Twist Moment Research Articles

On the periods of twisted moments of the Kloosterman connection

AbstractThis paper aims to study the Betti homology and de Rham cohomology of twisted symmetric powers of the Kloosterman connection of rank two on the torus. We compute the period pairing and, with respect to certain bases, interpret these associated period numbers in terms of the Bessel moments. Via the rational structures on Betti homology and de Rham cohomology, we prove the $$\mathbb {Q}$$ Q -linear and quadratic relations among these Bessel moments.

Experimental evaluation of the use of cruciform specimens for biaxial stability analysis

Novel research is proposed about the suitability of cruciform specimens for estimating the stress-strain response and buckling modes of flat laminates under equibiaxial compression. The experimental challenge lies in determining whether the specimen design and test procedure can be adequate to observe geometric instability at the coupon scale with small dimensions of the tested region. Although the literature on composite buckling is extensive, the number of studies that include experimental biaxial testing of flat laminates is limited, particularly when considering strong flexural-torsional coupling. In this work the region of interest of the cruciform specimen consists of a carbon-fibre reinforced [∓45]S laminate with shape and boundary conditions close to a clamped square plate. For the first time, the buckling mode of an anisotropic laminate is observed in the central region of a cross-shaped specimen using 3D deflection surface data recorded by Digital Image Correlation. The effect of flexural-torsional coupling at the bifurcation onset is experimentally corroborated through the orientation of the buckling mode, which is analytically utilized to quantify the proportion between bending and twist moments. Non-linearities exhibited in the stress-strain evolution of the biaxially loaded region are verified to be independent of the response of the sample's arms. Furthermore, no previous experimental investigation has shown the differences in local strain gauge measurements induced by the stress state at the ply level. Additionally, this work adapts the method for strength reduction to estimate the real critical stress of a bi-compressed laminate.

Assessment of structural mechanical effects related to torsional deformations of propellers

Lifting propellers are of increasing interest for Advanced Air Mobility. All propellers and rotors are initially twisted beams, showing significant extension–twist coupling and centrifugal twisting. Torsional deformations severely impact aerodynamic performance. This paper presents a novel approach to assess different reasons for torsional deformations. A reduced-order model runs large parameter sweeps with algebraic formulations and numerical solution procedures. Generic beams represent three different propeller types for General Aviation, Commercial Aviation, and Advanced Air Mobility. Simulations include solid and hollow cross-sections made of aluminum, steel, and carbon fiber-reinforced polymer. The investigation shows that centrifugal twisting moments depend on both the elastic and initial twist. The determination of the centrifugal twisting moment solely based on the initial twist suffers from errors exceeding 5% in some cases. The nonlinear parts of the torsional rigidity do not significantly impact the overall torsional rigidity for the investigated propeller types. The extension–twist coupling related to the initial and elastic twist in combination with tension forces significantly impacts the net cross-sectional torsional loads. While the increase in torsional stiffness due to initial twist contributes to the overall stiffness for General and Commercial Aviation propellers, its contribution to the lift propeller’s stiffness is limited. The paper closes with the presentation of approximations for each effect identified as significant. Numerical evaluations are necessary to determine each effect for inhomogeneous cross-sections made of anisotropic material.

Twisted first moment of quadratic and quadratic twist $L$-functions

Twisted first moment of quadratic and quadratic twist $L$-functions

Reliability Analysis of the Shaft Subjected to Twisting Moment and Bending Moment for The Exponential and Weibull Distributed Strength and Stress

Objectives: The purpose of the present work is to design a shaft subjected to twisting moment, bending moment and combined twisting and bending moment by determine the reliability of the shaft. Methods: Probabilistic approach is considered to find the lifetime of shaft by taking stress as random variable. Exponential and Weibull distributions are used to find lifetime of the equipment stress is considered as exponential and Weibull random variable. When the shaft is subjected to combined twisting and bending moment, the stress is found by using the two theories: (i) The maximum shear stress theory is used for ductile materials such as mild steel. (ii) The maximum normal stress theory is used for brittle materials such as cast iron. Findings: Reliability of the shaft is derived subjected to twisting and bending moments. The reliability is computed and compared for changing of the twisting moment, bending moment and diameter of the shaft. Novelty: To design a shaft by using reliability theory and to find reliability of the shaft by using the exponential and Weibull distribution is the novel idea. Keywords: Reliability, Weibull distribution, Shaft, Twisting moment, Bending moment, Combined twisting and bending moment, Exponential distribution, Maximum normal stress theory, Maximum shear stress theory

Averages of long Dirichlet polynomials with modular coefficients

AbstractWe study the moments ofL‐functions associated with primitive cusp forms, in the weight aspect. In particular, we obtain an asymptotic formula for the twisted moments of alongDirichlet polynomial with modular coefficients. This result, which is conditional on the Generalized Lindelöf Hypothesis, agrees with the prediction of the recipe by Conrey, Farmer, Keating, Rubinstein and Snaith.

Design and Development of Power Transmission System for Tractor Operated Hybrid Bio-Composite Mulch Sheet Laying Machine

Tractor 3 point hitch drawn hybrid bio-composite bio degradable mulch laying machine was designed and developed based on the formulation of the hybrid bio-composite mulch sheets with a intension of the integrate the field operations at easy pace and conserve the time and labour. The prototype was fabricated and tested in the fields in order to perform the operations such as hybrid bio-composite mulch sheet laying, Mulch sheet pressing and guiding and soil covering on the edges of the mulch sheets in one forward movement of the machine. The machine was fabricated with design of many components but the power transmission system was plays a major role in this machine as the entire forward movement of machine and performance of the mulch sheet laying unit was depends on the power transmission system only. Various components of power transmission system was designed such as shafts, chain, bearings and sprockets etc. The shaft design was done considering the two conditions of fields while in operation like considering twisting and bending moments of the shaft as well as sudden applied shocks and fluctuated loads. Considering the two conditions, the main shaft, counter shaft and rear wheel shafts diameters were designed based on this two conditions and obtained results were 30 mm, 40 mm and 25 mm respectively The chain and sprocket will be used for the transmitting the power from one shaft to other one. The length of the chain was calculated 162.56 cm and the HP transmitted by the selected chain and HP of chain drive system were calculated as 2.05 hp and 0.339 hp respectively. Based on the results, the calculated horse power was less than the horse power of selected chain that means required horse power was 0.339 hp but we have got 2.05 hp, hence the design was safe and machine will be operate without any hassles.

Experimental characterization of repaired cracked RC beams which strengthened with different healing methods subjected to torsion load

Crack on concrete structures and its expansion leads to the destruction of concrete elements. There are some measures that can be taken to repair the cracks and extend the life cycle of the structures. These methods are considered to prevent extensive human and financial losses. Some of them such as FRP (Fiber Reinforced Polymer) and NSM (Near Surface Mounted), are used for most concrete elements, but others, such as bacterial injections, using some special mortars, or other self-healing ways are more applicable to special buildings such as oil platforms. All sorts of loads including bending, shear, torsion, and axial force can contribute to creating cracks. This research pays particular attention to the torsional load; how it can create, and what kind of repairing material can be used. For this purpose, twenty reinforced concrete beams were constructed and the effect of methods such as FRP (Fiber Reinforced Polymer), NSM (Near Surface Mount), epoxy injection, Bactria injection, self-healing concrete by using encapsulated polyurethane (with the length of 100 and 10 cm), mineral material injection and grout injection was experimentally evaluated. The results of displacements, torsion load, torsion moment, and angle of twist proved that the use of FRP and grout had the most and the least effect on repairing. In addition, by considering criterion FRP's impact in the restoration of a cracked concrete beam under torsional load based on the ACI (318-08), some coefficients were calculated to present the contribution of each method in the healing process.

Twisted moments of GL(3) ×GL(2) L-functions

We compute an asymptotic formula for the twisted moment of [Formula: see text] [Formula: see text]-functions and their derivatives. As an application, we prove that symmetric-square lifts of [Formula: see text] Maass forms are uniquely determined by the central values of the derivatives of [Formula: see text] [Formula: see text]-functions.

Torsional behaviour of rectangular high-performance fibre-reinforced concrete beams

This study intends to compare the influence of polypropylene fibres (PPF) and steel fibres (SF) on the torsional performance of reinforced high-performance concrete (HPC) rectangular beams. Nine reinforced HPC beams were produced and tested under a torsion load. All specimens were designed to fail in torsion. In addition, SF and PPF were used at 0%, 1%, 2%, 3% and 4%, in terms of volume. One of the beams was used as a control without fibres. Thus, experimental results on the ultimate torsional moment, angle of twist, torsional stiffness, failure modes and maximum crack width of specimens were investigated. In addition, a comparison was performed between the experimental results and ACI models, and then a new model is proposed to predict the cracking and ultimate torque of HPC beams containing various fibres contents. Experiments showed that the use of PPF and SF improved both torsional moment and angle of twist while the torsional performance of HPC beams reinforced by PPF was higher than that of those reinforced by SF. Conversely, the positive influence of SF on the torsional stiffness of HPC beams was greater than that of PPF. Therefore, the use of 4% PPF and SF improved the torsional moment strength by about 122.3% and 85.2%, respectively.

Comparative biomechanics of the Pan and Macaca mandibles during mastication: finite element modelling of loading, deformation and strain regimes.

The mechanical behaviour of the mandibles of Pan and Macaca during mastication was compared using finite element modelling. Muscle forces were calculated using species-specific measures of physiological cross-sectional area and scaled using electromyographic estimates of muscle recruitment in Macaca. Loading regimes were compared using moments acting on the mandible and strain regimes were qualitatively compared using maps of principal, shear and axial strains. The enlarged and more vertically oriented temporalis and superficial masseter muscles of Pan result in larger sagittal and transverse bending moments on both working and balancing sides, and larger anteroposterior twisting moments on the working side. The mandible of Pan experiences higher principal strain magnitudes in the ramus and mandibular prominence, higher transverse shear strains in the top of the symphyseal region and working-side corpus, and a predominance of sagittal bending-related strains in the balancing-side mandible. This study lays the foundation for a broader comparative study of Hominidae mandibular mechanics in extant and fossil hominids using finite element modelling. Pan's larger and more vertical masseter and temporalis may make it a more suitable model for hominid mandibular biomechanics than Macaca.

Analytical study on torsional behavior of concrete beams strengthened with fiber reinforced polymer laminates using softened truss model

This study aimed at evaluating the torsional capacity of reinforced concrete (RC) beams externally wrapped with fiber reinforced polymer (FRP) materials. An analytical model was described and used as a new computational procedure based on the softened truss model (STM) to predict the torsional behavior of RC beams strengthened with FRP. The proposed analytical model was validated with the existing experimental data for rectangular sections strengthened with FRP materials and considering torque-twist relationship and crack pattern at failure. The confined concrete behavior, in the case of FRP wrapping, was considered in the constitutive laws of concrete in the model. Then, an efficient algorithm was developed in MATLAB environment to accomplish the analysis, solve the appropriate equations, and calculate the torsional moment and angle of twist at all points. The parametric study considered the effect of effective fiber strain to reach a better prediction for the full torsional behavior. The model was able to predict the torsional behavior of the RC beams strengthened with FRP materials before and after cracking stages with reasonable accuracy.

Explicit Expressions for Buckling Analysis of Thin-Walled Beams Under Combined Loads with Laterally-Fixed Ends and Application to Stability Analysis of Saw Blades

This paper studies the critical issue of thin-walled beams with laterally fixed ends. The method for defining the formulae of twist moment for the beams subjected to combined loads was elucidated. Based on this, the governing differential equations of the beam were developed. The procedure for determining the critical state of the beam by the energy method was presented. With this procedure, the critical state of the beam concerned under three types of loadings such as axial force [Formula: see text], bending moment [Formula: see text] and distributed load [Formula: see text] (or concentrated load [Formula: see text]) was examined deliberately. The outcomes were presented in explicit closed-form, which can be illustrated in 2D and 3D graphs. Also, the analytical solution obtained was in agreement with the numerical one obtained by the commercial software NX Nastran. Furthermore, the analytical solutions were applied straightforwardly to explore the stability and design optimization of the tooth-blade for the new frame-type saw machine under an eccentric load. The result can also be promisingly used to study problems of thin-walled beams with laterally fixed ends subjected to other types of loads.

Biomechanics of the mandible of Macaca mulatta during the power stroke of mastication: Loading, deformation, and strain regimes and the impact of food type

Mandible morphology has yet to yield definitive information on primate diet, probably because of poor understanding of mandibular loading and strain regimes, and overreliance on simple beam models of mandibular mechanics. We used a finite element model of a macaque mandible to test hypotheses about mandibular loading and strain regimes and relate variation in muscle activity during chewing on different foods to variation in strain regimes. The balancing-side corpus is loaded primarily by sagittal shear forces and sagittal bending moments. On the working side, sagittal bending moments, anteroposterior twisting moments, and lateral transverse bending moments all reach similar maxima below the bite point; sagittal shear is the dominant loading regime behind the bite point; and the corpus is twisted such that the mandibular base is inverted. In the symphyseal region, the predominant loading regimes are lateral transverse bending and negative twisting about a mediolateral axis. Compared with grape and dried fruit chewing, nut chewing is associated with larger sagittal and transverse bending moments acting on balancing- and working-side mandibles, larger sagittal shear on the working side, and larger twisting moments about vertical and transverse axes in the symphyseal region. Nut chewing is also associated with higher minimum principal strain magnitudes in the balancing-side posterior ramus; higher sagittal shear strain magnitudes in the working-side buccal alveolar process and the balancing-side oblique line, recessus mandibulae, and endocondylar ridge; and higher transverse shear strains in the symphyseal region, the balancing-side medial prominence, and the balancing-side endocondylar ridge. The largest food-related differences in maximum principal and transverse shear strain magnitudes are in the transverse tori and in the balancing-side medial prominence, extramolar sulcus, oblique line, and endocondylar ridge. Food effects on the strain regime are most salient in areas not traditionally investigated, suggesting that studies seeking dietary effects on mandible morphology might be looking in the wrong places.

Crystals of Benzamide, the First Polymorphous Molecular Compound, Are Helicoidal.

The growth of spontaneously twisted crystals is a common but poorly understood phenomenon. An analysis of the formation of twisted crystals of a metastable benzamide polymorph (form II) crystallizing from highly supersaturated aqueous and ethanol solutions is given here. Benzamide, the first polymorphic molecular crystal reported (1832), would have been the first helicoidal crystal observed had the original authors undertaken an analysis by light microscopy. Polymorphism and twisting frequently concur as they are both associated with high thermodynamic driving forces for crystallization. Optical and electron microscopies as well as electron and powder X-ray diffraction reveal a complex lamellar structure of benzamide form II needle-like crystals. The internal stress produced by the overgrowth of lamellae is shown to be able to create a twist moment that is responsible for the observed non-classical morphologies.

Crystals of Benzamide, the First Polymorphous Molecular Compound, Are Helicoidal

AbstractThe growth of spontaneously twisted crystals is a common but poorly understood phenomenon. An analysis of the formation of twisted crystals of a metastable benzamide polymorph (form II) crystallizing from highly supersaturated aqueous and ethanol solutions is given here. Benzamide, the first polymorphic molecular crystal reported (1832), would have been the first helicoidal crystal observed had the original authors undertaken an analysis by light microscopy. Polymorphism and twisting frequently concur as they are both associated with high thermodynamic driving forces for crystallization. Optical and electron microscopies as well as electron and powder X‐ray diffraction reveal a complex lamellar structure of benzamide form II needle‐like crystals. The internal stress produced by the overgrowth of lamellae is shown to be able to create a twist moment that is responsible for the observed non‐classical morphologies.

A Evaluation of the Dynamic Strength of the Shaft Line with Welded Rotors of Low Pressure Cylinders of the K-220-44-1 Turbine

To assess the danger of resonance vibrations, the calculations data of the critical rotational speeds and strength in case of a sudden short circuit in the generator of the shaft line of the upgraded K-220-44-1 turbine unit have been presented. The turbine unit comprising a high-pressure cylinder and two low-pressure cylinders has been in operation at nuclear power plants since the early 1970s. The shaft-line consists of a high-pressure all-forged rotor, two low-pressure welded rotors, an intermediate part and a generator rotor. For the rotors of the turbine unit constituting the shafting, rod models with concentrated masses and elastic-damping support were used. Recommendations on the choice of vertical compliance of supports for computational studies are given. Estimates of the critical speeds of the shafting are obtained without taking into account the lubricant layer of the support bearings. The dynamic state of the shafting is considered for two-phase and three-phase short circuits in the generator. The maximum twisting moments in the rotors' necks under the support bearings are estimated, and the safety factors for the limiting table torque in the plasticity state are determined. The calculations were performed using software packages developed in the A. Podgorny Institute of Mechanical Engineering Problems of NASU, Joint Stock Corporation "Turboatom". The calculation data show that no dangerous resonance vibrations of the shaft-line of the upgraded K-220-44-1 turbine unit are detected and the strength of the shaft-line in case of a sudden short circuit in the generator is in conformity with the requirements of regulatory and technical documents.

The effect of axial twist angle on in vitro cumulative injury load tolerance: a magnitude-weighting approach for axial twist exposures

Axial twisting exposures have been repeatedly identified as a risk factor for occupational low back pain and injury, but there is a need for an improved understanding of the role of axial twist magnitude and associated joint moment as modifiers of the cumulative load tolerance of intervertebral joints. The purpose of this study was to mathematically characterise the relationship between axial twist motion magnitudes and the cumulative load tolerance of porcine cervical functional spinal units. Twenty-four porcine functional spinal units were fixed in a mechanical testing system under compressive load (15% of compressive tolerance) and in a neutral flexion-extension posture. Specimens were axially twisted to 5, 7.5, 10, 12.5, 15 or 17.5 degrees at 1 Hz until failure or 21,600 total cycles. Cumulative applied axial twist moment was recorded, and exponential functions were fit to the twist magnitude-cumulative twist moment measures. Weighting-factor functions for cumulative axial twist moment injury risk were developed based on absolute axial twist magnitude and twist normalised to maximum range of motion. While caution should be used in extrapolating these findings to human evaluation, a developed non-linear weighting-factor model has potential for use in assessment of cumulative axial twist injury risk in occupational tasks.

Twisted quadratic moments for Dirichlet $L$-functions at $s=2$

Let c, n be given positive integers. Let q > 2 be coprime with c. Let X q be the multiplicative group of order φ(q) of the Dirichlet characters modulo q. Set M (q, c, n) := 2 φ(q) χ∈Xq χ(−1)=(−1) n χ(c)|L(n, χ)| 2. The goal of this paper is to explain how one can compute explicit formulas for M (q, c, n) for a given small integers n and c. As an example, we give explicit formulas for M (q, c, 2) for c ∈ {1, 2, 3, 4, 6} and for M (p, 5, 2) for p a prime integer. As a consequence, we show that a previously published formula for M (p, 3, 2) is false. 0 2010 Mathematics Subject Classification. Primary. 11M06.

Experiment on Torsional Behaviour of Reinforced Concrete Beams

Structural beams in construction are subjected to significant torsional moment which affects the design of structures.Eight beams were produced with two distinct grade of concrete with two ratios of longitudinal as well as transverse reinforcements.An experiment for evaluation of torsional strength of reinforced concrete beams is presented in this paper.The main objective of this study is to access the role of varying percentage of transverse and longitudinal reinforcements on torsional strength of beams.Concrete grades of M 20 and M 30 beams were cast with 0.56% and 0.85% of longitudinal reinforcement as well as 50 mm and 75 mm spacing of stirrups.The experimental results are presented.The reported results include the behavioural curves and the values of torsional moment and angle of twist for entire 8 beams