Dynamic modeling of ultra-precision fly cutting machine tool and the effect of ambient vibration on its tool tip response

The dynamic performances of an ultra-precision fly cutting machine tool(UFCMT)has a dramatic impact on the quality of ultra-precision machining.In this study,the dynamic model of an UFCMT was established based on the transfer matrix method for multibody systems.In particular,the large-span scale flow field mesh model was created;and the variation in linear and angular stiffness of journal and thrust bearings with respect to film thickness was investigated by adopting the dynamic mesh technique.The dynamic model was proven to be valid by comparing the dynamic characteristics of the machine tool obtained by numerical simulation with the experimental results.In addition,the power spectrum density estimation method was adopted to simulate the statistical ambient vibration excitation by processing the ambient vibration signal measured over a long period of time.Applying it to the dynamic model,the dynamic response of the tool tip under ambient vibration was investigated.The results elucidated that the tool tip response was significantly affected by ambient vibration,and the isolation foundation had a good effect on vibration isolation.

DYNAMIC RESPONSE OF SHAPE MEMORY ALLOY SYSTEM AND ITS VIBRATION CONTROL

A hysteric model is represented to describe the dependence of restoring force on deformation of pseudoelastic SMA.The dynamic response of the system is investigated by means of mathematical models.The result shows that this kind of vibration absorbing system can suppress vibration with large amplitude effectively.Furthermore,the vibration absorbing system can work in optimum state by adjusting temperature and using piezoelectric sensors and actuators.

NONLINEAR DYNAMIC RESPONSE AND ACTIVE VIBRATION CONTROL OF THE VISCOELASTIC CABLE WITH SMALL SAG

The problem considered is an initially stressed viscoelastic cable with small sag. The cable material is assumed to be constituted by the hereditary differential type. The partial differential equations of motion is derived first. Then by applying Galerkin's method, the governing equations are reduced to a set of third order nonlinear ordinary differential equations which are solved by Runge-Kutta numerical integration procedures. Only after the transverse vibration of the plane is considered and the nonlinear terms are neglected, can the nonlinear ordinary differential equations be expressed as a continuous state equation in the state space. The matrix of state transition is approximated stepwise by the matrix exponential; in addition, the state equation is discretized to a difference equation to improve the computing efficiency. Furthermore, an optimal control of procedure system based on the minimization of a quadratic performance index for state vector and control forces is developed. Finally, the effect of dynamic response of the cable, which is produced by viscoelastic parameters, is testified by the research of digital simulation.

Dynamic Response of Two-Degree-of-Freedom Riserless Drill String for Vortex-Induced Vibration Suppression and Enhancement

The mechanical behavior,dynamic evolution,and flow-field distribution of a two-degree-of-freedom riserless drill string were simulated numerically by using FLUENT fluid simulation software with the user-defined function embedded.The rotation angular velocities before and after the critical rotation angular velocity were used as independent variables,and the reduced velocity range was 3-14.Fluid-structure coupling was realized based on the dynamic overset grid and the SST k-ωturbulence model.Results reveal that the dynamic response of the riserless drill string was considerably affected by rotation and flow velocity,which are coupled with each other.The cross-flow average dimensionless displacement increased with the rotation angular velocity,and rotation considerably enhanced the in-line maximum average dimensionless displacement.However,the cross-flow amplitude caused by vortex-induced vibration was suppressed when the rotation angular velocity reached a certain value.The in-line and cross-flow frequencies were the same,thereby causing the trajectory to deviate from the standard'figure-eight'shape and become a closed circle shape.The vortex did not fall behind the cylinder at low reduced velocity with high-rotation angular velocity,and the structure of the near-wake vortex remained U-shaped.The wake of the cylinder was deflected along the cross-flow direction,thereby leading to vibration asymmetry and resulting in increased vibration instability and disordered vibration trajectories,especially at high-rotation angular velocities.

Dynamic Response Analysis of A 5 MW NREL Wind Turbine Blade under Flap-Wise and Edge-Wise Vibrations

A wind turbine is subjected to a regime of varying loads.For example,each rotor revolution causes a complete gravity stress reversal in the low-speed shaft,and there are varying stresses from the out-of-plane loading cycle due to fluctuating wind load.Consequently,wind turbine blade design is governed by fatigue rather than ultimate load considerations.Previous studies have adopted many different beam theories,using different techniques and codes,to model the National Renewable Energy Laboratory(NREL)5MWoffshore wind turbine blade.There are differences,from study to study,in the free vibration results and the dynamic response.The contribution of this study is to apply the code written by the authors to the different beam theories used with the aim of comparing the different beam theories presented in the literature and that developed by the authors.This paper reports the investigation of the effects of deformation parameters on the dynamic characteristics of the NREL 5 MW offshore wind turbine blades predicted by the different beam theories.The investigation of free vibrations is a fundamental step in the analysis of structural dynamics,and this study compares different computational structural methods and investigates their effect on the predicted dynamic response.The modal characteristics of every model examined have been combined with strip theory to determine the dynamic response of the blade.

Ice-Induced Vibrational Response of Single-Pile Offshore Wind-Turbine Foundations

Important challenges must be addressed to make wind turbines sustainable renewable energy sources.A typical problem concerns the design of the foundation.If the pile diameter is larger than that of the jacket platform,traditional mechanical models cannot be used.In this study,relying on the seabed soil data of an offshore wind farm,the m-method and the equivalent embedded method are used to address the single-pile wind turbine foundation problem for different pile diameters.An approach to determine the equivalent pile length is also proposed accordingly.The results provide evidence for the effectiveness and reliability of the model based on the equivalent embedded method.

Dynamic Response of Tensile Membrane Structure under Coupling Effect of Wind and Rain

Because of the small stiffness and high flexibility, the tension membrane structure is easy to relax and damage or even destroy under the action of external load, which leads to the occurrence of engineering accidents. In this paper, the damped nonlinear vibration of tensioned membrane structure under the coupling action of wind and rain is approximately solved, considering the geometric nonlinearity of membrane surface deformation and the influence of air damping. Applying von Karman’s large deflection theory and D’Alembert’s principle, the governing equations are established for an analytical solution, and the experimental results are compared with the analytical results. The feasibility of this method is verified, which provides some theoretical reference for practical membrane structure engineering design and maintenance.

Analysis of the Dynamic Response of a Shield Tunnel in Soft Soil Under a Metro-Train Vibrating Load

This paper concerns the impact of an operating metro train on the structure of a shield tunnel lining and its soft foundation. An elastoplastic 3D dynamic finite difference model was established by using the FLAC3D numerical soft- ware. By fully considering the joints, the A-B-K segments and the soft stratum, the dynamic response of the shield tunnel buried in thick, soft soil under the vibrating load induced by a metro train was numerically simulated. The simulation result, for which the joint was considered, was compared with the result when the joint was not considered. The results show that an operating metro train induces a significant dynamic response in the structure of the lining of the shield tunnel and its soft foundation. The severe dynamic response zones of the lining structure are largely distributed in the range of the lower half of the segment-ring and the nearer to the bottom of the segment-ring, the more severe the response. Of two horizontally symmetric, corresponding places on the segment lining, the one near the joint is more severe in its dynamic response than that of the one far from the joint; the nearer the zone of the foundation soil to the lower half of the seg- ment-ring, the more severe the dynamic response. The maximum shear strain of the foundation soil takes place near the joint between two normal segments at the bottom. The dynamic response influenced by joints is more severe than the response not influenced by joints, showing that the non-joint assumption is somewhat impractical.

The Effect of Internal Fluid on the Response of Vortex-Induced Vibration of Marine Risers

Based on Iwan′s wake oscillator model developed with the classical van der Pol equation, the differential equation for the response of the vortex-induced vibration (VIV) of the riser considering the effect of the internal flowing fluid and the external marine environmental condition is derived. The effect of the internal flowing fluid on the response of VIV of the riser is studied by means of the Finite Element Method. The results show that the effect of the internal fluid velocity on the VIV of the riser is strong when the natural frequency of the riser is close to the vortex shedding frequency. In addition, the increase of the top tension can decrease the sensitivity of the riser to the internal fluid velocity.

Effects of topography on dynamic responses of single piles under vertical cyclic loading

This paper describes model tests of single piles subjected to vertical cyclic compressive loading for three kinds of topography: sloping ground, level ground, and inclined bedrock. Comprehensive dynamic responses involving cyclic effects and vibration behaviours are studied under various load combinations of dynamic amplitude, mean load,frequency and number of cycles. Test results show that permanent settlement can generally be predicted with a quadratic function or power function of cycles.Sloping ground topography produces more pronounced settlement than level ground under the same load condition. For vibration behaviour,displacement amplitude is weakly affected by the number of cycles, while load amplitude significantly influences dynamic responses. Test results also reveal that increasing load amplitude intensifies nonlinearity and topography effects. The strain distribution in a pile and soil stress at the pile tip are displayed to investigate the vibration mechanism accounting for sloping ground effects. Furthermore, the dynamic characteristics among three kinds of topography in the elastic stage are studied using a three-dimensional finite method. Numerical results are validated by comparing with experimental results for base inclination topography. An inclined soil profile boundary causes non-axisymmetric resultant deformation, though a small difference in vertical displacement is observed.

Steady-state responses of a belt-drive dynamical system under dual excitations

The stable steady-state periodic responses of a belt-drive system with a one-way clutch are studied. For the first time, the dynamical system is investigated under dual excitations. The system is simultaneously excited by the firing pulsations of the engine and the harmonic motion of the foundation. Nonlinear discrete-continuous equations are derived for coupling the transverse vibration of the belt spans and the rotations of the driving and driven pulleys and the accessory pulley. The nonlinear dynamics is studied under equal and multiple relations between the frequency of the fir- ing pulsations and the frequency of the foundation motion. Furthermore, translating belt spans are modeled as axially moving strings. A set of nonlinear piecewise ordinary differ- ential equations is achieved by using the Galerkin truncation. Under various relations between the excitation frequencies, the time histories of the dynamical system are numerically simulated based on the time discretization method. Further- more, the stable steady-state periodic response curves are calculated based on the frequency sweep. Moreover, the convergence of the Galerkin truncation is examined. Numer- ical results demonstrate that the one-way clutch reduces the resonance amplitude of the rotations of the driven pul- ley and the accessory pulley. On the other hand, numerical examples prove that the resonance areas of the belt spans are decreased by eliminating the torque-transmitting in the opposite direction. With the increasing amplitude of the foun- dation excitation, the damping effect of the one-way clutch will be reduced. Furthermore, as the amplitude of the firing pulsations of the engine increases, the jumping phenomena in steady-state response curves of the belt-drive system with or without a one-way clutch both occur.

Bifurcation and dynamic response analysis of rotating blade excited by upstream vortices

A reduced model is proposed and analyzed for the simulation of vortexinduced vibrations （VIVs） for turbine blades. A rotating blade is modelled as a uniform cantilever beam, while a van der Pol oscillator is used to represent the time-varying characteristics of the vortex shedding, which interacts with the equations of motion for the blade to simulate the fluid-structure interaction. The action for the structural motion on the fluid is considered as a linear inertia coupling. The nonlinear characteristics for the dynamic responses are investigated with the multiple scale method, and the modulation equations are derived. The transition set consisting of the bifurcation set and the hystere- sis set is constructed by the singularity theory and the effects of the system parameters, such as the van der Pol damping. The coupling parameter on the equilibrium solutions is analyzed. The frequency-response curves are obtained, and the stabilities are determined by the Routh-Hurwitz criterion. The phenomena including the saddle-node and Hopf bifurcations are found to occur under certain parameter values. A direct numerical method is used to analyze the dynamic characteristics for the original system and verify the va- lidity of the multiple scale method. The results indicate that the new coupled model is useful in explaining the rich dynamic response characteristics such as possible bifurcation phenomena in the VIVs.

Effect of cross-wind on spatial vibration responses of train and track system

By taking cross-wind forces acting on trains into consideration, a dynamic analysis method of the cross-wind and high-speed train and slab track system was proposed on the basis of the analysis theory of spatial vibration of high-speed train and slab track system. The corresponding computer program was written by FORTRAN language. The dynamic responses of the high-speed train and slab track under cross-wind action were calculated. Meanwhile, the effects of the cross-wind on the dynamic responses of the system were also analyzed. The results show that the cross-wind has a significant influence on the lateral and vertical displacement responses of the car body, load reduction factor and overturning factor. For example, the maximum lateral displacement responses of the car body of the first trailer with and without cross-wind forces are 32.10 and 1.60 mm, respectively. The maximum vertical displacement responses of the car body of the first trailer with and without cross-wind forces are 6.60 and 3.29 mm, respectively. The maximum wheel load reduction factors of the first trailer with and without cross-wind forces are 0.43 and 0.22, respectively. The maximum overturning factors of the first trailer with and without cross-wind forces are 0.28 and 0.08, respectively. The cross-wind affects the derailment factor and lateral Sperling factor of the moving train to a certain extent. However, the lateral and vertical displacement responses of rails with the crnss-wind are almost the same as those without the cross-wind. The method presented and the corresponding computer program can be used to calculate the interaction between trains and track in cross-wind.

Wind-induced responses of super-large cooling towers

Traditional gust load factor(GLF)method,inertial wind load(IWL)method and tri-component method(LRC+IWL)cannot accurately analyze the wind-induced responses of super-large cooling towers,so the real combination formulas of fluctuating wind-induced responses and equivalent static wind loads(ESWLSs)were derived based on structural dynamics and random vibration theory.The consistent coupled method(CCM)was presented to compensate the coupled term between background and resonant response.Taking the super-large cooling tower(H=215 m)of nuclear power plant in Jiangxi Province,China,which is the highest and largest in China,as the example,based on modified equivalent beam-net design method,the aero-elastic model for simultaneous pressure and vibration measurement of super-large cooling tower is firstly carried out.Then,combining wind tunnel test and CCM,the effects of self-excited force on the surface pressures and wind-induced responses are discussed,and the wind-induced response characteristics of background component,resonant component,coupled term between background and resonant response,fluctuating responses,and wind vibration coefficients are discussed.It can be concluded that wind-induced response mechanism must be understood to direct the wind resistant design for super-large cooling towers.

Dynamic Response of Fluid-Single Leg Gravity Platform-Soil Interaction System

An approximate method is presented to investigate the earthquake response of the fluid-single leg (shortened for S. L.) gravity platform-soil interaction system. By assuming a suitable form of the velocity potential of the radiation waves and by using the motion equation and the boundary conditions, the unknown coefficients can be obtained. Thereafter the function of frequency for the interaction system may also be obtained. In this paper, the difference of the system dynamic response between rigid foundation is analyzed and the influences of the various foundation geometric dimension and the various water-depth on the hydrodynamic loading and dynamic response of the system is illustrated.

Wind-induced response analysis of conical membrane structures

Conical membrane structures are a typical form of tensile membrane structures. In the past, most studies focused on the static performance, but few on dynamic performance. In this paper, systematic parameter analysis of wind-induced response of conical membrane structures has been performed with nonlinear random simulation method in a time domain, by considering some parameters, such as span, rise-span ratio, prestress of membrane, and characteristic of the approaching wind flow. Moreover, formulas of the dynamic coefficient and nonlinear adjustment factor are advised, which can be conveniently used in wind-resistant design of conical membrane structures.

THE DESIGN AND ANALYSIS OF VIBRATION STRUCTURE OF VERTICAL DYNAMIC BALANCING MACHINE

A new type of vibration structure (i.e. supporting system, called swing frame cus- tomarily) of vertical dynamic balancing machine has been designed, which is based on an analysis for the swing frame of a traditional double-plane vertical dynamic balancing machine. The static unbalance and couple unbalance can be e?ectively separated by using the new dynamic balancing machine with the new swing frame. By building the dynamics model, the advantages of the new structure are discussed in detail. The modal and harmonic response are analyzed by using the ANSYS7.0. By comparing the ?nite element modal analysis with the experimental modal analy- sis, the natural frequencies and vibration modes are found. There are many spring boards in the new swing frame. Their sti?nesses are di?erent and assorted with each other. Furthermore, there are three sensors on the measuring points. Therefore, the new dynamic balancing machine can measure static unbalance and coupling unbalance directly, and the interaction between them is faint. The result shows that the new vertical dynamic balancing machine is suitable for inertial measurement of ?ying objects, and can overcome the shortcomings of traditional double-plane vertical dynamic balancing machines, which the e?ect of plane-separation is inferior. The vertical dynamic balancing machine with the new vibration structure can ?nd wide application in the future. The modelling and analysis of the new vibration structure will provide theoretical basis and practical experience for designing new-type vertical dynamic balancing machines.

Study on dynamic response of multi-degree-of-freedom explosion vessel system under impact load

In order to study the dynamic response and calculate the axial dynamic coefficient of the monolayer cylindrical explosion vessel,the wall of vessel is simplified as a multi-degree-of-freedom(MDoF) undamped elastic foundation beam.Decoupling the coupled motion equation and using Duhamel's integrals,the solutions in generalized coordinates of the equations under exponentially decaying loads,square wave loads and triangular wave loads are calculated.These solutions are consistent in form with the solutions of single-degree-of-freedom(SDoF) undamped forced vibration simplified model.Based on the model,equivalent MDoF design method(also called MDoF dynamic coefficient method) of cylindrical explosion vessel is proposed.The traditional method can only predict the dynamic coefficient of torus portion around the explosion center,but this method can predict that of the vessel wall at any axial n dividing point position.It is verified that the prediction accuracy of this model is greatly improved compared with the SDoF model by comparing the results of this model with SDoF model and numerical simulation in different working conditions.However,the prediction accuracy decreases as the scaled distance decreases and approaches the end of the vessel,which is related to the accuracy of the empirical formula of the implosion load,the simplification of the explosion load direction,the boundary conditions,and the loading time difference.

The effect of subgrade inhomogeneity induced by freeze-thaw on the dynamic response of track-subgrade system

The developed vertical coupling model of Vehicle-Track-Subgrade which considered subgrade layer vibration is present- ed. The equations of motion for the ballast, top and bottom subgrade layers are presented in detail. Through inputting different coefficients, the dynamic response of track-subgrade system in a seasonal frozen region in different seasons is obtained by the developed model and the uneven freeze-thaw action of subgrade soil is presented in this model. The ef- fect of subgrade inhomogeneity induced by uneven freeze-thaw on the dynamic response of track-subgrade system was studied and the conclusions are as follows. The force at the interface of ballast and top subgrade layer and the defor- mation of ballast induced by a passing train changed sharply at the stiffness mutation zone. The force and deformation decreased with increasing stiffness ratio with the same amplitude of irregularities as the excitation source. The force and deformation were larger with larger amplitudes of irregularities. There was an obvious effect of uneven deformation and stiffness of subgrade on the dynamic response of track-subgrade system.

Dynamic Response of Double-Sided Loess Slope under Vehicle Load

In order to verify and study the dynamic response law on the double-sided loess slope under the action of the waves generated by automobile traffic,we select a double-sided loess slope from the long section of Anzi Road as the research object.Both field investigations and on-site monitoring processes are conducted,for the purpose of providing robust basis for road protection in these conditions.In detail,vehicleinduced vibration signals are different according to different vehicle types,speeds,as well as positions,and thus are collected,respectively.Based on the statistical analysis of the signals,the vibration response law and frequency spectrum characteristics of the slope are summarized.The results show that:①The dynamic response of the doublesided loess slope increases as the vehicle load increases,and the strong vibration response area is located in the middle of the side slope;②When the vehicle load is small,the vibration wave amplification effect is obvious.On the contrary,when the vehicle load is large,the vibration wave amplification effect is weakened;③The spectrum distribution of the X-direction wave is single-peak shape,and the dominant frequency is concentrated in 30-50 Hz;the frequency spectrum distribution of the Zdirection wave shows a multi-peak shape,and the dominant frequency is concentrated in 20-180 Hz;④The vibration wave propagates in the slope.The frequency change shows little correlation with the type,speed and position of the vehicle,and instead,it is mainly determined by the slope itself.This study reveals the dynamic response on doubled-sided loess slopes and provides both theoretical and practical significance for the road protection in such situations.