Torsional Coupling Research Articles

Response Sensitivity and the Assessment of Nonlinear Vibration Using a Nonlinear Lateral–Torsional Coupling Model of Vehicle Transmission System

The eigensensitivity analysis does not meet the increasing industrial requirements of the dynamic performance of a vehicle transmission system. To reduce vibration, it is necessary to include response sensitivity in the guideline in the design stage. In this study, we developed a nonlinear lateral–torsional coupling spur gear system model considering the effect of time-varying mesh stiffness, clearance, mass eccentricity, and transmission error. Then the dynamic response sensitivity to system parameters was systematically analyzed by taking the shaft torsional stiffness, for example. The equation of response sensitivity was deduced by a direct method (DM) based on the fitting of the clearance function curve using a polynomial function. In allusion to the characteristic of the aperiodicity of response sensitivity curves of the nonlinear system in the time domain, a novel assessment method—differential sensitivity based on the root mean square (RMS) of response is proposed. This method provides statistical results in a certain range, thus avoiding the inaccuracy of the partial amplitude. The vibrational energy of modified system (MS) can also be estimated. All the abovementioned characteristics make it possible to provide the theoretical support for dynamic modification, model updating, and optimal design.

A large torsion beam finite element model for tapered thin-walled open cross sections beams

A 3D finite element beam element model is investigated for the behavior, the buckling and the post-buckling analyses of thin-walled tapered beams with open cross sections. For the purpose, a non-linear model is performed in large torsion context according to a new kinematics that accounts for large torsion, flexural–torsional coupling and the presence of tapering terms in bending and torsion. The equilibrium equations are carried out and new tapering stress resultants are then present. This model is extended to finite element formulation in the same circumstances. 3D beams elements with two nodes and seven degrees of freedom per node are adopted. Due to large torsion assumption and flexural–torsional coupling, new matrices are established in both the geometric and the initial stress parts of the tangent stiffness matrix. The Arclength method is adopted as solution strategy of the non-linear equations. Many applications are presented that deal with the behavior, the buckling and the post-buckling equilibrium. Comparisons are made with some available solutions and with shell elements of a commercial code. The bifurcation points are in accordance with non-linear stability solutions. Moreover, the present element is also compared to similar tapered beam finite element without the new tapering terms. The proposed beam element is efficient and accurate in both linear and non-linear behavior analyses. It follows a non negligible gain in computation time especially when the post-buckling behavior is performed.

Modeling the coupled bending–torsional vibrations of symmetric laminated composite beams

A shear-deformable beam theory is proposed to model the coupled bending and twisting vibration in a symmetric laminated beam with a rectangular cross section. The warping of the beam cross section and Poisson effect are considered in the formulation. The governing equations of motion for the symmetric laminated beams exhibiting bending–torsional coupling are derived by using the Hamilton’s principle, and the dynamic stiffness matrix is formulated from the exact analytical solutions of the homogeneous governing differential equations. Numerical results of appropriately chosen symmetric laminated beams are presented and compared with the previously published numerical and experimental solutions whenever possible. The influences of Poisson effect, layup, and boundary condition on the natural frequencies of symmetric laminated beams are extensively investigated.

Bound states and persistent currents in presence of torsion and Rashba spin-orbit coupling

We study a model of an electron on a cylindrical surface, which is coupled to the torsion field due to a dislocation along the axis of the cylinder. We discuss the effect of this torsion field on the energy spectrum of the electrons and analytically calculate persistent currents in the presence of Rashba spin-orbit coupling. We also analyze bound state energy spectra in presence of Rashba spin-orbit interaction. Our results show that the presence of the torsional field due to the dislocation significantly modifies the energy spectrum of the system. The dislocation induced persistent spin current in this system is calculated, and we find a correspondence between the dislocation mediated spin current and the azimuthal spin current.

Concentric Tube Robots as Steerable Needles: Achieving Follow-the-Leader Deployment.

Concentric tube robots can enable new clinical interventions if they are able to pass through soft tissue, deploy along desired paths through open cavities, or travel along winding lumens. These behaviors require the robot to deploy in such a way that the curved shape of its shaft remains unchanged as the tip progresses forward (i.e., "follow-the-leader" deployment). Follow-the-leader deployment is challenging for concentric tube robots due to elastic (and particularly torsional) coupling between the tubes that form the robot. However, as we show in this paper, follow-the-leader deployment is possible, provided that tube precurvatures and deployment sequences are appropriately selected. We begin by defining follow-the-leader deployment and providing conditions that must be satisfied for a concentric tube robot to achieve it. We then examine several useful special cases of follow-the-leader deployment, showing that both circular and helical precurvatures can be employed, and provide an experimental illustration of the helical case. We also explore approximate follow-the-leader behavior and provide a metric for the similarity of a general deployment to a follow-the-leader deployment. Finally, we consider access to the hippocampus in the brain to treat epilepsy, as a motivating clinical example for follow-the-leader deployment.

Seismic response of torsionally coupled building with passive and semi-active stiffness dampers

The seismic response of single-storey, one-way asymmetric building with passive and semi-active variable stiffness dampers is investigated. The governing equations of motion are derived based on the mathematical model of asymmetric building. The seismic response of the system is obtained by numerically solving the equations of motion using state-space method under different system parameters. The switching and resetting control laws are considered for the semi-active devices. The important parameters considered are eccentricity ratio of superstructure, uncoupled lateral time period and ratio of uncoupled torsional to lateral frequency. The effects of these parameters are investigated on peak lateral, torsional and edge displacements and accelerations as well as on damper control forces. The comparative performance is investigated for asymmetric building installed with passive stiffness and semi-active stiffness dampers. It is shown that the semi-active stiffness dampers reduce the earthquake-induced displacements and accelerations significantly as compared to passive stiffness dampers. Also, the effects of torsional coupling on effectiveness of passive dampers in reducing displacements and accelerations are found to be more significant to the variation of eccentricity as compared to semi-active stiffness dampers.

Operational model updating of low-order horizontal axis wind turbine models for structural health monitoring applications

Rotational machinery such as horizontal axis wind turbines exhibits complex and nonlinear dynamics (e.g. precession and Coriolis effects, torsional coupling) and is subjected to nonlinear constrained conditions (i.e. aeroelastic interaction). For those reasons, aeroelastic and computer-aided models reproduced under controlled conditions may fail to predict the correct non-stationary loading and resistance patterns of wind turbines in actual operation. Operational techniques for extracting modal properties under actual non-stationary loadings are needed in order to improve computer-aided elasto-aerodynamic models to better characterize the actual behavior of horizontal axis wind turbines in operational scenarios, monitor and diagnose the system for integrity and damage through time, and optimize control systems. For structural health monitoring applications, model updating of stochastic aerodynamic problems has gained interest over the past decades. A probability theory framework is employed in this study to update a horizontal axis wind turbine model using such a stochastic global optimization approach. Structural identification is addressed under regular wind turbine operation conditions for non-stationary, unmeasured, and uncontrolled excitations by means of stochastic subspace identification techniques. This numerical framework is then coupled with an adaptive simulated annealing numerical engine for solving the problem of model updating. Numerical results are presented for an experimental deployment of a small horizontal axis wind turbine structure.

Wing Flutter Analysis Parameters during Flight

This paper adapts finite element analysis of dynamic structure to analysis airfoil based on the phenomenon that torsion coupling may happen to airfoil during flying,, which verifies flutter mechanism of swing under subsonic and transonic condition. Modal frequency error can be changed into stiffness error by error analysis. The errors of bending and torsion frequency are verified by adjusting stiffness and mass distribution. Meanwhile the concept of modal strain energy is introduced to character and identify different positions and structures of damages.

Analysis of line broadening and spectral asymmetry in an all-fiber torsional acousto-optic band-pass filter

The transmission properties of an all-fiber torsional acousto-optic (AO) band-pass filter with a sub-nm bandwidth is studied. The device is based on torsional AO coupling in a highly birefringent (HB) optical fiber. The full width at half maximum (FWHM) measured in a conventional band (C-band) is 0.88 nm, which is compared with the theoretical value of 0.45 nm estimated by using the coupled mode theory. The line broadening and the spectral asymmetry observed in experiments are investigated in detail through our theoretical model and full numerical analyses. The influence of the non-uniformity in the birefringence of the HB fiber on the filter’s transmission is analyzed quantitatively in terms of the change in the filtering bandwidth, the sidelobe asymmetry, and the resonance shift.

Torsional flexural steady state response of monosymmetric thin-walled beams under harmonic loads

Starting with Hamilton's variational principle, the governing field equations for the steady state response of thin-walled beams under harmonic forces are derived. The formulation captures shear deformation effects due to bending and warping, translational and rotary inertia effects and as well as torsional flexural coupling effects due to the cross section mono-symmetry. The equations of motion consist of four coupled differential equations in the unknown displacement field variables. A general closed form solution is then developed for the coupled system of equations. The solution is subsequently used to develop a family of shape functions which exactly satisfy the homogeneous form of the governing field equations. A super-convergent finite element is then formulated based on the exact shape functions. Key features of the element developed include its ability to (a) isolate the steady state response component of the response to make the solution amenable to fatigue design, (b) capture coupling effects arising as a result of section mono-symmetry, (c) eliminate spatial discretization arising in commonly used finite elements, (d) avoiding shear locking phenomena, and (e) eliminate the need for time discretization. The results based on the present solution are found to be in excellent agreement with those based on finite element solutions at a small fraction of the computational and modelling cost involved.

Flutter analysis of bending–torsion coupling of aero-engine compressor blade with assembled clearance

In this paper, the flutter of a compressor blade is investigated to explore the fracture failure mechanism of the blade with an assembled clearance, cubic structural nonlinearity and aerodynamic forces. Firstly, the stability of the linearized system is studied in the neighborhood of an equilibrium point and the threshold speed of the linear flutter of the blade is obtained. Then the response equations of limit cycle oscillations (LCOs) are deduced by using the averaging method, and the stability of LCOs is analyzed based on the first-order approximate theory. Comparisons with the results from the fourth-order Runge–Kutta scheme are carried out, and the accuracy of the first-order approximation of the averaging method is discussed. Finally, the influence of clearance parameter, bending stiffness and torsional rigidity on the flutter characteristics of the blade is analyzed.

Advancements in subsea riser analysis using quasi-rotations and the Newton–Raphson method

Beam structures undergoing finite deflections and rotations in space have extensive application in the subsea industry particularly for the analysis of holistic systems with larger numbers of mooring and riser components. In using the finite element analysis approach, there is an increasing requirement for large element sizes which preserve accuracy with regard to the coupling of axial, bending and torsion response.The authors outline a method for improving the current state of practice for the analysis of riser systems. The approach draws on the convected coordinates method, Euler–Bernoulli beam theory, the principle of virtual work and the finite element method. Two quasi-rotation measures are developed including a quasi-material rotation definition for rotational deformation relative to the convected axis of a beam and a quasi-space rotation definition to deal with the path dependent nature of rotations in three dimensions.The novel aspect of this work is to relate the rate of change of the quasi-material rotation vector along the beam axis to a linear transformation of the beam axis rate-of-rotation vector through utilising the convected coordinates axes system. In this way, incremental values of quasi-material rotation are directly linked to incremental values of nodal quasi-space rotation and a global Newton–Raphson solution technique for interconnecting beam elements is straightforward to assemble.Furthermore, this leads to accurate definitions of coupled axial, bending and torque response for beams with significant deflection. The approach has particular advantages in the analysis of subsea riser sections. Also, the accuracy of the solution is preserved for a fewer number of elements compared to alternative solutions for computationally sensitive load cases with highly non-linear loading regimes.

An Analytical Investigation of the Trapeze Effect Acting on a Thin Flexible Ribbon

This paper systematically explores the extensional–torsional coupling due to the trapeze effect acting on a thin flexible ribbon subjected to combined tension and torsion. Kinematic relationships as well as expressions for the restoring torque associated with this effect are analytically derived. Additionally, the locus of points about which the cross sections of a twisted ribbon under tension rotate is derived. These points, called torsional centers, are found to be coincident with the centroids of the axial stress field at each station along the ribbon. More generally, it is shown that when a flexible slender member is in tension, combined transverse forces must act at the centroid of the axial stress field to produce pure bending and no twist. As a result, the elastic axis (EA) of the member shifts from the locus of shear centers to the locus of centroids of the axial stress field. A numerical model is developed to investigate the effect of the position of the EA on the prediction of steady-state deformations and natural frequencies of a rotating ribbon with tip mass. By assuming the EA to be the locus of the shear centers, the tip twist is overpredicted by a factor of 2 for small twist angles, and up to 2.5 for large twist deformations. In addition, assuming the EA to be the locus of shear centers results in an error of up to 60% in the predicted natural frequencies at large twist angles.

Band-rejection filtering based on lossy torsional acousto-optic coupling in a single polarization fiber.

We propose and demonstrate novel band-rejection filtering scheme based on lossy torsional acousto-optic (AO) coupling in a single polarization fiber. Simulation results show that the polarization insensitive notch depth of -30 dB is achievable for a 2-m-long fiber in the state-of-the-art fiber manufacturing technology. More efficient band-rejection in excess of -44 dB could be also feasible in practical fiber length. Good agreement between our numerical simulations and proof-of-principle experiments is obtained in optical communication C-band. The measured notch depth is -29.4 dB for a low loss polarization mode after propagating an AO interaction length of 49.8 cm. The filtered wavelength could be tuned linearly by the variable acoustic transducer frequency with the slope of 0.61 nm/kHz, and the polarization dependence of notch depth was measured to 0.8 dB in our setup. Our experiments confirm the validity and practicality of the approach, and illustrate the in-fiber torsional AO band-rejection filter with simpler device configuration is achievable.

Torsion-mediated interaction between adjacent genes.

DNA torsional stress is generated by virtually all biomolecular processes involving the double helix, in particular transcription where a significant level of stress propagates over several kilobases. If another promoter is located in this range, this stress may strongly modify its opening properties, and hence facilitate or hinder its transcription. This mechanism implies that transcribed genes distant of a few kilobases are not independent, but coupled by torsional stress, an effect for which we propose the first quantitative and systematic model. In contrast to previously proposed mechanisms of transcriptional interference, the suggested coupling is not mediated by the transcription machineries, but results from the universal mechanical features of the double-helix. The model shows that the effect likely affects prokaryotes as well as eukaryotes, but with different consequences owing to their different basal levels of torsion. It also depends crucially on the relative orientation of the genes, enhancing the expression of eukaryotic divergent pairs while reducing that of prokaryotic convergent ones. To test the in vivo influence of the torsional coupling, we analyze the expression of isolated gene pairs in the Drosophila melanogaster genome. Their orientation and distance dependence is fully consistent with the model, suggesting that torsional gene coupling may constitute a widespread mechanism of (co)regulation in eukaryotes.

Dynamic characteristics of wind-excited linked twin buildings based on a 3-dimensional analytical model

The present work investigates the effects of structural links on the modal properties and wind-induced responses of a linked building system (LBS) by using an advanced three-dimensional analytical model. The LBS in this study refers to a system consisting of twin buildings horizontally connected by structural links such as skybridges and skygardens. The proposed analytical model of the LBS is derived by assembling the structural-property matrices of a rigid floor diaphragm model of the buildings and those of a beam model of each link. The accuracy of the analytical model is then compared with and validated by a detailed finite element method (FEM) model. By employing the analytical model together with the layer-by-layer wind force time histories measured in a wind tunnel, the modal properties and wind-induced dynamic responses are computed for LBSs with different link properties. The results show that the link can substantially alter the modal properties of the system, and hence the structural responses. In some cases, the wind-induced responses of LBSs are reduced in comparison with those of two independent towers (without a link), attributing to the additional link stiffness as mobilizing the stiffness of an individual tower to resist the lateral wind loads. In other cases, the structural responses are increased, due to the extra link mass and the lateral–torsional coupling induced by the link. Therefore, caution should be exercised in the wind-resistant design of a LBS, in particular in regard to the link properties, to avoid undesirable wind-induced responses.

Modeling of torsion actuation of beams using inclined piezoelectric actuators

The present work is preliminary studies on the development of finite element model for static analysis of advanced beam structure subjected to axial, transverse, and torsion loads in addition to the torsion actuation due to the piezoelectric actuators. These types of smart structures can be used as element of mechanical system, helicopter rotor blade, and/or blades for turbomachinery. The equation of motion of the structure system is derived using the energy variation approach. The model assumes that the structure behaves as a Bernoulli–Euler beam in bending and extension, while torsion is introduced by utilizing a cross-sectional warping function, which dependent upon the cross- section geometry of the structure. A linear and hermit cubic shape functions are used to model the axial and transverse deformations, while quadratic interpolation shape function is introduced to model the torsion deformation. The bending, torsion, and axial coupling are introduced in the stiffness and mass matrices. The electric potential is considered as function of the thickness and the length of the beam element. A MATLAB interactive code is developed to validate the model. The obtained results are compared to the available analytical and finite element results and found reasonable.

Black hole solutions in Chern-Simons AdS supergravity

We study charged AdS black hole solutions in five-dimensional Chern-Simons supergravity. The minimal supergroup containing such AdSxU(1) configurations is the superunitary group SU(2,2|N). For this model, we find analytic black hole solutions that asymptote to locally AdS spacetime at the boundary. A solution can carry U(1) charge provided the spacetime torsion is non-vanishing. Thus, we analyze the most general configuration consistent with the local AdS isometries in Riemann-Cartan space. The coupling of torsion in the action resembles that of the universal axion of string theory, and it is ultimately due to this field that the theory acquires propagating degrees of freedom. Through a careful analysis of the canonical structure the local degrees of freedom of the theory are identified in the static symmetric sector of phase space.

Research on the Optimization Design of Gas-Solid Coupling of Wind Turbine Blades

The effects of high-altitude wind shear of wind speed should be considered, the appropriate number of distribution group should be determined and the distribution of wind speed hybrid model parameters and solving should be loaded onto the blades. When the stress of rotor blade is analyzed, the elastic deformation of the blades and the effects of the vibration of oscillating flow field on reaction of the blades must be considered during the operation. Thus the laws of blade load distribution and the corresponding deformation can be accurately calculated to analyze the interplay between deformation vibration airflow and paddle, to determine the law of deformation of rotor blades, the surface pressure distribution, stress distribution and blade design safety factors. When wind load changes with the wind speed, the adaptive blades are powered by aeroelastic, the law of wielding and flapping of the blade will be studied. The torsion coupling effects of adaptive blade, blade bending ,the law of torsional deformation variation of the angle of attack and the impact on aeroelastic blades structural strength will be explored. The results of this study design will be optimized as the power factor, improving the stability of the design of wind turbine power output, reducing material consumption blades absorb vibration and reducing wind load maneuvering to avoid blade stall achieve pitch control. Thus it provides a theoretical basis for optimal design of strength and stiffness of the elongated paddles.

Tangent Stiffness Matrix of Spatial Beam Element Considering Bend and Torsion Coupling Effect

Based on the spatial beam-column differential equations, the slope deflection equations considering second-order and bend-torsion coupling effect are established. The additional moment caused by torsion and bend deflection are taken into account. Then the finite element pattern of spatial beam-column considering the couple effect of torsion and bend is given. The tangent stiffness matrix and relevant program for nonlinear analysis are further obtained. By the nonlinear calculation and stability analysis of single component which has high accuracy or precise solution, the precision of the FEM model given in this paper is verified by comparing the results with that given in references.