for functionally graded shells. The most general form of power-law model which is known as four-parameter power-law is utilized to provide a clear understanding for the qualification of functionally graded material. A Ritz-based solution algorithm being capable of representing all combinations of symmetric and asymmetric boundary conditions by a penalty method is also introduced. In addition to the capability of satisfying all boundary conditions, the presented solution method is very fast in terms of convergence and computational effort. Various parametric studies are provided and practical results are reported.

Large rigid-body displacement parameters extraction of segmented mirror in pose co-phasing adjustment simulation analysis using constrained optimization method

Large rigid-body displacement parameters within finite element analysis results are hard to be extracted. We propose an algorithm to solve this problem. Firstly, the constraint equations are established. The linear coordinate equations and objective function are then constructed. By using Lagrange multiplier method and Taylor series expansion, the solution algorithm is derived. Numerical simulation results reveal that the algorithm can separate ultra-large rigid-body rotation within the range of ±180° with the accuracy of less than 1‰ and the solving efficiency is more than twice that of the trigonometric function method. The application experiments show that the algorithm can meet the actual engineering requirements.

Crack tip asymptotic fields in anisotropic planes: Importance of higher order terms

This paper introduces the series expansion of the crack tip asymptotic fields in an anisotropic plane. Using stress-based definitions of the fracture loading modes, we present the series solutions of stresses, strains and displacements associated with the modes I and II in a cracked anisotropic plane. Special care is given to the first non-singular terms of the stress field, deriving expressions of the T-stress and the crack rigid body rotation. We then present the elasticity solution of an infinite anisotropic plane containing an inclined central crack subjected to uniaxial or biaxial loading. Under such conditions, exact analytical solutions are obtained for all coefficients of the crack tip series expansion. Our results show that the T-term is the only stress parameter that depends on the elastic constants of the anisotropic material. Finally, we evaluate the dependency of the T-stress on the material properties, and show that how significantly the higher order terms, particularly the T-stress, can contribute to the stresses near the crack tip.

Rolling of non-wetting droplets down a gently inclined plane

Abstract

Formation and stability of conformal spirals in confined 2D crystals

We investigate the ground-state and dynamical properties of nonuniform two-dimensional (2D) clusters of long-range interacting particles. We demonstrate that, when the confining external potential is designed to produce an approximate 1/r 2 density profile, the particles crystallize into highly ordered structures featuring spiral crystalline lines. Despite the strong inhomogeneity of the observed configurations, most of them are characterized by small density of topological defects, typical of conformal crystals, and the net topological charge induced by the simply-connected geometry of the system is concentrated near the cluster center. These crystals are shown to be robust with respect to thermal fluctuations up to a certain threshold temperature, above which the net charge is progressively redistributed from the center to the rest of the system and the topological order is lost. The crystals are also resilient to the shear stress produced by a small nonuniform azimuthal force field, rotating as a rigid body (RB). For larger forces, topological defects proliferate and the RB rotation gives place to plastic flow.

Speckle tracking echocardiography and left ventricular twist mechanics: predictive capabilities for noncompaction cardiomyopathy in the first degree relatives.

In non-compaction cardiomyopathy (NCCM), there are several echocardiographic and cardiac magnetic resonance (CMR)-based quantitative diagnostic indices, current criteria mainly placed on morphological features, and none of the diagnostic indices includes left ventricular (LV) function. LV function and hemodynamics could be normal in NCCM patients. Evaluation of left ventricular function at the subclinical stage, strain echocardiographic parameters could be used alternative to standard echocardiographic examinations. The aim of this study to evaluate; NCCM patients, their first-degree relatives, ventricular motion patterns, strain characteristics, and the predictive capabilities of these features for early diagnosis of cardiomyopathy. This cross-sectional, case-control study included 32 NCCM patients, 30 first-degree relatives (father, mother, siblings and children) and 31 healthy volunteers. All patients evaluated with baseline echocardiography, strain measurements, and ventricular wall motion pattern. There were no differences between the groups in terms of age, weight, and body surface area. We observed a statistically significant decrease in ejection fraction (EF), fractional shortening (FS), E/E' and global strain values in patients' relatives compared to healthy volunteers (Patients' relatives: LVEF:60.9 ± 7.2%, FS:0.34 ± 0.07, E/E':7.51 ± 1.83, GLS: - 18.6 ± 3.6, GLSr: - 1.1 ± 0.1, GCS: - 17.1 ± 3.1, GCSr: - 1.2 ± 0.1, GRS:37.1 ± 6.2, GRSr:1.7 ± 0.1; all p values< 0.05). 'Rigid Body Rotation (RBR)' movement pattern was also observed in some of the patient's relative's like in the patients. RBR movement pattern determined patients; EF, longitudinal strain-strain rate, and basal layer rotation values were significantly lower, but radial strain values were higher with the RBR movement pattern (for all values p < 0.05). RBR movement pattern, deterioration of strain parameters, and accompanying echocardiographic features like LVEF, fractional shortening (FS), E/E' in patients' relative groups may contribute to reveal the subclinical status of disease and could be predictive for early diagnosis of cardiomyopathy.

Pyruvate kinase from Plasmodium falciparum: Structural and kinetic insights into the allosteric mechanism

During its intra-erythrocytic growth phase, the malaria parasite Plasmodium falciparum relies heavily on glycolysis for its energy requirements. Pyruvate kinase (PYK) is essential for regulating glycolytic flux and for ATP production, yet the allosteric mechanism of P. falciparum PYK (PfPYK) remains poorly understood. Here we report the first crystal structure of PfPYK in complex with substrate analogues oxalate and the ATP product. Comparisons of PfPYK structures in the active R-state and inactive T-state reveal a ‘rock-and-lock’ allosteric mechanism regulated by rigid-body rotations of each subunit in the tetramer. Kinetic data and structural analysis indicate glucose 6-phosphate is an activator by increasing the apparent maximal velocity of the enzyme. Intriguingly, the trypanosome drug suramin inhibits PfPYK, which points to glycolysis as a set of potential therapeutic targets against malaria.

Full-Field Measurement of Residual Stresses in Composite Materials Using the Incremental Slitting and Digital Image Correlation Techniques

The slitting method is a widely used destructive technique for the determination of residual stresses. Because of the rich data content of the full-field methods, optical techniques such as digital image correlation (DIC) are replacing strain gages for surface measurements. The objective of the current paper is to overcome the difficulties that arise in using the DIC technique combined with the slitting method. The present noise, low signal-to-noise ratio, and systematic errors are the main impediments to the use of DIC in the slitting method. An approach based on the eigenstrain concept was exploited to ascertain the optimum region of interest (ROI) for the analysis. After that, a robust procedure was implemented to utilize the DIC method while excluding the rigid body motion and rotation artifacts from the obtained displacements. Different slitting steps may cause dissimilar rigid body motions and rotations of the specimen. The proposed method was able to eliminate all of these different shears and stretches in the images simultaneously. The slitting experiment was conducted on a symmetric cross-ply composite specimen, and the slit progressed down to half the thickness. Although some rigid body motions were large, the method managed to exclude all of them for eight slitting steps. A comparison made between the results of the current method and those of the strain gage technique shows that they are in acceptable agreement with each other, and this full-field method can be extended to smaller scales or other destructive techniques.

Rotational properties of annulus dusty plasma in a strong magnetic field

AbstractThe collective dynamics of an annulus dusty plasma formed between a co‐centric conducting (non‐conducting) disk and ring configuration is studied in a strongly magnetized radiofrequency (rf) discharge. A superconducting electromagnet is used to introduce a homogeneous magnetic field to the dusty plasma medium. In the absence of the magnetic field, the dust grains exhibit thermal motion around their equilibrium position. The dust grains start to rotate in the anticlockwise direction with increasing magnetic field (B &gt; 0.02 T), and the constant value of the angular frequency at various strengths of the magnetic field confirms the rigid body rotation. The angular frequency of dust grains linearly increases up to a threshold magnetic field (B &gt; 0.6 T) and after that its value remains nearly constant in a certain range of magnetic field. Further increase in magnetic field (B &gt; 1 T) lowers the angular frequency. Low value of the angular frequency is expected by reducing the width of the annulus dusty plasma or the input rf power. The azimuthal ion drag force due to the magnetic field is assumed to be the energy source which drives the rotational motion. The resultant radial electric field in the presence of a magnetic field determines the direction of rotation. The variation of floating (plasma) potential across the annular region at given magnetic field explains the rotational properties of the annulus dusty plasma in the presence of a magnetic field.

Geometric Origin of the Tennis Racket Effect.

The tennis racket effect is a geometric phenomenon which occurs in a free rotation of a three-dimensional rigid body. In a complex phase space, we show that this effect originates from a pole of a Riemann surface and can be viewed as a result of the Picard-Lefschetz formula. We prove that a perfect twist of the racket is achieved in the limit of an ideal asymmetric object. We give upper and lower bounds to the twist defect for any rigid body, which reveals the robustness of the effect. A similar approach describes the Dzhanibekov effect in which a wing nut, spinning around its central axis, suddenly makes a half-turn flip around a perpendicular axis and the monster flip, an almost impossible skateboard trick.