Torsional Frequencies Research Articles

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.

Torsional vibration of irregular single-walled carbon nanotube incorporating compressive initial stress effects

Abstract This study is an attempt to show the impacts of surface irregularity and compressive initial stresses on the torsional vibration of a single-walled carbon nanotube (SWCNT). The governing equation and corresponding closed-form solutions were derived with the aid of Hamilton's principle. Then, the natural frequencies were obtained analytically and the influences of surface irregularity and compressive initial stresses on the torsional vibration were studied in detail. Numerical results analyzing the torsional vibration incorporating compressive initial stress effects were discussed and presented graphically. The effects of surface irregularity on the natural frequency of torsional vibrations of nanomaterials, especially for SWCNTs, have not been investigated before, and most of the previous research works have been carried for a regular carbon nanotube. Therefore, it must be emphasized that the torsional vibrations of irregular SWCNTs are novel and applicable for the design of nano-oscillators and nanodevices, in which SWCNTs act as the most prevalent nanocomposite structural element. The analytical solutions and numerical results revealed that the surface irregularity and compressive initial stress have notable effects on the natural frequency of torsional vibrations. It has been observed that, as the surface irregularity and compressive initial stress parameters increase, the torsional natural frequency of vibrations of SWCNTs also increases. Since SWCNTs have very small size, they are always subject to initial stresses from different resources; therefore, understanding the influences of compressive initial stresses on the torsional frequency of nanotubes helps the engineers and researchers to design proper nanodevices for different applications with irregular shapes.

Intermolecular vibrational states far above the van der Waals minimum: Combination bands of the polar N2O dimer

Infrared combination bands of the polar isomer of the N2O dimer are observed for the first time, using a tunable infrared laser source to probe a pulsed slit-jet supersonic expansion in the N2O ν1 region (≈2240 cm−1). One band involves the torsional (out-of-plane) intermolecular mode and yields a torsional frequency of 19.83 cm−1 if associated with the out-of-phase fundamental (N2O ν1) vibration of the N2O monomers in the dimer. The other band, which is highly perturbed, yields an intermolecular in-plane geared bend frequency of 22.74 cm−1. The results are compared with high level ab initio calculations. The less likely alternate assignment to the in-phase fundamental would give torsional and geared bend frequencies of 17.25 and 20.16 cm−1, respectively.

Modal Analysis of Fixed - Free Beam Considering Different Geometric Parameters and Materials

The early studying of natural frequencies and associated mode shapes for different geometric parameters and different boundary conditions is considered an integral approach that has received great attention in industrial applications to prevent catastrophic failure in machines. The effect of different diameters (Solid and Hollow) on the transverse bending and torsional natural frequencies on a uniform steel beam with a circular cross-section is studied. The effect of different materials and different beam lengths on the fundamental transverse bending and torsional natural frequencies are introduced for Fixed-Free supported beam. Theoretical analysis calculation and the Finite Element Methods using ANSYS Workbench 17 software results are introduced. Theoretical and numerical methods give approximately the same results. Figures of effects of the beam length, material types, and different inner diameters on the transverse bending, and torsional natural frequencies of the uniform beam are performed.

Vibration stability of a cantilevered thin plate with inner fluid circulation

The vibration of a cantilevered thin plate with inner fluid circulation is a typical situation in engineering. The plate’s vibration can be considered a combination of bending motion and torsional motion. With the force generated by the inner fluid circulation on the plate, these two types of motion affect each other and raise the problem of stability. In the present study, the vibration stability of different vibrating pattern thus generated is investigated. It is found that with the increase of the flow velocity, torsional mode frequencies decrease synchronously, whereas their modal shapes remain unchanged, which results in the buckling of the plate. Under the circumstance of coupled vibration, because both bending and torsional modal frequencies vary with the flow velocity, a phenomenon of coupled-mode flutter occurs between a certain pair of modes with frequency orders of (2k) and (2k − 1) and vibration becomes unstable.

Research on Torsional Property of Body-In-White Based on Square Box Model and Multiobjective Genetic Algorithm

In order to assess the performance of a vehicle in the conceptual design stage, a square box model was proposed to predict the torsional stiffness and the first-order torsional frequency of Body-in-White. The structure of Body-in-White was decomposed into eight simple structural surfaces, from which a square box model was constructed. Based on the finite element method, modified shear stiffness of each simple structure surface was calculated and the torsional stiffness was obtained. Then, simple structural surfaces of Body-in-White were constructed into an eight degree-of-freedom series spring system to calculate the first-order torsional frequency. Furthermore, a multiobjective genetic algorithm was used to determine the thickness and structural reinforcement of panels with small stiffness, so as to achieve the goal of increasing the stiffness while reducing the mass of the panel. The result shows that the optimal values of thickness are reduced by around 9.9 percent without affecting their performance by the proposed method. Compared to the prediction results obtained with the complicated numerical simulation, the relative error of the square box model in predicting the torsional stiffness is 6.04 percent and in predicting the first-order torsional frequency is 0.95 percent, indicating that the prediction model is effective.

Nonlinear integrated dynamic analysis of drill strings under stick-slip vibration

Stick-slip torsional vibration raising from bit-formation contact is a catastrophic dynamic phenomenon occurring in deep-water oil and gas drilling systems. The torsional vibrations can result in premature fatigue failure of drilling equipment and reduce drilling efficiency. Thus, studying the dynamics of the system is a vital key to identify the roots of the vibration and establish appropriate mitigation and remediation methods. In this paper, an efficient approach for finite element (FE) modeling of stick-slip vibrations of the full drill strings was proposed. The model was developed based on a rate-dependent formulation of bit-rock interaction, in which the cutting process was integrated through the frictional contact. The nonlinear effects of the large rotations and the geometrically nonlinear axial-torsional coupling were taken into account. The effect of energy dissipation due to the presence of drill mud along the drill pipes and drill collars was incorporated through Rayleigh viscous damping. Modal analysis was conducted to determine the natural frequencies and the mode shapes of the drill string. Furthermore, a five degree-of-freedom lumped parameter model was developed. The performance of the developed models was verified through comparisons with example stick-slip results from a field test. The study showed that the self-excited torsional vibrations may also occur at fundamental frequencies lower than the first natural torsional frequency of the drill string, depending on operational parameters. The conducted research work resulted in a robust and practical integrated FE model to simulate the entire drill string system dynamics under torsional vibrations.

Experimental research on free vibration of curved composite box-girders with corrugated steel webs

The curved composite box-girders (CBGs) with corrugated steel webs (CSWs) have been used widely in bridges due to their great advantages and the demand of the road alignment, but the curvature makes both the static and dynamic behaviors more complex. To research the free vibration performance of the curved CBGs with CSWs, 5 simply-supported test girders were designed with the span-to-radius ratio (n=L/R), the number of the cells of the box section, and the number of the diaphragms as parameters. The natural frequencies and mode shapes were measured in the experiment. The experimental results were compared with the numerical results using ANSYS software, and a satisfying agreement was obtained. The parametric analysis shows that for the curved CBG with CSWs, the vertical mode shapes are combined flexural and torsion, and the contribution of the torsional effects to the mode shapes and frequencies improve with the increase of n, which leads to a decrease in the vertical and lateral frequencies and increase in the torsional frequency. The corrugated angle of the steel web has little effect on the natural frequencies of the curved CBGs with CSWs. Increasing the thickness of the steel web and the number of the diaphragms can improve the torsional rigidity of the curved CBG with CSWs effectively; while the deck width has a great contribution on the lateral rigidity.

Wind Resistant Analysis of 5000m Hyperbolic Parabolic Spatial Mixed Cable Suspension Bridge

Combined with the engineering background of a 5000-meter Strait Suspension Bridge, the configuration study of the hyperbolic parabolic space cable suspension bridge was carried out, and the ANSYS finite element analysis model was established to analyze and study the structural internal force and dynamic modal characteristics. The research shows that the hyperbolic parabolic space mixed cable suspension bridge has excellent spatial stiffness and wind stability performance, its torsional frequency and torsional frequency ratio are significantly improved, the critical wind speed of flutter is greatly improved. In order to further improve the wind stability of the hyperbolic parabolic space mixed cable suspension bridge, temporary wind resistance cable measures adopted during strong typhoons are proposed. This method can ensure that the 5000-meter-level hyperbolic parabolic space mixed cable suspension bridge has the ability to withstand 120 m / s rare extreme typhoons.

Estimation of Damage Rotor Shaft of Turbogenerators with a Diode Brushless Excitation System

The damage to the rotor shafts of high-power turbo generators is estimated as a result of the resonant in-teraction between the generator and the exciter caused by the operation of the automatic excitation regulator (AER) by mathematical modeling. The analysis covers turbo generators with a capacity of 300 to 1000 MW with a diode brushless excitation system (DBES). The simulated circuit includes a turbo generator with a block transformer, a power transmission line, an exciter in the form of a reversed synchronous generator with a rotat-ing rectifier diode converter unit, a static thyristor converter, and a sub-exciter in the form of a synchronous machine with permanent magnets. When modeling the electrical part, an approach is used from the positions of its own coordinates, which ensures maximum methodological consistency of the models of the listed devices and allows directly reproducing resonant phenomena at torsional vibration frequencies with the determination of instantaneous values of currents, voltages and electromagnetic moments of the turbo generator and exciter. The mechanical system is presented taking into account the exciter and sub-exciter as a seven-mass system. AER is introduced into the mathematical model by means of transfer functions with corresponding coefficients and time constants. The control system of the thyristor converter is represented in the model by a generator of line-arly increasing signals, a body for comparing these signals with the signal from the AER and a control pulse generator. To assess the damage rate, the deformation criterion for soft and hard loads in the zone of low-cycle fatigue and the force criterion in the zone of multi-cycle fatigue were used. A comparative quantitative assess-ment of the damage in the neck of the G-E shaft line in the resonant interaction between the exciter and the generator with different automatic excitation control systems is given. The influence of attenuation of electro-magnetic transients and damping of torsional vibrations on the damage values is analyzed. The results ob-tained can be used to analyze the functioning and determine the settings of the AER.

Numerical Analysis of Rotor Dynamics of Dredge Pump Shafting

The operating condition of dredge pump is highly complicated, a technical issue is the shaft vibration problems, which has great effects on the operation safety and stability of pumps. This paper introduces a mathematical model of rotor dynamics for the dredge pump, which is used to numerically investigate critical speeds and mode shapes of the pump shaft under different bearing stiffness and damping. The effects of bearing stiffness and damping on shafting vibration characteristics are considered. The results show that the stiffness has great effect on 1st and 3rd order critical speed and the damping effect can be ignored. The stiffness has little effect on shafting axial and torsional natural frequency, but has great effect on lateral natural frequency. The analysis method of rotor dynamics dealt with in this paper can provide a foundation for the design of dredge pump shafting.

Simple models for the quick estimation of ground state hydrogen tunneling splittings in alcohols and other compounds.

Models for the quick estimation of energy splittings caused by coherent tunneling of hydrogen atoms are evaluated with available experimental data for alcohols and improvements are proposed. The discussed models are mathematically simple and require only results from routine quantum chemical computations, i.e. hybrid DFT calculation of the equilibrium geometry and the transition state within the harmonic approximation. A benchmark of experimental splittings spanning four orders of magnitude for 27 alcohol species is captured by three evaluated models with a mean symmetric deviation factor of 1.7, 1.5 and 1.4, respectively, i.e. the calculated values deviate on average by this factor in either direction. Limitations of the models are explored with alcohols featuring uncommon properties, such as an inverted conformational energy sequence, a very light molecular frame, an elevated torsional frequency, or a coupling with a second internal degree of freedom. If the splitting of either the protiated or deuterated form of an alcohol is already experimentally determined, the one of the second isotopolog can be estimated by three additional models with a mean symmetric deviation factor of 1.14, 1.19 and 1.15, respectively. It is shown that this can be achieved with a novel approach without any quantum chemical calculation by directly correlating experimental splittings of isotopologs across related species. This is also demonstrated for other classes of compounds with hydrogen tunneling, such as amines, thiols, and phenols. Furthermore, it is found that the isotope effect can even be anticipated without any further knowledge about the system solely from the size of either splitting with a mean symmetric deviation factor of 1.3. This is based on an extensive sample of 77 pairs of splittings spanning eight orders of magnitude for isotopologs of chemically diverse compounds.

A vibration analysis strategy for quantitative fracture healing assessment of an internally fixated femur with mass-loading effect of soft tissue

Vibration analysis methods have been studied to evaluate bone stiffness as a quantifiable mechanical parameter that associates with the degree of fracture healing. However, the effects of soft tissue on the bone frequency response still remain as significant challenges in successfully implementing vibration analysis-based methods as an effective clinical assessment tool. This study presents a computational investigation on the mass-loading effect of soft tissue on a fractured femur bone fixated with an intramedullary nail. An oblique fracture is modelled by a 3 mm osteotomised region, where its elastic modulus is varied from 0% to 100% of the pristine bone elastic modulus to simulate the stages of fracture bone healing. The findings indicate that the first-order torsional and second-order bending modal frequencies change significantly as the fracture region regains stiffness and the significant increase in third-order bending mode amplitude suggests the fracture stiffness has recovered over 1% of the pristine bone stiffness. Furthermore, mass-loading soft tissue does not affect the torsional mode and has negligible effects on the second-order bending modes. An additional inertia strategy is employed to determine a bone healing parameter relating to the femur stiffness by utilising the torsional modal frequency. A normalised torsional flexibility scoring procedure is then devised to evaluate the healing stages of an internally fixated femur. The subsequent results serve as an important pre-requisite to develop a quantifiable bone union measure and for future efficacy testing.

A study on the response of high aspect ratio composite wing structures due to gust load

The purpose of this study is to acquire the correlation between composite tailoring at symmetric balanced laminate and gust response on high aspect ratio wing. As a flexible structure, the high aspect ratio wing had a susceptibility from dynamic loading. Gust or turbulence load is one of dynamic loading which can have a bad impact on the wing structure. There are many incidents caused by turbulence load, hence to obtain structural response is important. Because gust load is a stiffness problem, one way to handle these effects is to make the airframe more rigid which is not favorable due to the weight penalty in the gross weight of the aircraft. Plies orientations can be an alternative to make structure stiffer without adding structural weight. From this study, plies-orientations at symmetrically laminated composite had been varied starting from 0 to 90 degrees with 5 degrees increment at the skin of the wing. Bending and torsional natural frequencies have changed where changed in play orientation as well as the vibration response from the gust load. The discrete gust cases defined in the EASA requirements are used in this study. The structural response from the gust problem had different characteristics between angle plies laminate, cross-plies laminate, and various plies orientation. As a result of this research that symmetrically balanced laminate composite with fiber direction ±15 or ±75 degrees had a good bending characteristic, nevertheless that direction have the lowest bending stiffness. Further research needs to optimize the plies orientation to design the high aspect ratio wing which has a good aeroelastic response and minimize weight.

Torsion frequency response function of a train driving wheelset

The driven wheelset is used in traction rail vehicles (locomotives, electric trains, trams, etc.) to support part of the weight of the vehicle and to drive and brake the vehicle. The wheelset consists of the axle on which two wheels and the drive gear are mounted. The torsion vibrations of the driven wheelset may be induced by the variation of the adhesion force at the level of the contact between the wheels and the track but may also result from electromechanical interactions between the electric traction motor and the motor axle. In this paper, a mechanical model of the driven wheelset consisting of a circular shaft free at both ends and three rigid discs representing the two wheels and the drive gear is considered. The modal analysis method is used to solve vibrational motion equations in steady state harmonic behavior. The frequency response function of the system and the impact of the positioning of the drive gear on the wheelset shall be highlighted. For the verification of the proposed mechanical model, the numerical results are compared with the results obtained by experimental determinations carried out on a laboratory stand.

Aerodynamic performance of Π-shaped composite deck cable-stayed bridges including VIV mitigation measures

This study systematically investigates the influence of the cross-sectional aspect ratio (B/H) and four different aerodynamic mitigation measures, i.e., the fairing, lower central stability plate, inverted L-shaped edge plate, and lower horizontal edge plate, on the performance of cable-stayed bridges, with π-typed composite deck, i.e., π section, due to vortex-induced vibrations (VIV). The study utilized wind tunnel tests and limited CFD simulations by varying bridge dimensions. First, based on a survey of existing cable-stayed bridges with the π-typed composite deck, three-section models with different aspect ratios were studied and their corresponding vibration characteristics for the vertical and torsional VIVs were analyzed. Then, the vibration suppression effects of mitigation measures with several variants in shape were investigated to determine an effective mitigation measure, i.e., with favorable aerodynamic stability, for the π section deck. The vibration suppression mechanism for three selected cases was further assessed using numerical simulation. The results show that: (a) for the π section model with the aspect ratio in the range of 9.05–11.96, increasing the ratio value will delay the onset wind speed of the vertical and torsional VIVs; (b) In the case of a low ratio of the torsional frequency to vertical bending frequency, there are often special phenomena where the vertical and torsional vibrations coexist. However, a larger aspect ratio would result in more independent vertical and torsional vibrations; (c) Regarding the vibration suppression effect, based on the limited studied cases, a small fairing can be superior to large fairings; (d) Different forms of the lower central stability plate have a good suppression effect on the vertical VIV; (e) The use of inverted L-shaped edge plate with a ​= ​23H and b ​= ​12H is identified to result in the best vibration suppression for both the vertical and torsional vibrations among the considered mitigation measures, where a and b are the size parameters of the inverted L-shaped edge plate; and (f) The lower horizontal edge plate cannot effectively improve the torsional VIV performance. This study offers guidance on the performance of composite cable-stayed bridge with the π section in isolation and equipped with mitigation measures to aid in the engineering design practice.

Analytical study on free vertical and torsional vibrations of two- and three-pylon suspension bridges via d'Alembert's principle

This study derives the differential equations of free vertical bending and torsional vibrations for two- and three-pylon suspension bridges using d'Alembert's principle. The respective algorithms for natural vibration frequency and vibration mode are established through the separation of variables. In the case of the three-pylon suspension bridge, the effect of the along-bridge bending vibration of the middle pylon on the vertical bending vibration of the entire bridge is considered. The impact of torsional vibration of the middle pylon about the vertical axis on the torsional vibration of the entire bridge is also analyzed in detail. The feasibility of the proposed method is verified by two engineering examples. A comparative analysis of the results obtained via the proposed and more intricate finite element methods confirmed the former feasibility. Finally, the middle pylon stiffness effect on the vibration frequency of the three-pylon suspension bridge is discussed. It is found that the vibration frequencies of the first- and third-order vertical bending and torsional modes both increase with the middle pylon stiffness. However, the increase amplitudes of third-order bending and torsional modes are relatively small with the middle pylon stiffness increase. Moreover, the second-order bending and torsional frequencies do not change with the middle pylon stiffness.

A Simulation-Based Method to Detect Mechanical Parameters of I-Beams and Hollow Cylinders

Abstract Impulse excitation technique is a simple, convenient, and standard nondestructive method to detect mechanical parameters (dynamic Young’s modulus and dynamic torsional modulus) that only utilizes the first-order flexural resonant frequency, first-order torsional resonant frequency, and dimensions of structures. However, the mechanical parameter detection formulas are well established only for standard uniform specimens with uniform rectangular and circular cross sections. This study suggests a simulation-based method to detect mechanical parameters. A response surface method (RSM) is introduced to design numerical simulation experiments to build up experimental formulas to detect mechanical parameters. Numerical simulations are performed by the finite element method (FEM) to obtain enough simulation data for RSM analysis. After calculations, the two relationships (experimental formulas) can finally be obtained, i.e., the relationship of the dynamic Young’s modulus and first-order flexural resonant frequency with respect to dimensions of structures and the relationship of the dynamic torsional modulus and first-order torsional resonant frequency associated with dimensions of structures. Numerical simulations and experimental investigations show that the simulation-based method can be used to detect mechanical parameters in I-beams and hollow cylinders. More generally, this method can be further developed to detect the mechanical parameters of more complex structures than standard uniform specimens using a combination of FEM simulation and RSM.

Effect of torsional component of earthquakes on response of symmetric/asymmetric buildings

Although buildings are excited by translational and rotational earthquake components, only translational components are considered in seismic loads. The effects of earthquake torsional components on building responses were studied in this work. For this purpose, the torsional component of 14 earthquakes was extracted from their translational components. Symmetric and asymmetric idealised single-storey models were analysed by considering the torsional and translational components. The models considered five different values of the uncoupled torsional frequency to uncoupled translational frequency ratio (Ω = ωθ/ωx = 1·5, 1·25, 1, 0·75, 0·5), with their lateral period varying from 0·05 to 2 s. The displacements of the left-hand side, right-hand side and centre of the diaphragm, the diaphragm rotation about the centre of mass and the base shear were studied. The results indicated that the effect of the torsional component on the non-linear responses of the building was considerable, and ignoring this effect led to an underestimation of the responses. The increase in the building's responses due to the torsional component was found to depend significantly on the value of Ω and the stiffness eccentricity. The maximum growth of the displacement of torsionally stiff and torsionally flexible buildings was 51% and 155%, respectively. The diaphragm rotation can be increased to 154% in the asymmetric systems.

Nonlinear Coupled Torsion/Lateral Vibration and Sommerfeld Behavior in a Double U-Joint Driveshaft

Abstract Many driveline systems are designed to accommodate angular misalignment by the use of flexible couplings or Universal Joints (U-Joints) which link individual shaft segments. The Sommerfeld effect is a nonlinear phenomenon observed in some rotor systems being driven through a critical speed when there is not enough power to accelerate the rotor through resonance. Previous studies have shown that rotor speed can become captured when transitioning through natural frequencies due to nonlinear interactions between a non-ideal driving input and rotor imbalance. This paper, for the first time, shows that this type of rotor speed capture phenomena can also be induced by driveline misalignment. During rotor spinup under constant motor torque, it is found that misalignment-induced rotor speed capture phenomena can occur as the shaft speed approaches ½ the first elastic torsional natural frequency. Depending on misalignment level and motor torque, the shaft speed will either dwell near this speed and then pass through, or the speed will become trapped. Here, a nonlinear rotordynamics model of a segmented driveshaft connected by two U-joints including effects of angular misalignment and load torque is developed for the study. This analysis also determines the minimum driveline misalignment angle for which the shaft speed capture phenomena will occur for a given motor torque and load torque condition.