Torsional Rotation Research Articles

Exact finite beam element for open thin walled doubly symmetric members under torsional and warping moments

Starting with total potential energy variational principle, the governing equilibrium coupled equations for the torsional-warping static analysis of open thin-walled beams under various torsional and warping moments are derived. The formulation captures shear deformation effects due to warping. The exact closed form solutions for torsional rotation and warping deformation functions are then developed for the coupled system of two equations. The exact solutions are subsequently used to develop a family of shape functions which exactly satisfy the homogeneous form of the governing coupled equations. A super-convergent finite beam element is then formulated based on the exact shape functions. Key features of the beam element developed include its ability to (a) eliminate spatial discretization arising in commonly used finite elements, and (e) eliminate the need for time discretization. The results based on the present finite element solution are found to be in excellent agreement with those based on exact solution and ABAQUS finite beam element solution at a small fraction of the computational and modelling cost involved.

A 10-Week Program of Combined Hippotherapy and Scroth's Exercises Improves Balance and Postural Asymmetries in Adolescence Idiopathic Scoliosis: A Randomized Controlled Study.

Introduction: The most frequent type of spine abnormality throughout adolescence was adolescent idiopathic scoliosis (AIS). Hippotherapy improved posture, balance and gait of different musculoskeletal conditions. Therefore, this study aims to see how hippotherapy combined with Schroth exercises affected postural asymmetry and dynamic balance in AIS compared to traditional physiotherapy (Schroth exercises) alone. Materials and methods: In this randomized controlled trial, fifty-two patients with AIS (10–18 years, 37 girls and 15 boys) participated. They were arbitrarily allocated into two groups: experimental (19 female/8 male; aged 14.74 ± 1.79 years; Cobb angle 18.59 ± 2.66 degrees) and control (18 female/7 male; aged 15.04 ± 1.81 years; Cobb angle 19.32 ± 2.69 degrees) groups. Both groups received Schroth exercises for 10 weeks, three days/week. The experimental group additionally received hippotherapy training. Pre-treatment and post-treatment assessment for the scoliotic, kyphotic angle, pelvic obliquity, pelvic torsion and vertical spinal rotation and the anteroposterior, mediolateral and overall stability indices were assessed using the formetric system 4D and Biodex Balance System, respectively. Results: After intervention, both groups illustrated significant improvements in all examined variables (p < 0.05). The experimental group illustrated significant improvements in scoliotic angle, kyphotic angle, pelvic obliquity, pelvic torsion and vertical spinal rotation and the stability indices compared to the control group (p < 0.05). Conclusion: In adolescence idiopathic scoliosis, hippotherapy training combined with Schroth exercises improves posture asymmetry and balancing ability more effectively than Schroth exercises alone.

Computational analysis of shear deformation effects on open thin-walled beams

When subjected to eccentric lateral or vertical loads, Open Thin-Walled Members (OTWMs) will suffer the risk of torsional failure for their relatively low torsional rigidity. The classic torsional theory, Vlasov’s theory, was found to greatly underestimate the torsional rotation especially for OTWMs with lower span-depth ratio or lower shear modulus. Shear deformation along the middle line of cross section, which is neglected in Vlasov’s theory, was considered and quantified in this paper. Two examples (U-beams and I-beams) were taken to be calculated by the proposed method, Vlasov’s theory and finite element analysis. Results of average errors 2.90% and 1.77% guaranteed the applicability and accuracy of the proposed method. Besides, parametric analysis including different configurations, boundary conditions and span-height ratio were conducted to evaluate the effects of shear deformation on the torsional rotation of OTWMs. It was revealed that stronger boundary constraint and smaller span-depth ratio lead to greater effects of shear deformation, which cannot be neglected. The critical criteria to consider or ignore the shear effects under different boundary conditions were also defined.

Evaluation of the reliability of lower extremity alignment measurements using EOS imaging system while standing in an even weight-bearing posture

This study aimed to analyze the reproducibility and reliability of the alignment parameters measured using the EOS image system in both limbs while standing with an even weight-bearing posture. Overall, 104 lower extremities in 52 patients were analyzed retrospectively. The patients stood with an even load over both lower extremities then rotated 15° in both directions. Two EOS images were acquired and 104 pairs of lower extremities were compared according to the position of the indexed lower extremities. Then, the inter-observer reliability of the EOS system and the inter-modality reliability between EOS and computed tomography (CT) were evaluated. Femoro-tibial rotation (FTR) and tibial torsion demonstrated a significant difference between the anterior and posterior positions of the indexed lower extremity. In the inter-observer reliability analysis, all values except for FTR and tibial torsion demonstrated good or very good reliability. In the anterior position, FTR demonstrated moderate, and tibial torsion demonstrated poor reliability. In the posterior position, both FTR and tibial torsion demonstrated poor reliability. In the reliability analysis between the three-dimensional (3D) EOS model and 3D CT images, all measurements of the femur demonstrated very good reliability, but measurements of the tibia did not. For the coronal and sagittal alignment parameters measured by the EOS 3D system with rotated standing posture, except for the measurement including tibial torsion., there were no significant difference for either position of the indexed extremities with high agreement between the observers as well as with the CT 3D model.

Conversion of ortho and para nuclear spin isomers of methanol studied by internal axis method

Quantum statistics of identical nuclei in molecules gives rise to nuclear spin isomers. Except for methanol (CH3OH) that has internal rotation (i.e., torsion), all the studied molecules so far have overall rotational symmetry. Methanol does not rotate around the overall rotational symmetry axis but the methyl group axis. The identical nuclei in the methyl group produce a specific type of nuclear spin isomers of the ortho-CH3OH and para-CH3OH in methanol. Conversions between these two spin isomers have been observed in the experiment and a theory based on the rho-axis method (RAM) for partially explaining their conversions has been developed by us recently. However, besides RAM the internal axis method (IAM) is a classical method commonly used by many researchers and the coupling of the angular momenta between torsion and overall rotation in methanol can be completely separated from each other in the IAM. In this paper, as a series work we present a general theoretical model about conversion of ortho–para methanol using the IAM based on quantum relaxation theory. The expressions of the ortho–para state-mixing strengths induced by the nuclear spin–spin and nuclear spin–rotation interactions have been analytically deduced and numerically calculated. We found that the ortho–para states-mixings and ortho–para conversion can be induced by all these two intramolecular interactions whereas the nuclear spin–rotation interaction plays a major role. The conversion rate at temperature 300 K and pressure 1 Torr summed over eight ortho–para level pairs with gaps less than 2.7 GHz is calculated to be 1.4 × 10−2 s−1, which is close to the measured value of 2.1 (3) × 10−2 s−1, indicating the quantum relaxation is the leading process in the spin isomers conversions of methanol and suggesting our theory to be valid for other gaseous methanol-like molecules having torsion tunneling of symmetrical group. The most probable gateways in methanol for collision-induced population transfers are found to be levels-pairs in the ground-state A–E species of (υtJ, K, p) = (0, 24, 4, 1)−(0, 25, 2, 1) by nuclear spin–spin coupling, (0, 22, 5, p)−(0, 21, 6, −1) and (3, 34, 1, 0)−(3, 35, 0, 1) by nuclear spin–rotation coupling.

Shaking table tests of a resilient bridge system with precast reinforced concrete columns equipped with springs

AbstractThis paper presents the shake table test results of a novel system for the design of precast reinforced concrete bridges. The specimen comprises a slab and four precast columns. The connections are dry and the columns are connected to the slab by an ungrouted tendon. One of the tendon ends is anchored above the slab, in series with a stack of washer springs, while the other end is anchored at the bottom of the column. The addition of such a flexible restraining system increases the stability of the system, while keeping it relatively flexible allowing it to experience negative post‐uplift stiffness. It is a form of seismic isolation. Anchoring the tendon within the column, caps the design moment of the foundation, and reduces its size. One hundred and eighty‐one shake table tests were performed. The first 180 caused negligible damage to the specimen, mainly abrasion at the perimeter of the column top ends. Hence, the system proved resilient. The 181stexcitation caused collapse, because the tendons unexpectedly failed at a load less than 50% of their capacity (provided by the manufacturer), due to the failure of their end socket. This highlights the importance of properly designing the tendons. The tests were used to statistically validate a rigid body model. The model performed reasonably well never underestimating the median displacement response of the center of mass of the slab by more than 30%. However, the model cannot predict the torsion rotation of the slab that was observed in the tests and is due to imperfections.

Loss of left ventricular rotation is a significant determinant of functional mitral regurgitation

AimTo evaluate insufficient rotational movement of the left ventricle (LV) as a potential novel mechanism for functional regurgitation of the mitral valve (FMR). Methods and resultsWe compared reference subjects and patients with LV dysfunction (LVD, ejection fraction EF < 50%) with and without FMR (regurgitant volume RVol>10 ml). Subjects without structural mitral valve pathology undergoing cardiac MRI were evaluated. Delayed enhancement, global LV remodeling parameters, systolic twist and torsion were measured (using manual and novel automated cardiac MRI tissue-tracking). The study included 117 subjects with mean ± SD age 50.4 ± 17.8 years, of which 30.8% were female. Compared to subjects with LVD without FMR (n = 31), those with FMR (n = 37) had similar clinical characteristics, diagnoses, delayed enhancement, EF, and longitudinal strain. Subjects with FMR had significantly larger left ventricles (EDVi:136.6 ± 41.8 vs 97.5 ± 26.2 ml/m, p < 0.0001) with wider separation between papillary muscles (21.1 ± 7.6 vs 17.2 ± 5.7 mm, p = 0.023). Notably, they had lower apical (p < 0.0001) but not basal rotation and lower peak systolic twist (3.1 ± 2.4° vs 5.5 ± 2.5°, p < 0.0001) and torsion (0.56 ± 0.38°/cm vs 0.88 ± 0.52°/cm, p = 0.004). In a multivariate model for RVol including age, gender, twist, LV end-diastolic volume, sphericity index and separation between papillary muscles, only gender, volume and twist were significant. Twist was the most powerful correlate (beta −2.23, CI -3.26 to −1.23 p < 0.001). In patients with FMR, peak systolic twist negatively correlates with RVol (r = −0.73, p < 0.0001). ConclusionReduced rotational systolic LV motion is significantly and independently associated with RVol among patients with FMR, suggesting a novel pathophysiological mechanism and a potential therapeutic target.

Reversible Torsional Actuation of Hydrogel Filled Multifilament Fibre Actuator

Twisted polymer fibre actuators provide high torsional rotation from stimulated volume expansion, induced either by chemical fuelling, thermal stimulation, or electrochemical charging. One key limitation of these actuators is the irreversibility of torsional stroke that limits their feasibility when considering real-life smart applications. Moreover, scaling the torsional stroke of these actuators becomes difficult when these are integrated into practically usable systems such as smart textiles, due to the external and variable opposing torque that is applied by the adjacent non-actuating fibres. Herein, a simple composite type torsional actuator made of hydrogel coated commercial textile cotton multifilament fibre is demonstrated. This novel actuator is of high moisture responsiveness, given that hydrogels are capable of providing huge volume expansion and twisting the overall system can transform the volumetric expansion to fibre untwisting based torsional actuation. Theoretical treatment of torsional actuation is also demonstrated based on the change in torsional stiffness of dry and wet fibres as well as a few externally applied torques. The agreement between experimental measurements and theoretical estimation is found reasonable, and the investigation allows the near-appropriate estimation of torsional stroke before integrating an actuator into a smart system.

Abnormal femur rotation in patients with recurrent patellar dislocation: A study on upright standing three-dimensionally reconstructed EOS images

BackgroundThe measurements of lower extremity rotational deformities in patients with recurrent patellar dislocation (RPD) in the standing position are available with the application of the EOS imaging system. The aim of our case–control study was to identify the differences on the femur rotation between the supine and standing positions, and to investigate the differences of anatomical and functional femur rotation between RPD patients and controls. MethodsThirty-five lower extremities affected by RPD from 30 patients and 27 intact lower extremities from 27 controls with acute meniscus tear or anterior cruciate ligament injury were recruited. Anatomical femoral anteversion (AFA), functional femoral anteversion (FFA), femorotibial rotation (FTR) and distal femoral torsion (DFT) of all subjects were measured with the EOS imaging system. Computed tomography scans were carried out to analyze the AFA and FFA in the supine position in PRD patients. The differences in FFA between supine and standing position and in AFA, FTR and DFT between RPD and controls were analyzed. The predictor importance of each variable on RPD was observed after cluster analysis. ResultsThe EOS images were available in all subjects. The FFA was significantly smaller in the standing position than in the supine position (P < 0.05) in RPD patients. When comparing with the controls, RPD patients showed higher AFA, FTR and DFT (P < 0.05) but comparable FFA (P < 0.05). The cluster model prompted that FTR and DFT had higher predictor importance than AFA. ConclusionLarger AFA but comparable FFA in patients with RPD than the controls in an upright standing position suggested more internally rotated distal femur in the RPD patients. AFA may be inadequate and FFA should also be considered while planning the treatment for RPD. DFT and FTR should be taken into consideration when evaluating the abnormalities in femur rotation in RPD patients.

Evidence of C-F···H-C Attractive Interaction: Enforced Coplanarity of a Tetrafluorophenylene-Ethynylene-Linked Porphyrin Dimer.

The formation of C-F···H-C "hydrogen bonds" has been a controversial subject because, in principle, fluorine is hardly an acceptor for less acidic protons contrasting to the C-F···H-O and C-F···H-N hydrogen bonds. Nevertheless, the interaction is emerging as a powerful implement for confining the torsional rotation in the design of fully coplanar π-conjugated polymers. Heretofore, no evidence of the C-F···H-C interaction has been observed in solutions. We herein disclose comprehensive evidence that the C-F···H-C interaction produces an attractive force. A 19F-1H heteronuclear Overhauser effect experiment elucidated the close proximity of the F and H atoms in the doubly edge-facing C-F···H-C interactions of a meso-tetrafluorophenylene-ethynylene-conjugated porphyrin dimer (1). Extensive electronic and photophysical property investigations confirmed that all the aromatic units were torsionally restricted by the C-F···H-C interactions. Moreover, the enforced coplanarity invoked a markedly high π-staking propensity. Thus, we have firmly established the formation of a C-F···H-C interaction that produces a hydrogen-bond-like attractive force in solution.

Analyzing Hydration Differences in Cocrystal Polymorphs: High-Resolution X-ray Investigation of Caffeine–Glutaric Acid Cocrystals

Two polymorphic forms of caffeine (CAF)–glutaric acid (GLU) cocrystals have been studied via high-resolution X-ray crystallography and Bader’s quantum theory of atoms in molecules (QTAIM). For both the monoclinic, 1, and triclinic, 2, systems the experimental charge density distributions of the 1:1 ratio of CAF and GLU polymorphs have been determined and compared. Previous studies have determined that 1 is less stable than 2, in relative humidity (RH) testing. A topological analysis of the electron density distribution (EDD) revealed little difference between the two polymorph internal systems. The packing densities (0.76 vs 0.74) and lattice energies (−101.1 vs −107.1 kJ mol–1) of 1 and 2, respectively, are nearly equivalent, implying that the differences in hygroscopicity between the two polymorphs are not due to crystal lattice porosity or stability. A topological analysis of the number and strength of hydrogen bonds for 1 and 2 revealed nine hydrogen bonds in both polymorphs. “Classical” (O–H···X) hydrogen bonds were similarly present in both polymorphs, stabilizing the cocrystals. However, the sum of the stability produced from the “nonclassical” (C–H···X) bonds is higher in 2: −27.6 vs −38.2 kJ mol–1 for 1 and 2, respectively. One of the nine hydrogen bonds in 1 and 2 varies from the others, caused by the torsional rotation of the aliphatic carbon chain in GLU. This bond is critical for packing stabilization, creating a parallelogram-like packing arrangement in 2 in comparison to ribboning in 1. A Hirshfeld surface analysis found that the percentages of O–H···X hydrogen bonds were nearly identical in 1 and 2 (23.9% vs 22.1%); however, the H···H contacts were higher in 2 (61.4% vs 65.8% for 1 and 2, respectively), suggesting that more hydrogen-based contacts require competitive displacement by water in the hydration of 2 in comparison to 1. Additionally, a stabilizing aromatic cycle stack between CAF molecules is present in 2 due to the varied parallelogram packing arrangement, which was absent in 1; this provided ∼11.3 kJ mol–1 of stability to the system of 2. The solid-state entropies and molecular dipole moments (MDMs) of 1 and 2 supported the relative stability of the individual polymorphs, with 1 having a higher entropy and dipole moment in comparison to 2 (123.2 vs 112.8 J K–1 mol–1 and 7.45 and 4.93 D for 1 and 2, respectively), implying that it has the potential to hydrate more rapidly. These findings are in good agreement with previous experimental RH stability studies, giving further insight into the information gained from thermally averaged ground-state crystal electron density data.

Analytical and meshless numerical approaches to unified gradient elasticity theory

The unified gradient elasticity theory with applications to nano-mechanics of torsion is examined. The Reissner stationary variational principle is invoked to detect the differential and boundary conditions of equilibrium along with the consistent form of the constitutive laws. An efficient meshless numerical approach is established by making recourse to the Reissner variational functional wherein independent series solution of the kinematic and kinetic field variables are proposed. Suitable forms of the coordinate functions, in terms of the Chebyshev polynomials, are introduced to fulfill a set of kinematic and higher-order boundary conditions in the elastic torsion of nano-bars with practical kinematic constraints. Torsional behavior of the unified gradient elastic bar is studied for structural schemes of applicative interest. An excellent agreement between the torsional responses of the nano-bar detected based on the established meshless method and obtained exact analytical solution is realized. The proposed meshless numerical approach is confirmed to have a fast convergence rate and an admissible convergence region in determination of the torsional rotation field with high accuracy. The introduced meshless method is demonstrated to be highly efficacious in characterizing both the softening and stiffening structural behaviors at nano-scale. The presented numerical approach therefore paves the way ahead in mechanics of nano-structures.

A Review on Seismic Performance of L-Shaped Building Through Plan Irregularities

The patterns of sporadic structure development have quickly expanded because of tasteful and restricted accessibility of land. Past examinations have indicated that the structures with design abnormality are harmed under solid ground movement. Auxiliary inconsistencies are significant elements which decline the seismic exhibition of the structures. Structures having basic anomalies bring about the lopsided circulation of the story float, exorbitant twist, etc. The irregularity discussed here are about plan irregularity which is available in re-participant corners and torsional anomaly which is caused by abrupt changes in firmness and twist enhancement factor in building. This study is to propose a feasible solution to build this kind of structure in seismically active areas using analytical methods with the assistance of ETABS software. The analysis shall be done through a comparable static horizontal power technique and reaction range examination (dynamic investigation). The basic reactions will estimated regarding story displacement, inter-story drift ratio, torsional irregularity ratio, torsional diaphragm rotation, normalized base shear force, and overturning moment, which are also called seismic response demands. The structure will be analyzed and compare with different types of other shape plan.

Mechanistic insight into the fluorescence activity of forensic fingerprinting reagents

Fingerprint detection is still the primary investigative technique for deciphering criminal inquiries and identifying individuals. The main forensic fingerprinting reagents (FFRs) currently in use can require multiple treatment steps to produce fingerprints of sufficient quality. Therefore, the development of new, more effective FFRs that require minimal chemical treatment is of great interest in forensic chemistry. In this work, prudently crafted density functional theory and time-dependent density functional theory calculations are utilized to derive mechanistic insight into the optical activity of the non-fluorescent product of ninhydrin, diketohydrindylidenediketohydrindamine (DYDA), and fluorescent product of DFO (1,8-diazafluoren-9-one). We investigate various protonation sites to gain an understanding of isomeric preference in the solid-state material. A relaxed scan of a single torsion angle rotation in the S1 minimized geometry of the O-protonated DYDA isomer suggests a conical intersection upon ∼10° rotation. We show that the absence of a rigid hydrogen-bonded network in the crystal structure of DYDA supports the hypothesis of torsion rotation, which leads de-excitation to occur readily. Conversely, for the fluorescent DFO product, our calculations support an avoided crossing suggestive of a non-radiative mechanism when the torsion angle is rotated by about ∼100°. This mechanistic insight concurs with experimental observations of fluorescence activity in DFO and may aid the photophysical understanding of poorly visualized fingerprints due to weak fluorescence. We show that identifying suggestive avoided crossings via the method described here can be used to initialize thoughts toward the computational design of FFRs.

Free vibration analysis of rotating composite Timoshenko beams with bending-torsion couplings

The free vibration of rotating bending-torsional composite Timoshenko beams (CTBs) with arbitrary boundary conditions is analyzed. The composite material coupled rigidity, Coriolis effects and the separation of the cross-section’s mass and shear centers are considered and they will cause the bending-torsion coupled vibration of the beam. Based on the Hamilton’s principle, the governing partial differential matrix equation of motion of the beam are formulated with variable coefficients. Those equations containing variable coefficients are expressed in a special matrix form in terms of the flexural translation, rotation of cross section and torsional rotation of the beam. The differential transform matrix method (DTMM), which is an improved approach from the traditional differential transform method (DTM), is proposed to deal with the governing matrix equation with corresponding boundary conditions. The mode shapes and natural frequencies of the beam are obtained. Cantilevers are calculated as examples to verify the present theory and investigate the dynamic characteristics of the rotating CTB. The present results are consistent with those reported in the literature and those calculated from COMSOL. The influence of the composite material rigidity, rotation speed, hub radius and axial load on the natural frequencies and mode shapes of the beam are studied, while the frequency veering and mode shift phenomena are observed. Furthermore, the beam’s critical buckling loads corresponding to the axial load are found.

Porphyrin dimer as efficient optical thermometer: Experimental and computational evaluation of the barrier to torsional rotation

The photophysics of conjugated metal-linked oligomers of porphyrins has been investigated spectroscopically and by quantum chemical calculations. The influence of the conformation on the ground and first singlet excited states has been studied. The absorption spectra and quantum chemical calculations have revealed two different dimer conformations. The UV–vis spectra calculated by the TD-DFT method are quite comparable with the experimental spectra of the two species. The calculated value of the torsional energy barrier is ΔЕ = 3.4 kJ‧mol−1. Studies of the temperature dependence of the dimer fluorescence spectrum have shown the fundamental possibility of using it as a contactless luminescent temperature sensor. Information about the local temperature can be obtained from the calculated temperature dependence of FIR, which represents a monotonic pseudo-linear trend.

Impact of pulmonary valve replacement on left ventricular rotational mechanics in repaired tetralogy of Fallot

BackgroundIn repaired tetralogy of Fallot (rTOF), abnormal left ventricular (LV) rotational mechanics are associated with adverse clinical outcomes. We performed a comprehensive analysis of LV rotational mechanics in rTOF patients using cardiac magnetic resonance (CMR) prior to and following surgical pulmonary valve replacement (PVR).MethodsIn this single center retrospective study, we identified rTOF patients who (1) had both a CMR ≤ 1 year before PVR and ≤ 5 years after PVR, (2) had no other intervening procedure between CMRs, (3) had a body surface area > 1.0 m2 at CMR, and (4) had images suitable for feature tracking analysis. These subjects were matched to healthy age- and sex-matched control subjects. CMR feature tracking analysis was performed on a ventricular short-axis stack of balanced steady-state free precession images. Measurements included LV basal and apical rotation, twist, torsion, peak systolic rates of rotation and torsion, and timing of events. Associations with LV torsion were assessed.ResultsA total of 60 rTOF patients (23.6 ± 7.9 years, 52% male) and 30 healthy control subjects (20.8 ± 3.1 years, 50% male) were included. Compared with healthy controls, rTOF patients had lower apical and basal rotation, twist, torsion, and systolic rotation rates, and these parameters peaked earlier in systole. The only parameters that were correlated with LV torsion were right ventricular (RV) end-systolic volume (r = − 0.28, p = 0.029) and RV ejection fraction (r = 0.26, p = 0.044). At a median of 1.0 year (IQR 0.5–1.7) following PVR, there was no significant change in LV rotational parameters versus pre-PVR despite reductions in RV volumes, RV mass, pulmonary regurgitation, and RV outflow tract obstruction.ConclusionIn this comprehensive study of CMR-derived LV rotational mechanics in rTOF patients, rotation, twist, and torsion were diminished compared to controls and did not improve at a median of 1 year after PVR despite favorable RV remodeling.

The Effect of a Course of Up-cholugi and Yup-chagi Exercises on the Kinematic Indices of the Knee and the Incidence of Bow-leggedness (Genu Varum) in Professional Taekwondo Practitioners

Objective: Knee brace is one of the lower limb abnormalities. This study aimed to investigate the effect of knee kinematical parameters on the development of knee Genu Varum. Methods: This study’s statistical sample was 32 taekwondo practitioners with red and black belts of sports clubs in the northeast of Tehran, determined using G-Power software and in two groups of 16 people in terms of gender, age, and membership in the field. The 8-week training intervention, which included 3session of 1-hour training sessions emphasizing performing the techniques of up-chulogi and yup-chaggy, was performed for the experimental group. The control group did not have any specific activity during this period. Knee kinematic indices include naval drop size tests, tibial torsion, Q angle, androgen enterogen, internal and external hip rotation, and knee hyperextension in the two groups of healthy and injured in pre and posttest was evaluated. The data were statistically analyzed using descriptive analysis using t-test and SPSS V. 23 software. Results: According to the study results, a significant positive relationship was observed between the variables of the selected technique of up-chology and the technique of up-chugi on the incidence of knee Genu Varum. Also, there was a significant difference between the indices of naval drop (P=0.003), torsion (P=0.006), Q angle (P=0.005) and knee hyperextension (P=0.001) in pre-test to post-test results. Conclusion: The selected exercises have increased the distance between the knees and functional disorders. Because the braced knee may play a role in influencing athletes’ negative performance and injury in training and competition, it is necessary to consider it in studies related to the prevention of potential injuries.

Torsional static and vibration analysis of functionally graded nanotube with bi-Helmholtz kernel based stress-driven nonlocal integral model

A torsional static and free vibration analysis of the functionally graded nanotube (FGNT) composed of two materials varying continuously according to the power-law along the radial direction is performed using the bi-Helmholtz kernel based stress-driven nonlocal integral model. The differential governing equation and boundary conditions are deduced on the basis of Hamilton’s principle, and the constitutive relationship is expressed as an integral equation with the bi-Helmholtz kernel. Several nominal variables are introduced to simplify the differential governing equation, integral constitutive equation, and boundary conditions. Rather than transforming the constitutive equation from integral to differential forms, the Laplace transformation is used directly to solve the integro-differential equations. The explicit expression for nominal torsional rotation and torque contains four unknown constants, which can be determined with the help of two boundary conditions and two extra constraints from the integral constitutive relation. A few benchmarked examples are solved to illustrate the nonlocal influence on the static torsion of a clamped-clamped (CC) FGNT under torsional constraints and a clamped-free (CF) FGNT under concentrated and uniformly distributed torques as well as the torsional free vibration of an FGNT under different boundary conditions.

Large amplitude inversion tunneling motion in ammonia, methylamine, hydrazine, and secondary amines: From structure determination to coordination chemistry

• Molecular structures of ammonia derivatives captured by spectroscopy. • Tunneling motion as essential information to understand coordination complexes. • Structures and internal dynamics from experimental and theoretical points of view. • Using the structures of isolated ligand to determine the structure of complexes. Inversion tunneling in a symmetric double minimum potential is a challenging large amplitude motion problem which causes all rotational energy levels to split into a symmetric and an antisymmetric level. Not like other types of large amplitude motion such as internal rotation, inversion tunneling appears much rarer, but the fundamental knowledge gained from this motion is essential to understand the complex structures in coordination chemistry. A double minimum potential needed for inversion tunneling requires the symmetry of the frame to which the inversion object is attached to be C s or higher, while there is no restriction on the symmetry of the frame for internal rotation. This review summarizes four most classic examples of molecules featuring inversion tunneling motion and their coordination complexes. The textbook example, ammonia, with its umbrella motion during which the nitrogen atom passes from one side of the plane formed by the three hydrogens to the other, will be presented with information on its group theoretical considerations, theoretical studies, electronic ground state spectra in the infrared range, and its coordination complexes, especially those formed with calcium and copper. In the second classic example, methylamine, CH 3 NH 2 , the inversion motion of the amino group –NH 2 is coupled with a methyl internal rotation –CH 3 . The spectrum of methylamine can be treated using a tunneling formalism applying the G 12 permutation-inversion symmetry group. Extensive studies on the ground state, the first and second excited torsional states ν 15 , the inversion wagging state ν 9 , and the C-N stretching band ν 8 exist along with their combinations. Pertubations and blends have made the analysis of methylamine very challenging. The third subject is on hydrazine with complex internal dynamics governed by three large amplitude motions: two –NH 2 tunneling motions and an internal rotation (torsion) of the two amino groups around the N-N bond. Regarding the spectrum of hydrazine, the vibrational ground state lies in the microwave region. The first, second, and third excited torsional band ν 7 , symmetric wagging ν 6 , and asymmetric wagging ν 12 are found in the infrared range. Group theoretical treatment and tunneling formalism can only be used to fit sub-bands individually, while global fits still remain a difficult task. Metal complexes with hydrazine and methylamine are introduced, proving the importance of spectroscopic understanding of molecular structures for the knowledge of coordination chemistry. Finally, secondary amines feature inversion tunneling of the hydrogen atom attached to the nitrogen, which is accompanied by two methyl internal rotations but not coupled with them so that they can be treated separately. For this class of molecules, only spectra of the vibrational ground state in the microwave domain will be considered.