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This work aims to improve the vibrational behaviors of the rotor-active magnetic bearings (AMB) system via proposing a new control methodology for such lateral vibrations. Accordingly, the rotor-AMB system model is modified by integrating the conventional proportional–derivative (PD) controller along with the positive position feedback (PPF) controller to the considered system. The control currents in the rotor-AMB system are designed to become a combination of two control signals: One of them is generated via the PD controller, and the other one comes from the PPF controller. Based on the suggested control method, the whole dynamical system model is derived and then analyzed by the multiple time-scale perturbation method. Then, the bifurcation diagrams of both the spinning speed and rotor eccentricity response curves are investigated before and after control. The obtained analytical results showed that the integrating of the PPF controller to the considered system could mitigate the system lateral vibration close to zero. Moreover, the system quasiperiodic motions have been stabilized after control and the sensitivity to the initial conditions has eliminated. Finally, numerical validations for the obtained analytical results are performed that illustrated an excellent agreement with the analytical ones.

This paper presents an active control method for reducing the lateral vibration transmission in a shaft-hull coupled system of submerged vehicles under the excitation of propeller forces. In this method, a 6-DOF (degree of freedom) active stern support and the local velocity feedback control strategy are employed to suppress vibration transmission from the shaft to the hull. The dynamic model of the shaft-hull system embedded with the active stern support is established with the FRF (frequency response function)-based synthesis method and the FEM/BEM (finite element method/boundary element method). The six-channel local velocity feedback control strategy is employed to suppress vibrations of the strut-hull interface. Numerical results indicate that a noticeable attenuation of vibration and sound radiation can be achieved by the active stern support. In addition, the combination control at the stern support and the thrust bearing is able to obtain better attenuation at some critical frequencies. Suppression of the mean square velocity and radiated sound power of the hull surface are observed.

In this paper, a lateral walking design force per person is proposed and compared with Imperial College test results. Numerical simulations considering the proposed walking design force which is incorporated into the neural-oscillator model are carried out placing much emphasis on the synchronization (the lock-in phenomenon) for a pedestrian bridge model with the span length of 50 m. Numerical analyses are also conducted for an existing pedestrian suspension bridge. As compared with full scale measurements for this suspension bridge, it is confirmed that the analytical method based on the neural-oscillator model might be one of the useful ways to explain the synchronization (the lock-in phenomenon) of pedestrians being on the bridge., {"references":["Dallard, P., Fitzpatrick, A. J., Flint, A., Le Bourva, S., Low, A., Ridsdill Smith, R. M. and Willford, M. ,\"The London Millennium Footbridge\", The Structural Engineer, vol.79, no.22, 2001, pp.17-33.","Fujino, Y., Pacheco, M. B., Nakamura, S. and Pennung, W., \"Synchronization of Human Walking Observed during Lateral Vibration of a Congested Pedestrian Bridge\", Earthquake Engineering and Structural Dynamics, vol.22, 1993, pp.741-758.","Matsuoka, K., \"Sustained Oscillations Generated by Mutually Inhibiting Neurons with Adaptations\", Biological Cybernetics, 52, 1985, pp.367-376.","Williamson, M., \"Neural Control of Rhythmic Arm Movements\", Neural Networks, 11, 1998, pp.1379-1394.","Yoneda, M. and Fukae, M., \"A Fundamental Study on Neural-oscillator-based Algorithm for Human-induced Lateral Vibration on Congested Pedestrian Bridges\", Journal of Structural Engineering, 54A, 2008, pp.218-227. (in Japanese)."]}

In an ultra-deep mining cable elevator, the guideway consists of several tensioned cables from the surface to thousands of meters underground. The interaction dynamics between the cage and the flexible guideway is approximate as a spring-damping system, and the cage is subject to external disturbances. Lateral vibration suppression of the mining cable elevator is addressed in this paper, where an adaptive output-feedback boundary controller is designed for coupled hyperbolic PDEs with spatially-varying coefficients and on a time-varying domain, of which the uncontrolled boundary is coupled by an ODE subject to uncertain disturbances. The asymptotic convergence to zero of the ODE state and the boundedness of the PDE states are proved via Lyapunov analysis. The performance of the proposed controller on lateral vibration suppression of a mining cable elevator is verified in the numerical simulation.

This study focuses on the nonlinear lateral vibration of drillstring in curved wells. One of the most important features of this work is that the drillstring dynamics in curved wells (including both vertical, deflecting and horizontal well structures) are modeled and presented in actual drilling engineering scale. In the proposed model, beam finite element (FE) method is employed to calculate the drillstring dynamics in curved wells. The model is solved by the generalized- α method and verified by reproduction of the field data. The model has coupled the lateral, torsional and longitudinal vibrations of the drillstring, while we only pay our attention to the nonlinear lateral vibration of drillstring in curved wells. The efficient length of lateral vibration of a field curved well is firstly proposed, and the influences of rotation speed, weight on bit (WOB), coefficient of friction (COF) and stabilizer (STB) on the lateral vibration of drillstring in curved wells are discussed.

Vehicle-based tire testing can potentially make it easier to reparametrize tire models for different road surfaces. A passenger car equipped with external sensors was used to measure all input and output signals of the standard tire interface during a ramp steer maneuver at constant velocity. In these measurements, large lateral force vibrations are observed for slip angles above the lateral peak force with clear peaks in the frequency spectrum of the signal at 50 Hz and at multiples of this frequency. These vibrations can lower the average lateral force generated by the tires, and it is therefore important to understand which external factors influence these vibrations. Hence, when using tire models that do not capture these effects, the operating conditions during the testing are important for the accuracy of the tire model in a given maneuver. An Ftire model parameterization of tires used in vehicle-based tire testing is used to investigate these vibrations. A simple suspension model is used together with the tire model to conceptually model the effects of the suspension on the vibrations. The sensitivity of these vibrations to different operating conditions is also investigated together with the influence of the testing procedure and testing equipment (i.e., vehicle and sensors) on the lateral tire force vibrations. Note that the study does not attempt to explain the root cause of these vibrations. The simulation results show that these vibrations can lower the average lateral force generated by the tire for the same operating conditions. The results imply that it is important to consider the lateral tire force vibrations when parameterizing tire models, which does not model these vibrations. Furthermore, the vehicle suspension and operating conditions will change the amplitude of these vibrations and must therefore also be considered in maneuvers in which these vibrations occur.

Modern rotating machineries require vibration suppression devices with simple structure and wide band effective vibration suppression frequency range, so a grounded nonlinear energy sink (GNES) with piecewise linear stiffness is developed to satisfy the requirements. Firstly, the structure and working principles of the GNES is explained. Then, the piecewise linear stiffness characteristic of elastic rods is analyzed and the dynamic equations for the rotor-GNES system are established, in which the rotor system is assumed to be either isotropic or anisotropic; numerical simulations are then carried out to study the vibration suppression effect of the GNES, and the wide-band vibration suppression capability of the GNES is assessed; comparison is made between the vibration suppression effect of the GNES and that of the dynamic vibration absorbers. Finally, experiments are carried out on a rotor-GNES system test platform to verify the suppression effects. The results show that the GNES is effective at suppressing vibrations in terms of both transient and steady-state vibrations within a rotor system. In the numerical simulation an optimal vibration suppression rate of 78% is achieved and in the test a rate of 68% is achieved.

In this paper, the vortex-induced vibrational characteristics and heat transfer mechanisms of three tubes with different cross-sectional shapes are numerically studied. The results show that the characteristics of vortex-induced vibration of the vertical elliptical tube and circular tube are obvious. At low flow velocities, the vortex shedding force can affect the vibrational characteristics of horizontal elliptical tube, but the effect is not obvious with increasing flow velocity. When the frequency is locked, the vibrational amplitude of the vertical elliptical tube is the largest, followed in descending order by that of the circular tube, and that of the horizontal elliptical tube. The local heat transfer coefficients of tube at different vibration time are different. High local heat transfer coefficients are produced when vortices form on local walls or—when the relative velocity between the fluid and the heat transfer wall is relatively large. The effects of vortex-induced vibration enhancement heat transfer of these three kinds of tubes are different. The vertical elliptical tube can enhance the heat transfer by 28.6%, the circular tube can enhance it by 21.3%, and the horizontal elliptical tube can only enhance it by 3.7%.

In this paper, Bouc–Wen type magnetorheological fluid damper has been used to monitor the ride quality of a prevailing rail vehicle in lateral vibrations. Modelling of the rail vehicle is done in such a manner that it has an entire 9 degrees of freedom by significant considerations of lateral, roll and yaw motions of the car body, rear, and the front chassis. 200 km/h is considered as train speed for tracks with two varying disturbances. A system consisting of multibody in VI-rail software is provided by a track input and ergo, wheel response it obtained. SIMULINK (software) is responsible for the representation of the motions of the wheel as mathematical models. Two different types of analysis are done firstly with conventional passive lateral damper and secondly with semi-active MR lateral damper in subordinate suspension. To diminish lateral vibrations, the disturbance refusal and non-stop state controller algorithms were executed to manage the damper force. Results acquired are in the form of acceleration and displacement of the center of mass of the body under consideration is done by comparing in terms of reduction indices of their vibrations. A significant improvement in the index is seen in which a semi-active lateral damper is mounted. The results show that the proposed system significantly improves both, the vibration attenuation ability and the ride quality of the vehicle.

Mechanical behavior of oilwell drillstring coming at the motions of penetrating rock is associated with drilling safety and wellbore quality. A poor performance can be attended by elastic stability loss in a slender drillstring exerting undesired buckling and vibration phenomena in the working process. Devoting to investigating the dynamic buckling behavior is an efficient way to avoid fatigue failure of the drillstring components and enhance drilling rate. A dynamic analysis of the buckling behavior of the entire column considering violent lateral vibrations is presented as a result available. Analytical equations of the drilling system are integrated numerically with finite element method. A virtual contact element implemented between the drillstring and the borehole, in conjunction with Hertzian contact assumption, gives the direct access to calculate the contact force and positions. Lateral deflection, critical length and the effects of drilling parameters and stabilizer on the buckling deformation are captured to experience the realistic buckling response of a typical drillstring in a vertical well. Simulation results indicate that spiral pitch and wave numbers of a nonlinear spiral shape prevailing in the lower zone of drillstring are deeply associated with the cutting force at the bit. Improving a drillstring behavior performance in a real oilfield is observed that this model can assist in evaluating the properties of the working security and buckling resistance with complex boundary conditions.

Lateral vibration modeling of certain BHA (bottomhole assembly) designs has shown great sensitivity to the proximity of stabilizer blades. In a previous paper, the BHA chatter vibration mode was presented, including the basic theory and three field examples. In each case, lower drilling rates were associated with higher levels of BHA dynamic dysfunction as determined using a lateral vibration model. One case clearly illustrated a reduction in effective weight applied to the bit, determined using bit dull grade results. This paper will further explore the mechanisms in which BHA dynamic contact forces can act to reduce the effective weight on bit. The contact forces that push a stabilizer blade to be constrained within a borehole include both static and dynamic components. The dynamic forces are difficult to visualize as they are generated by the BHA in motion, and a well-formulated dynamic model is required to evaluate these forces. In drilling, we simply see the effects as worn and damaged drillstring components. A frequency-domain BHA lateral vibration model represents lateral vibration flexural waves propagating in the BHA. This model can be used to calculate dynamic side forces acting at stabilizer and LWD tool blade contacts with the borehole for reference excitation forces. These contact forces may be strong functions of rotary speed and BHA contact spacing, and they typically create a non-trivial level of residual drag that impedes getting weight to bit. The physics of dynamic contact forces are similar in some respects to static contact forces. Superposition of the dynamic modes illustrate that, although an individual component may vanish momentarily, additional modes and phases can constructively combine such that the total force summation does not vanish. The net result is that dynamic forces can generate significant lateral forces that are similar to static contact forces. Static effects are known to impede application of weight to bit in deviated and horizontal wells, and small ledges can prevent a stabilizer blade from moving forward. Dynamic effects from improper stabilizer placement are potent sources of lateral dysfunction that can have a similar effect. BHA dynamics have the potential to both create borehole irregularities and resist forward motion resulting from contact forces between drilling tools and the borehole.

This paper presents a nonlinear dynamic analysis approach; its aim is to study the effect of the transition curve on the dynamic behavior of the superconducting magnetic levitation UAQ4 experimental bogie. The levitation working principle is based on the magnetic interaction between bulk high-temperature superconductors set on the vehicle and permanent magnets distributed along the track. Numerical simulations of a suspended bogie were conducted by using a three degrees-of-freedom model supported by experiments. First of all, two different mixed rectilinear/curvilinear magnetic track path types, one with transition curves between straight lines and a circular curve and the other without any transition curves between straight lines and a circular curve, were considered and analyzed. Then, a series of parametric dynamic analyses were performed in order to calculate the bogie lateral dynamic response by varying the radius of the circular curve, the length of the transition curves, and the running speed. The results prove that the addition of a right transition curve between straight lines and the circular curve reduces the amplitude of the lateral vibrations of the bogie by several factors, and it consequently allows the bogie's critical running speed to increase over the path. Finally, the results were synthesized in an abacus in order to evaluate the design value of the transition curve length according to the system input parameters.

The nonlinear dynamic behavior of a viscoelastic beam in axially variable motion under time delay is studied. Considering that the axial velocity pulsation and radial tension change periodically with time under the action of time delay, the viscous damping and finite support stiffness are taken into account, and the viscoelastic constitutive relationship adopts Kelvin model. A mathematical model of lateral vibration of an axially moving viscoelastic beam with changes in axial velocity and tension under time delay is established, and a partial differential-integral control equation describing the lateral nonlinear vibration of an axially moving beam is given. Based on the Galerkin truncation method, the control equations established based on the mechanical model are discretized, so that the direct multi-scale method obtains the numerical solution of the lateral nonlinear vibration of the axially moving beam under the action of time delay, and determines the nonlinear dynamic behavior of the system under the action of time delay. By analyzing the numerical solution of the vibration displacement and velocity at the midpoint of the beam, the whole process of the average velocity of the axially moving structure along the axis, the amplitude of the disturbance tension and the change of the viscoelastic coefficient is simulated. It provides a numerical theoretical basis for the study of the nonlinear dynamic behavior of axially moving beams under time delay. Through the research in this article, the introduction of time delay is studied, and the time delay is used to analyze the axial force that changes along the radial direction of the beam caused by the speed pulsation, and the theoretical framework for nonlinear vibration analysis of the axially moving viscoelastic beam is constructed to expand the time delay. The application scope of the nonlinear vibration theory and nonlinear dynamics theory, the development and improvement of the approximate analysis and numerical solution of the nonlinear continuum (especially the gyro body) under the action of time delay, to provide a theoretical basis for the analysis and design of the corresponding engineering system and technical reserves.

Lateral vibration modeling of certain BHA (bottomhole assembly) designs has shown great sensitivity to the proximity of stabilizer blades. This paper will explore the nature of the vibrational dysfunction that we call BHA chatter. A frequency-domain model that has been field-proven shows how this dysfunction occurs, its rotary speed dependence, and mitigation methods and results. A frequency-domain BHA lateral vibration model will be used to illustrate the role of the nodal point constraint in the determination of the dynamic side forces acting at stabilizer and LWD tool blade borehole contacts. These contact forces may be strong functions of rotary speed and BHA contact spacing, especially if the spacing is close. The relationship between the dynamic contact forces and vibration index model results will be described in relation to the solution to the lateral vibration model. Examination of the dynamic contact side forces associated with these vibration indices reveals the nature of the dysfunction that the indices represent. The contact forces that push a stabilizer blade to be constrained within a borehole include both static and dynamic components. The static forces are well understood. However, the dynamic forces are difficult to visualize as they are generated by the BHA in motion, and a well-formulated dynamic model is required to evaluate these forces. Dynamic dysfunction at a particular location along the BHA is revealed by examining the underlying states of a dynamic model. Charts of the dynamic contact side force quantify the amount of dysfunction. Vibration indices comprising the integrated, length-averaged bending strain energy provide a good summary of the overall BHA response that is particularly useful in BHA design investigations, but it is the dynamics of the individual contact points that drive the dynamic response of the model. Examples of field BHA designs illustrate both good and bad drilling results, generally in agreement with expectations based on the modeling. The literature is full of references to the whirl mode of lateral vibrations. This is commonly accepted. Chatter is a different mode that occurs primarily in response to the spacing of blade contacts. It is difficult for two blades that are close together to simultaneously serve as nodal points. A lateral vibration wave propagating along the BHA may generate alternating wall contact at the two blades, causing a dynamic chatter dysfunction.