Torsional Coupling Research Articles

Sensitivity Study of the Influence of Blade Sectional Stiffness Parameters on the Aeroelastic Response of Wind Turbines

With the development of wind turbines as a result of large-scale and offshore trends, the wind turbine size is becoming increasingly larger. The passive control technique is used to alleviate the increasing loads on the blade for the sake of improving the durability of the wind turbine. The ply design of shells considering the coupling effect of bending and torsion is one of the passive control techniques. The bending torsion coupling stiffness is one of the parameters of the blade section stiffness matrix. In order to fully understand the influence of each blade stiffness parameter on the aeroelastic responses of wind turbines and to consider the influence of structural characteristics on the aeroelastic responses in blade design, the influences and sensitivity of each stiffness parameter in the 6 × 6 stiffness matrix of the blade sections on the aeroelastic responses of the wind turbines are systematically studied under steady wind condition. The aerodynamic forces in the aeroelastic model are calculated by an AeroDyn module based on blade element momentum theory, and the structural dynamic responses of the blade are calculated using generalized Timoshenko beam theory and geometric exact beam theory. The NREL baseline 5 MW wind turbine and blade properties are used in this study, where the diagonal stiffness parameters and non-diagonal stiffness parameters of the matrixes of each blade section are scaled according to certain principles. The results show that the axial stiffness, the flap-wise stiffness, and the torsional stiffness in the diagonal are sensitive to the root loads and tip displacement of the blade. The flap-wise bending torsion coupling stiffness, the flap-wise shear-torsion coupling stiffness, and the edge-wise shear-torsion coupling stiffness in the non-diagonal are also sensitive to the aeroelastic responses. For completeness, the effects of other stiffness parameters on the aeroelastic responses are also analyzed and discussed.

Vibration analysis of composite wing with geometric and material coupling

Composite wing design is complicated but inevitable to enlighten modern airplanes while maintaining the required performance. Using the dynamic transfer method, this paper discusses intensively the dynamic characteristics of a cantilever composite wing with both torsion and bending coupling to represent both material and geometric coupling. The governing differential equations are obtained based upon the principle of Hamilton and are solved analytically using a harmonic oscillation assumption. For this purpose, a MATLAB code is developed and results are validated in comparison with published work. Such a comparison shows a good agreement between both results. Finally, a parametric study is carried out to show the influence of the variation of both geometric coupling and torsion bending coupling rigidity on the free vibration analysis of the composite wing. The study shows the crucial effect of both factors on the dynamic behavior of the composite wing. The current research can be considered as a base for aeroelasticians while designing composite structures.

Time-Domain Dynamic Modeling and Analysis of Complex Heavy-Duty Gearbox Considering Floating Effect

Expert insights into the time-domain dynamic behavior of heavy-duty gearboxes form the foundations of design evaluation and improvement. However, in the existing lateral–torsional coupling (LTC) modeling method for gearboxes that is normally used for frequency-domain dynamic behavior, the meshing forces are modeled as spring dampers with fixed acting points on the meshing gears to simulate only the transient LTC effect, and thus the steady state characteristic in the time domain cannot be obtained due to the unrealistic distortion of positions and orientations as the gear angles increase. In this paper, a novel and generally applicable LTC modeling method for heavy-duty gearboxes, mainly planetary gear sets with floating components, is proposed by using space-fixed spring dampers with floating acting points on the meshing gears to study the time-domain dynamic response and to support the dynamic design of heavy-duty gearboxes. Based on the proposed method, a LTC model of a 2 megawatt (MW) wind turbine gearbox with floating components considering the time-varying meshing stiffness, bearing stiffness, torsional stiffness, and floating effect was established. The simulated results of representative components were in accordance with experimental results on a test rig, and dynamic behavior was calculated.

Optimization of vibration performance of range extender based on structural parameters

In this paper, the simulation model of the range extender system is established to calculate the torsional vibration performance of the shafting system, and the calculation results of the speed nonuniformity and torsional vibration amplitude are obtained. After analyzing the influence of shafting structural parameters on vibration results, the design parameters of torsional damper, flywheel, generator rotor and coupling are optimized through grouping calculation and neural network model based on optimization, so as to improve the vibration performance of shafting.

Electronic, vibrational, and torsional couplings in N-methylpyrrole: Ground, first excited, and cation states.

The electronic spectrum associated with the S1 ← S0 (Ã1A2←X̃1A1) one-photon transition of jet-cooled N-methylpyrrole is investigated using laser-induced fluorescence (LIF) and (1 + 1) resonance-enhanced multiphoton ionization (REMPI) spectroscopy; in addition, the (2 + 2) REMPI spectrum is considered. Assignment of the observed bands is achieved using a combination of dispersed fluorescence (DF), two-dimensional LIF (2D-LIF), zero-electron-kinetic energy (ZEKE) spectroscopy, and quantum chemical calculations. The spectroscopic studies project the levels of the S1 state onto those of either the S0 state, in DF and 2D-LIF spectroscopy, or the ground state cation (D0 +) state, in ZEKE spectroscopy. The assignments of the spectra provide information on the vibrational, vibration-torsion (vibtor), and torsional levels in those states and those of the S1 levels. The spectra are indicative of vibronic (including torsional) interactions between the S1 state and other excited electronic states, deduced both in terms of the vibrational activity observed and shifts from expected vibrational wavenumbers in the S1 state, attributed to the resulting altered shape of the S1 surface. Many of the ZEKE spectra are consistent with the largely Rydberg nature of the S1 state near the Franck-Condon region; however, there is also some activity that is less straightforward to explain. Comments are made regarding the photodynamics of the S1 state.

Influence of soil flexibility and plan asymmetry on seismic behaviour of soil-piled raft-structure system

Ever-increasing scarcity of land and demand for high-rise structures has significantly contributed to the use of combined piled raft foundations (CPRF) in soft ground. However, utility, design constraints and aesthetic considerations bring asymmetry to superstructures, making structures more vulnerable during seismic excitations. Traditional design practices involve designing superstructure elements and foundation considering fixity at the base of the superstructure and ignoring soil-structure interaction (SSI) which may result in under-estimation of forces and displacement in the system. Hence, the present study aims at developing new seismic design guideline pertaining to asymmetric single and multi-storied structure supported on CPRF embedded in soft clay. Some important parameters, such as torsional coupling mode of vibration and multi-storey idealisation involving the effect of higher modes are investigated incorporating seismic SSI effect. The study broadly reveals that the torsional to lateral period ratio considerably influence the seismic response of asymmetric structural system on the piled raft foundation due to the incorporation of SSI. Furthermore, multi-storey building idealisation gives a higher estimation of response compared to single storey idealization in superstructure and pile head which may be due to the effect of higher modes of vibration and SSI

Test and Numerical Model of Curved Steel-Concrete Composite Box Beams under Positive Moments.

Compared with straight steel–concrete composite beams, curved composite beams exhibit more complicated mechanical behaviors under combined bending and torsion coupling. There are much fewer experimental studies on curved composite beams than those of straight composite beams. This study aimed to investigate the combined bending and torsion behavior of curved composite beams. This paper presents static loading tests of the full elastoplastic process of three curved composite box beams with various central angles and shear connection degrees. The test results showed that the specimens exhibited notable bending and torsion coupling force characteristics under static loading. The curvature and interface shear connection degree significantly affected the force behavior of the curved composite box beams. The specimens with weak shear connection degrees showed obvious interfacial longitudinal slip and transverse slip. Constraint distortion and torsion behavior caused the strain of the inner side of the structure to be higher than the strain of the outer side. The strain of the steel beam webs was approximately linear. In addition, fine finite element models of three curved composite box beams were established. The correctness and applicability of the finite element models were verified by comparing the test results and numerical calculation results for the load–displacement curve, load–rotational angle curve, load–interface slip curve, and cross-sectional strain distribution. Finite element modeling can be used as a reliable numerical tool for the large-scale parameter analysis of the elastic–plastic mechanical behavior of curved composite box beams.

Effects of Soil-Structure Interaction on Torsionally Coupled Base Isolated Machine Foundation under Earthquake Load

In this paper, the influence of soil-structure interaction (SSI) on a torsionally coupled turbo-generator (TG) machine foundation is studied under earthquake ground motions. The beneficial effects of base isolators in the TG foundation under earthquake ground motions are also studied duly, considering the effects of SSI. A typical TG foundation is analyzed using a three-dimensional finite element (FE) model. Two superstructure eccentricity ratios are considered to represent the torsional coupling. Soft soil properties are considered to study the effects of SSI. This research concludes that the effects of torsional coupling alter the natural frequencies, if ignored, could lead to unsafe design. The deck accelerations and displacements are increased with an increase in superstructure eccentricity. On the other hand, the deck accelerations and displacements are greatly reduced with the help of base isolators, thus confirming the beneficial use of base isolators in machine foundations to protect the sensitive equipment from the strong earthquake ground motions. However, the effects of SSI reduce the natural frequencies of the TG foundation resting on soft soil conditions and activate the higher mode participation, resulting in amplifying the response.

Chiral torsional effects in anomalous fluids in thermal equilibrium

Using the similarity between spacetime torsion and axial gauge couplings, we study torsional contributions to the equilibrium partition function in a stationary background. In the case of a charged fluid minimally coupled to torsion, we spot the existence of linear torsional magnetic and vortical effects, while the axial-vector current and the spin energy potential do not receive corrections in the torsion at linear order. The covariant energy-momentum tensor, on the other hand, does contain terms linear in the torsion tensor. The case of a two-flavor hadronic superfluid is also analyzed, and the torsional contributions to the constitutive relations computed. Our results show the existence of a torsional electric chiral effect mediated by the charged pions.

A novel chiral metamaterial with multistability and programmable stiffness

Chiral metamaterials are widely studied for their unique mechanical properties, but still have problems such as low stiffness and few available scenarios. Based on the tetra-chiral metamaterial, a type of metamaterial with programmable stiffness and multistability is designed in this paper. The stiffness of two-dimensional (2D) metamaterial can be adjusted programmatically by changing its geometric parameters. The equivalent elastic modulus and Poisson’s ratio were obtained by using an analytical solution and finite element method. Then the 2D metamaterials were extended to cylindrical tubes with multistability. The deformation patterns of the 2D metamaterials and cylindrical tubes with different geometric parameters were investigated. It is found that the cylindrical tubes can exhibit compression–torsion coupling and multistability deformation characteristics. This work can provide a valuable reference for designs of novel metamaterials with coupled deformation, as well as further expanding the field of application.

Coupling of torsion and OH-stretching in tert-butyl hydroperoxide. II. The OH-stretching fundamental and overtone spectra.

The vibrational spectra of gas phase tert-butyl hydroperoxide have been recorded in the OH-stretching fundamental and overtone regions (ΔvOH = 1-5) at room temperature using conventional Fourier transform infrared (ΔvOH = 1-3) and cavity ring-down (ΔvOH = 4-5) spectroscopy. In hydroperoxides, the OH-stretching and COOH torsion vibrations are strongly coupled. The double-well nature of the COOH torsion potential leads to tunneling splitting of the energy levels and, combined with the low frequency of the torsional vibration, results in spectra in the OH-stretching regions with multiple vibrational transitions. In each of the OH-stretching regions, both an OH-stretching and a stretch-torsion combination feature are observed, and we show direct evidence for the tunneling splitting in the OH-stretching fundamental region. We have developed two complementary vibrational models to describe the spectra of the OH-stretching regions, a reaction path model and a reduced dimensional local mode model, both of which describe the features of the vibrational spectra well. We also explore the torsional dependence of the OH-stretching transition dipole moment and show that a Franck-Condon treatment fails to capture the intensity in the region of the stretch-torsion combination features. The accuracy of the Franck-Condon treatment of these features improves with increasing ΔvOH.

Coupling of torsion and OH-stretching in tert-butyl hydroperoxide. I. The cold and warm first OH-stretching overtone spectrum.

The infrared (IR) spectrum of tert-butyl hydroperoxide (TBHP) in the region of the first OH-stretching overtone has been observed under jet-cooled and thermal (300 K, 3 Torr) conditions at ∼7017 cm-1. The jet-cooled spectrum is recorded by IR multiphoton excitation with UV laser-induced fluorescence detection of OH radical products, while direct IR absorption is utilized under thermal conditions. Prior spectroscopic studies of TBHP and other hydroperoxides have shown that the OH-stretch and XOOH (X = H or C) torsion vibrations are strongly coupled, resulting in a double well potential associated with the torsional motion about the OO bond that is different for each of the OH-stretching vibrational states. A low barrier between the wells on the torsional potential results in tunneling split energy levels, which leads to four distinct transitions associated with excitation of the coupled OH-stretch-torsion states. In order to interpret the experimental results, two theoretical models are used that include the OH-stretch-torsion coupling in TBHP. Both methods are utilized to compute the vibrational transitions associated with the coupled OH-stretch-torsion states of TBHP, revealing the underlying transitions that compose the experimentally observed features. A comparison between theory and experiment illustrates the necessity for treatments that include OH-stretch and COOH torsion in order to unravel the spectral features observed in the first OH-stretching overtone region of TBHP.

Validation of a 20 m Wind Turbine Blade Model

In the projects Smartblades and Smartblades 2 a full-scale 20 m rotor blade for the NREL CART3 wind turbine was designed, built and tested. The rotor blade was intended to have a strong bending–torsion coupling. By means of the experiments, the proof for the technology in question was supposed to be provided. The experimental work was accompanied by simulations. The aim of the paper was to describe and publish a reference finite element model for the 20 m rotor blade. The validation procedure is presented, as are the modelling strategy and the limitations of the model. The finite element model is created using quadratic finite shell elements and quadratic solid elements. Different data sets were used for the validation. First, the data of static test bench experiments were used. The validation comprised the comparison of global displacement and local strain measurements for various flap and edge bending tests and for torsion unit loading tests. Second, the blades’ eigenfrequencies and eigenvectors in clamped and free–free scenarios were used for validation. Third, the mass distributions of the finite element and real blade were investigated. The paper provides the evaluated experimental data, and all analysed scenarios and the corresponding finite element models in Abaqus, Ansys and Nastran and formats as a reference dataset.

Theoretical analysis on the stiffness of compression–torsion coupling metamaterials

The compression–torsion coupling metamaterials constructed by cells based on chiral mechanism of inclined rods with weak transverse constraints, display superior compression–torsion properties among the metamaterials reported previously. Aiming at metamaterials of this type, a general representative cell is extracted to reveal the relationship between the load and the deformation with considering the compression–torsion coupling effect. The stiffness matrix of the chiral 3D cell is derived based on Euler beam theory and applying dummy-load method, which is expressed as functions of the geometry parameters of cell structures and the mechanical properties of base material. The analytical predictions show good agreement with the numerical simulations. Results show that there exist optimal inclined angles of the rods corresponding to the maximal shear stiffness and the maximal compression–torsion coupling stiffness, respectively, which are both determined by the ratio of circular loop diameter to inclined rod length. This work provides guidelines for the design and analysis of compression–torsion coupling metamaterials, and opens a new avenue for theoretically analyzing the deformation coupling problem.

Large deformation analysis of spontaneous twist and contraction in nematic elastomer fibers with helical director

A cylindrical rubber fiber subject to a twist will also elongate: a manifestation of Poynting’s effect in large strain elasticity. Here, we construct an analogous treatment for an active rubber fiber actuated via an axisymmetric pattern of spontaneous distortion. We start by constructing an exact large-deformation solution to the equations of elasticity for such fiber subject to imposed twist and stretch, which reveals spontaneous warping and twisting of the fiber cross section absent in passive rubbers. We then compute the corresponding non-linear elastic energy, which encompasses the Poynting effect but is minimized by a finite spontaneous twist and stretch. In the second half of the paper, we apply these results to understand the twist-contraction actuation of nematic elastomer fibers fabricated with director fields that encode helical patterns of contraction on heating. We first consider patterns making a constant angle with respect to the local cylindrical coordinate system (conical spiral director curves) and verify the predicted spontaneous twist, contraction, and cross-section deformation via finite elements. Second, we consider realistic director distributions for the experimentally reported fibers fabricated by cross-linking while simultaneously applying stretch and twist. Counterintuitively, we find that the maximum actuation twist is produced by applying a finite optimal twist during fabrication. Finally, we illustrate that spontaneously twisting fibers will coil into spring-like shapes on actuation if the ends are prevented from twisting relative to each other. Such a twist–torsion coupling would allow us to make a tendril-like “soft-spring” actuator with low force and high linear stroke compared to the intrinsic contraction of the elastomer itself.

Soil–structure interaction effect on seismic response of controlled asymmetric buildings

Lateral torsional coupling of asymmetric buildings governs their seismic response. Other than building eccentricity, the extent of this impact depends on the interaction of the building foundation with the surrounding soil – soil–structure interaction (SSI). This study investigates the seismic response of a representative asymmetric building, equipped with semi-active dampers, by accounting for the effect of SSI. Two semi-active damping schemes – friction-type and two-step viscous – are considered and their relative efficiencies are measured when compared with passive dampers. All analyses, including building eccentricity, SSI and dampers, are performed under ten earthquakes with different characteristics and peak intensities. Results obtained imply that SSI can have a significant impact on the lateral torsional coupling of the building if not realistically considered, and thus can greatly influence the seismic response of an asymmetric building. Comparative assessment between semi-active and passive dampers, with respective optimal damping parameters and placement, reveals the superiority of friction-type dampers over the others in reducing the response of the asymmetric building during seismic shaking. Nevertheless, all dampers are found to be efficient in regulating the seismic response of the asymmetric building–SSI system by lowering the adverse effect of lateral torsional coupling on the seismic response of the building.

Dynamic Characteristics of Rotor System with a Slant Crack Based on Fractional Damping

The traditional modeling method of rotor system with a slant crack considers only integer-order calculus. However, the model of rotor system based on integer-order calculus can merely describe local characteristics, not historical dependent process. The occur of fractional order calculus just makes up for the deficiency in integer-order calculus. Therefore, a new dynamic model with a slant crack based on fractional damping is proposed. Here, the stiffness of rotor system with a slant crack is solved by zero stress intensity factor method. The proposed model is simulated by Runge-Kutta method and continued fraction Euler method. The influence of the fractional order, rotating speed, and crack depth on the dynamic characteristics of rotor system is discussed. The simulation results show that the amplitude of torsional excitation frequency increases significantly with the increase of the fractional order. With the increase of the rotating speed, the amplitude of first harmonic component becomes gradually larger, the amplitude of the second harmonic becomes smaller, while the amplitude of the other frequency components is almost invariant. The shaft orbit changes gradually from an internal 8-type shape to an ellipse-type shape without overlapping. With the increase of the slant crack depth, the amplitude of the transverse response frequency in the rotor system with a slant crack increases, and the amplitude in the second harmonic component also increases significantly. In addition, the torsional excitation frequency and other coupling frequency components also occur. The proposed model is further verified by the experiment. The valuable conclusion can provide an important guideline for the fault diagnosis of rotor system with a slant crack.

Analysis on dynamic eccentricity effect and torsional performance of steel reinforced concrete frame with special-shaped column

Based on the seismic simulation shaking table test of steel reinforced concrete frame model with special-shaped column, the lateral-torsional vibration response, dynamic eccentricity effect and nonlinear torsion response law of the model structure are studied. The results show that, under the action of three-way earthquake, the Y-direction and X-direction horizontal torsion coupling phenomena occur in the high-order vibration mode of the model structure, and the accidental eccentric torsion has a light influence on the seismic performance of the special-shaped column structure which does not exceed the height limit. The nonlinear torsion analysis shows that the inter-storey displacement angle of the model structure is affected by floor position, eccentricity and ground motion intensity. As the eccentricity and seismic intensity increases, the inter-storey torsion Angle of the model structure increases constantly. In case the relative eccentricity is less than or equal to 0.5 and the peak acceleration is less than or equal to 0.62g, then the amplitude of the inter-storey torsion Angle of the model increases slightly; In case the relative eccentricity is more than 0.5, then the lateral-torsional coupled effect of earthquake response of the structure is obvious, and the influence of eccentricity on torsion effect of the model structure is more obvious. The results show that steel reinforced concrete frame with special-shaped column has good ductility and torsion resistance.

WITHDRAWN: Seismic analysis of G + 9 framed structures made of reinforced concrete resting on hill slopes

This work is an attempt to understand the behavior of structures on hill slopes. Due to unavailability of plain lands, the construction of buildings is started on sloping grounds. A brief review of the literature is available on the geometrical configuration of structures resting on sloping ground, setback and step-back structures, and torsion coupling of asymmetric structures. A 9 storey structure configured for two different slopes and two regular structures for flat ground with 3 and 9 storeys were taken in consideration for analytical investigation. Various configured building structures resting on hill slopes were studied using a parametric study to avoid torsion and stiffness irregularities by placing shear walls at different locations and varying the height of ground supported columns. The results obtained from the analysis shown good agreement with the results obtained for building structures resting on flat grounds. From the results, it is identified that failure of structural elements can be avoided by placing shear walls and varying height of ground-level columns. It was observed that Step-back Set-back building configuration is suitable for building structures on hill slopes.

Coupled flexural torsional analysis and buckling optimization of variable stiffness thin-walled composite beams

Present work examines flexural–torsional coupling for static and stability analysis of thin-walled composite beams having variable stiffness. Variable stiffness composites (VSCs), manufactured with curvilinear fibers, are considered in this work. Compared to straight fiber laminates, variable angle tow (VAT) sections may significantly improve structural response as they redistribute the in-plane stresses. A generalized beam kinematic model which considers the effect of flexural, torsional and, warping deformation is adopted and using the principle of minimum potential energy, governing equations are derived. The variable fiber angles can be defined using a general Lagrangian polynomial and as a particular case, the solution is presented for linearly varying fiber angles. Stability analysis considers geometric nonlinearity. The present model neglects transverse shear deformations, and governing equations are numerically solved using a set of C 1 continuous finite elements. Important observations are made on the coupled response of thin-walled VSCs for static and stability analysis, which indicates the necessity of optimization study. An efficient ‘Teaching Learning Based Optimization’ (TLBO) algorithm is applied to obtain the most efficient curvilinear fiber path. The results show that lateral torsional buckling load capacity can be increased by approximately 15% in optimized VSCs compared to unidirectional fiber composites. The present kinematic model and numerical scheme can be easily extended to the optimization studies considering manufacturing constraints, which may be further implemented in commercial designs.