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This paper is dealing with the lateral vibration of simply supported beam induced by one crossing pedestrian. Effects of pedestrian on the structural vibration was simplified by deterministic, stationary, periodic forces, which were placed at the most efficient spot on the structure. A new approach to modeling of excitation of lateral vibration was also introduced. This model is based on the "real" trajectory of pedestrian's centroid and it also reflects fact, that the pedestrian is changing his position in time. Numerical solution of this problem was done by Newmark integration method with using modal decomposition technique.

Superconducting magnetically levitated transportation system (JR Maglev) has been studied in Japan. The electrodynamic suspension is used for levitation and guidance. Gap control is not required for this suspension system, but the damping factor of the system is small. The damper coil system is considered to increase damping of the levitation system. Running simulation of the bogie is undertaken when the bogie passes the guideway displacement. The damper coil decreases the oscillation of the bogie. However, the energy for running is increased because of the weight of the damper coil. By changing the shape of the damper coil, the weight of the damper coil becomes half of the conventional one. From the results, the current of damper coil increases. When weight-reduced coil is used in passive damper mode, damping factor is small. But in the semi-active mode, damping factor increases. Electromagnetic analysis has been undertaken. Improvements of oscillations of the bogie with the weight-reduced damper coils are shown. The convergence time is improved 58.0% in lateral displacement and 57.3% on rolling angle by the weight-reduced damper coils.

In this paper, a psychophysical experiment is designed and setup to perform the comparison between lateral and normal ultrasonic vibration for friction modulation on haptic devices at the same vibration amplitudes. Thanks to a simple analytical modelling relying on mechanical contact, the results obtained are explained. A parametric analysis of this comparison is then performed.

For the problem of relatively severe lateral vibration found in the vertical electrodynamic shaker experiment, an electromechanical coupling dynamic model of the electrodynamic shaker considering low-frequency lateral vibration is proposed. The reason and mechanism of the lateral vibration is explained and analyzed through this model. To establish this model, an electromagnetic force model of overall conditions is firstly built by fitting force samples with neural network method. The force samples are obtained by orthogonal test of finite element simulation, in which five factors of the moving coil including current, vertical position, flipping eccentricity angle, radial translational eccentric direction and distance are considered. Secondly, a 7-dof dynamic model of the electrodynamic shaker is developed with the consideration of the lateral vibration of the moving system. To obtain the transfer function accurately, the stiffness and damping parameters are identified. Finally, an electromechanical dynamic model is established by coupling the force model and the 7-dof dynamic model, and it is verified by experiments. The coupling model proposed can be further used for the control and optimization of the electrodynamic shaker.

An active stern support is proposed to suppress lateral vibration transmission in the shaft-hull system of underwater vehicles subjected to the excitation of propeller forces. The active stern support uses six active struts instead of a common bearing support to suppress vibration transmission from the shaft to the hull. The dynamic model of a shaft-hull system embedded with the active stern support is established on the Timoshenko beam theory and the FRF (frequency response function)-based synthesis method. Based on this model, the characteristics of vibration transmission in the system and the feasibility of active control are analyzed. An adaptive control algorithm is constructed and the performance of vibration suppression is evaluated. An experimental system is built as well to verify the effectiveness of the control method. Numerical and experimental results show that the active stern support is able to suppress the transmission of lateral vibration induced by the propeller forces, and the attenuation of the normal vibration of the hull structure can be achieved.

This paper tends to use a novel perspective to suppress the lateral vibration of high-speed trains (HST), i.e., making use of the periodicity of lateral dynamics. First, the dynamics of a quarter-vehicle model are analysed and modelled. Next, a backstepping controller is designed to suppress the lateral vibration of car body based on a 3-degree-of-freedom (3-DOF) simulation model. And lateral ride comfort improvements are achieved by implementing such control strategy in comparison with passive system. Finally, under the framework of back-stepping design, a repetitive learning control (RLC) scheme is presented to reduce the lateral vibration by periodic tracking control. The learning convergence is proved rigorously in a Lyapunov way and the simulation results demonstrate the control superiority compared with the backstepping controller.

Drilling is one of the most costly and risky activities in oil and gas reservoir exploration and field development. A portion of this high cost is related to unwanted vibrations of the drill string. Assumed as the primary cause of many problems, drill string vibration is an ongoing challenge for drillers. In this paper, the lateral vibration characteristics of drill string in the highly deviated well are quantitatively analyzed and the influence of different drilling parameters on lateral vibration are fully evaluated. In order to study the lateral vibration characteristics of drill string in the highly deviated wells under different drilling parameters, a drill string dynamics simulation apparatus was built according to the similarity theory, and the vibration response in different directions was measured. The lateral vibration frequency of drill string was calculated by Fast Fourier Transform (FFT) and the non-dimensional frequency was defined to quantitatively evaluate the relationship between the vibration frequency and the excitation frequency. Moreover, the average acceleration was defined to evaluate the movement of the drill string in a period of time. The results indicate that rotary speed is the determining factor of drill string's lateral vibration. The lateral vibration frequency is equal to the excitation frequency and the average acceleration generally increases at a relatively low rotary speed. As the rotary speed continues to increase, when it exceeds a certain critical point, the lateral vibration frequency doubles and the average acceleration encounters a shape increase. In addition, with the increase of the weight on bit (WOB), the vibration frequency and the average acceleration keep stable, but the phenomenon of doubling the vibration frequency is suppressed.

As a first endeavor, the present work deals with the primary resonance of lateral vibration of an Euler–Bernoulli beam with a sliding end and under both uniformly distributed heating and harmonic loads. The sliding end is subject to a pair of adjustable normal force and frictional force such that it is initially at a stick status, but may be slightly slipping due to the thermal expansion of the beam until it contacts a stop, i.e., the bound of the clearance. Moreover, this sliding end may also be slipping during the lateral vibration when the vibration amplitude is larger than a critical value. Firstly, based on the nonlinear relation between strain and displacement, a set of partial differential equations of the beam and the axial boundary condition for the sliding end are derived by utilizing Hamilton׳s principle, where both frictional force and temperature-dependent properties of material are taken into consideration. Then, Galerkin׳s approach is employed to simplify the partial differential equations to a set of ordinary differential equations. Subsequently, the average approach is used to determine the steady-state primary resonance. Finally, the analytical solutions are well verified through numerical simulations and the influences of system parameters, such as temperature rise and normal force, on the primary resonance of lateral vibration of the beam are discussed. The study shows that it is possible to adjust the primary resonance of lateral vibration of the heated beam with an axial stick–slip–stop boundary via the analytical solutions, which involve the normal force, the clearance and the temperature rise.

In this paper, a dynamic analysis model has been established to analyze lateral vibration of marine riser in installation. The governing differential equation has been deduced by variation method. The general formula of riser lateral dynamical response has also been obtained through analyzing the analysis model and the boundary conditions. In this model, the riser is regarded as a beam suspended in the floating drilling platform (ship) and subjected to the axial force and the lateral forces changes with time and water depth (WD). Finally, the expression of the lateral vibration has been obtained and the maximum lateral vibration displacement variations with WD, riser size, weight of Blow out preventers and Lower Marine Risers Package (BOPS/LMRP), wave height and wave period have also been discussed.

Manipulators used for the transportation of large panel-shape payloads often adopt long and slender links (or forks) with translational joins to carry the payloads. As the size of the payload increases, the length of the links also increases to hold the payload securely. The increased length of the link inevitably amplifies the effect of the flexure in the link. Intuitively, the translational motion of the link in its longitudinal direction should have no effect on the lateral vibration of the link because of the orthogonality between the direction of the translational motion and the lateral vibration. If, however, the link was flexible and translated horizontally (perpendicular to the gravitational field) the asymmetric deflection of the link caused by gravity would break the orthogonality between the two directions, and the longitudinal motion of the link would excite lateral motion in the link. In this paper, the lateral oscillatory motion of the flexible link in a large-scale solar cell panel handling robot is investigated where the links carry the panel in its longitudinal direction. The Newtonian approach in conjunction with the assumed modes method is used for derivation of the equation of motion for the flexible forks where non-zero control force is applied at the base of the link. The analysis illustrates the effect of longitudinal motion on the lateral vibration and dynamic stiffening effect (variation of the natural frequency) of the link due to the translational velocity. Lateral vibration behavior is simulated using the derived equations of the motion. A robust vibration control scheme, the input shaping filter technique, is implemented on the model and the effectiveness of the scheme is verified numerically.

The coupled longitudinal-lateral vibration of a shaft-plate system and its suppression by means of a feedback control scheme are discussed. A simplified model of the system is established through synthesis of frequency response functions (FRFs) and verified with the finite element method (FEM). This analytical model describes the coupled longitudinal-lateral vibration of the system induced by longitudinal periodic excitation at the free end of the shaft. Based on this model, vibration control via longitudinal actuation on the shaft and active vibration cancellation are studied. The active control scheme is based on an adaptive feedback scenario and a novel mechanism of adaptation of the controller’s gain, which is proposed for time-varying dynamics induced by the variation of the axial spring stiffness. Simulation results have demonstrated that the control scheme is effective in attenuating vibration of the system. Furthermore, axial actuation on the shaft is able to cancel the effect of the longitudinal disturbance acting at the free end of the shaft and consequently reduces the internal forces as well as the vibration in the plate. However, deviation of the actuation force from the shaft axis will deteriorate control of the lateral vibration and sufficiently small deviation needs to be guaranteed.

The lateral excessive sway motion caused by pedestrian traffic has attracted great public attention in the past decades years. However, the theories about exploring the effect of pedestrian on the lateral dynamic properties of structure are scarce. The new contribution of this paper is that a new pedestrian-structure system is proposed for exploring the effect of human on structural dynamic properties based on a sway assumption. Study shows that pedestrian deteriorates the natural frequency of structure and improves structural damping. The influence tendencies of pedestrian on structure can be supported by measurements. The further parametric study shows that the changes of human dynamic parameters have some evident impacts on structural dynamic performances. For example, the increase of leg damping can trigger an improvement of structural damping capacity. In addition, the walking step frequency closing structural harmonic natural frequency can incur the worst response. The increase of step width deteriorates lateral vibration and structural frequency but can slightly improve structural damping. One of essential reasons influencing structural lateral dynamic properties is the dynamic human system including body mass, damping, stiffness, and its motion behavior such as step frequency. This theory is proposed to analyze how pedestrian alters the lateral dynamic performances on those sensitive structures such as the footbridges or stadium bleachers. For example, how the variation of step width influences the change of natural frequency of structure?

The lack of damping of radial gas bearings leads to high vibration levels of a rotor supported by this type of bearing when crossing resonant areas. This is even more relevant for flexible rotors, as studied in this work. In order to reduce these high vibration levels, an active gas bearing is proposed. The control action of this active bearing is selected based on two different strategies: a simple proportional integral derivative controller and an optimal controller. Both controllers are designed based on a theoretical model previously presented. The dynamics of the flexible rotor are modelled aided by the finite element method and the rotor–fluid interaction in the gas bearing is included using the solution of a modified version of the Reynolds equation for compressible fluids, taking into account the piezoelectrically controlled jet action. Performance and accuracy of both model-based controllers are compared against experimental results, showing good agreement. Theoretical and experimental results show a significant increase in the damping ratio of the system, enabling the flexible rotor to run safely across the critical speeds and up to 12,000 rev/min, i.e. 50 percent over the second critical speed without any instability problems.

This paper presents the results of forced and free horizontal vibration tests conducted on 9.0-m long and 324-mm shaft diameter single and double-helix large-capacity helical piles as well ...

The dynamic response of an offshore pile in saturated soil subjected to lateral harmonic loading is theoretically investigated by considering the dynamic pile-water interaction. The governing equation of water is solved based on the separation of variable method, and the analytical expression of the hydrodynamic force applied on the pile is then obtained. Based on the continuous conditions at the pile-soil interface and pile-water interface, the analytical solution of the dynamic impedance of the offshore pile is derived by using transfer matrix method. To verify this solution, the dynamic impedance obtained for a cylinder in water is compared with that of a partially embedded pile. Based on this solution, the effect of hydrodynamic pressure and other parameters on the dynamic response of offshore piles is investigated. The results show that the analytical model ignoring the hydrodynamic force applied on the pile misestimates the impedance of the pile in the high frequency range.

A new flexible-pinion-shaft rotor model is presented to predict the response of the pinion shaft of an integrally geared compressor (IGC). The motion of the pinion shaft is driven by: (1) its own imbalance and (2) the axial reaction force developed by relative axial motion at the thrust collar (TC) that connects it to the pinion. The axial reaction force at the TC arises because of the relative axial motion between the pinion shaft and the bull gear (BG) at the overlapping area of the TC. The relative axial motion arises because of: (1) absolute axial motion of the pinion (assumed to be a rigid body), (2) pitch and yaw motion of the pinion at the TC, and (3) absolute axial motion of the BG at the TC overlap area. Because the axial reaction force acts at a radial distance from the mass center of the TC disk, it creates moments that couple the relative axial motion of the pinion and BG shafts to the radial motion of the pinion. The present model includes the local flexural stiffness of the BG. Excitation for the model is provided by: (1) runout from the BG at its running speed, Ω, acting through the axial reaction force of the TC, (2) runout from the pinion at its running speed, ω, acting through the axial reaction force of the TC, and (3) pinion TC mass imbalance at ω. Measured axial runouts of the BG and TC were taken from a test rig at the authors’ laboratory. Predictions for the TC oil-film axial stiffness and damping come from a proprietary Reynolds equation solution to the TC oil-film. The local axial stiffness of the BG at the overlap area was obtained from a finite element analysis of the authors’ test rig. The base rotordynamic model for the pinion was provided for a production IGC pinion by an IGC manufacturer including the bearings and structural dynamics model. Waterfall plots are presented from the model’s predictions of radial motion at the IGC’s Stage 1 compressor impeller. The response is dominated by synchronous response at the pinion speed, ω, and tracking subsynchronous response at the BG speed, Ω. The response at ω comes from the pinion’s imbalance, not the pinion runout at the TC. The response at Ω comes from the BG runout acting across the TC. The IGC manufacturer’s representatives state that predictions from the model are consistent with measurements from real IGCs, particularly in regard to the presence (and amplitudes) of tracking subsynchronous response amplitudes at the BG frequency. Obviously, more detailed models can be developed for the rotordynamics of IGCs, but the authors feel that this relatively simple, one-rotor model, is adequate to predict the observed tracking phenomena in IGCs. The analysis can be produced by modifying an existing rotor code or by simply downloading the rotor’s [M], [K], and [C] matrices over a range of speeds and then using MATLAB or similar codes.

Excessive vibration of temporary grandstand owing to crowd has lateral rhythmic motions can cause human in panic, which attracted increasing attention in recent years. This paper focuses on experiments that a temporary grandstand occupied 20 participants is oscillated by a shaking table with a series of random waves and induced by crowd with rhythmic swaying motions at lateral direction, respectively. And then a series of vibration perception questionnaires about crowd reaction are obtained. Evaluation of annoying level derives in concept of degree of membership and annoying rate method is proposed, then the human health risk of vibration serviceability of temporary grandstand is assessed with acceleration vibration dose value(VDV). From these results it is clear that standing crowd is more tolerant to vibration than seated crowd. The measured vibrations generated by crowd activities on temporary grandstand can cause panic in crowd. New relationship between the annoyance rate and structural acceleration VDV at logarithmic coordinate is proposed. The findings of this study can be utilized to manage the vibration of temporary grandstand and assess the human health risk.