Exciting Forces for a Wave Energy Device Consisting of a Pair of Coaxial Cylinders in Water of Finite Depth

Two coaxial vertical cylinders-one is a riding hollow cylinder and the other a solid cylinder of greater radius at some distance above an impermeable horizontal bottom,were considered.This problem of diffraction by these two cylinders,which were considered as idealization of a buoy and a circular plate,can be considered as a wave energy device.The wave energy that is created and transferred by this device can be appropriately used in many applications in lieu of conventional energy.Method of separation of variables was used to obtain the analytical expressions for the diffracted potentials in four clearly identified regions.By applying the appropriate matching conditions along the three virtual boundaries between the regions,a system of linear equations was obtained,which was solved for the unknown coefficients.The potentials allowed us to obtain the exciting forces acting on both cylinders.Sets of exciting forces were obtained for different radii of the cylinders and for different gaps between the cylinders.It was observed that changes in radius and the gap had significant effect on the forces.It was found that mostly the exciting forces were significant only at lower frequencies.The exciting forces almost vanished at higher frequencies.The problem was also investigated for the base case of no plate arrangement,i.e.,the case having only the floating cylinder tethered to the sea-bed.Comparison of forces for both arrangements was carried out.In order to take care of the radiation of the cylinders due to surge motion,the corresponding added mass and the damping coefficients for both cylinders were also computed.All the results were depicted graphically and compared with available results.

Effects of soil profile and characteristic of exciting force on propagation of ground vibrations

Ground-borne vibrations caused by vibration sources such as road traffic and construction exhibit complicated properties during propagation from the vibration source to the inside of a building. In the present paper, a numerical analysis technique for the system of vibration source and propagation path of ground vibration is developed in order to systematically determine the propagation properties of the vibration as part of developing a predictive technique for exposure evaluations by vibrations in three directions at receiving points of vibration in the human body. First, the exciting forces in three directions for input into the numerical computation are inversely-estimated by using the measured acceleration rec- ords of the measurement points, which are near the vibration source. The thin-layered element method is used for numerical computation of the ground vibration. Then, the calculation results for the ground vibration obtained by using the estimated exciting force are compared with the measured results, and the influence of the stratified structure of the ground on the exciting force and the propagation properties of the ground vibration are studied. From these results, in a prediction of the ground vibration in three directions, it is emphasized that it is necessary to consider the influence of horizontal exciting force, although attention has been paid to only the vertical exciting force for simulating ground vibration.

REGULARITY OF VIBRATION RESPONSE OF MECHANICAL SYSTEM UNDER AFFECT OF VARI-FREQUENCY EXCITING FORCE

The vibration response formulas of the mechanical system under the affect of thevari-frequency exciting force are deduced. It is proved by the theoretical analysis and experimentalresults that the vibration response amplitude of the mechanical system under the affect of thevari-frequency exciting force is far smaller than that under the affect of the constant frequency exciting force on condition that the exciting force amplitudes are just the same;while the vari-fre-quency rate a increases to 5 Hz per second the vibration amplitude will decrease to 10% only as lowas that under the affect of the constant frequency exciting force. All these conclusions will be of significance for revealing the mechanism of suppressing chatter in van-speed cutting and analyzing theexperimental results of sine-wave scanning exciting test.

THE ANALYSIS FOR THE AIRFLOW EXCITING-VIBRATION FORCE OF CONTROL STAGE OF STEAM TURBINE

Based on the hydrodynamics, the airflow exciting-vibration force of control stage of steam turbine is studied by using the momentum theorem. A formulation for calculating the air exciting-vibration force of the control stage of steam turbine is deduced first by using theoretical analysis method and taking all the design factors of vane and nozzles into consideration. Moreover, the exciting-vibration forces in different load cases are discussed respectively.

Dynamic stability of parametrically-excited linear resonant beams under periodic axial force

The parametric dynamic stability of resonant beams with various parameters under periodic axial force is studied. It is assumed that the theoretical formulations are based on Euler-Bernoulli beam theory. The governing equations of motion are derived by using the Rayleigh-Ritz method and transformed into Mathieu equations, which are formed to determine the stability criterion and stability regions for parametricallyexcited linear resonant beams. An improved stability criterion is obtained using periodic Lyapunov functions. The boundary points on the stable regions are determined by using a small parameter perturbation method. Numerical results and discussion are presented to highlight the effects of beam length, axial force and damped coefficient on the stability criterion and stability regions. While some stability rules are easy to anticipate, we draw some conclusions： with the increase of damped coefficient, stable regions arise; with the decrease of beam length, the conditions of the damped coefficient arise instead. These conclusions can provide a reference for the robust design of parametricallyexcited linear resonant sensors.

Minimizing electrostatic interactions from piezoresponse force microscopy via capacitive excitation

Piezoresponse force microscopy(PFM)has emerged as one of the most powerful techniques to probe ferroelectric materials at the nanoscale,yet it has been increasingly recognized that piezoresponse measured by PFM is often influenced by electrostatic interactions.In this letter,we report a capacitive excitation PFM(ce-PFM)to minimize the electrostatic interactions.The effectiveness of ce-PFM in minimizing electrostatic interactions is demonstrated by comparing the piezoresponse and the effective piezoelectric coefficient measured by ce-PFM and conventional PFM.The effectiveness is further confirmed through the ferroelectric domain pattern imaged via ce-PFM and conventional PFM in vertical modes,with the corresponding domain contrast obtained by ce-PFM is sharper than conventional PFM.These results demonstrate ce-PFM as an effective tool to minimize the interference from electrostatic interactions and to image ferroelectric domain pattern,and it can be easily implemented in conventional atomic force microscope(AFM)setup to probe true piezoelectricity at the nanoscale.

Side force control on slender body by self-excited oscillation flag

Strong asymmetrical vortices appear on the leeward of slender body at high angles of attack, which has very unfavorable effect on the stability and control of the aircraft. A method is developed to control the side force of slender body at high angles of attack, and is verified in wind tunnel. A thin-film triangular self-excited oscillation flag is fixed at the tip of the slender body model whose semi-apex angle is 10°. Side force is approximately linearly proportional to roll-setting angle of self-excited oscillation flag at high angles of attack, and the slop of fitting straight line obtained by the least square method is -0.158. The linear relationship between side force and roU-setting angle provides convenience for developing side force control law of slender body at high angles of attack. Experimental data shows that the side force coefficients vary linearly with roll-setting angles when a specific plastic self-excited oscillation flag is used as the control flag. The range of side force coefficient and roll-setting angle are, respectively, -3.2 to 3.0 and -20° to 20°. The device is simple, effective, and is of great potential in engineering application.

Countermeasure Against Regenerative and Forced Chatter of Flexible Workpieces in Milling Processs Using Bi-directional Excitation

A novel extended methodology for chatter suppression in milling process by applying external forced vibrations to the workpiece in two orthogonal directions which are the feed and cross-feed directions.Both the regenerative and forced chatter suppression during the milling process of flexible workpieces are investigated.Here,the workpiece is subject to a sinusoidal periodic force in the feed direction to disrupt the regenerative effect.Additionally,to minimize the forced chatter,the workpiece is subject to the periodic excitation force in cross-feed direction.This force is proportional to the magnitude of the estimated cutting force in cross-feed direction and has a phase opposite to the cutting force to minimize the vibration amplitudes.The effectiveness of the proposed method is evaluated numerically and experimentally,for the spindle speed located in both the local minima and local maxima of the stability lobe diagram.The numerical simulations indicate significant suppression effect in terms of vibration amplitudes,resulting in suppression of both the regenerative chatter and the forced chatter.Experiments were conducted by using a workpiece-mounted active stage composed of flexure hinges and driven by piezoelectric actuators.The experimental results agree qualitatively with the numerical simulations.The proposed method indicates a remarkable vibration reduction effect for both regenerative and forced chatters.

Transverse distribution law of airflow excitation force for SI-FLAT contactless shapometer

Aiming at the shape problems in production, the finite element model was built with the Fluent software to analyze the transverse distribution laws of airflow excitation force under different factors which affected the detection precision. For analyzing the shape errors caused by the non-uniform transverse distribution of airflow excitation force, the finite element model of strip is built with the ANSYS12.0 software. It is found in the study results that the airflow excitation forces display the same distribution laws under different rolling conditions, i.e. have an obvious attenuation at the edge of strip~ which causes large shape measurement errors. For reducing shape errors, the compensation project is put forward, and it gives a good foundation for improving the detection precision.

Study on Scattering Wave Force of Horizontal and Vertical Plate Type Breakwaters

The interaction between wave and horizontal and vertical plates is investigated by the boundary element method, and the relations of wave exciting force with plate thickness, submergence and length are obtained. It is found that： 1） The efficient wave exciting force exists while plate submergence is less than 0.5 m, and the plate is very thin with order O（0.005 m）. 2） The maximum heave wave exciting force exists, and it is the main factor for surface and submerged horizontal plate while the roll force can be ignored. 3） The maximum sway wave exciting force exists, it is the main factor for surface or submerged vertical plate, and the roll force is about 20 times of horizontal plate.

Simple and fast prediction of train-induced track forces,ground and building vibrations

A simple and fast prediction scheme is presented for train-induced ground and building vibrations.Simple models such as(one-dimensional)transfer matrices are used for the vehicle–track–soil interaction and for the building–soil interaction.The wave propagation through layered soils is approximated by a frequency-dependent homogeneous half-space.The prediction is divided into the parts“emission”(excitation by railway traffic),“transmission”(wave propagation through the soil)and“immission”(transfer into a building).The link between the modules is made by the excitation force between emission and transmission,and by the free-field vibration between transmission and immission.All formula for the simple vehicle–track,soil and building models are given in this article.The behaviour of the models is demonstrated by typical examples,including the mitigation of train vibrations by elastic track elements,the low-and high-frequency cut-offs characteristic for layered soils,and the interacting soil,wall and floor resonances of multi-storey buildings.It is shown that the results of the simple prediction models can well represent the behaviour of the more time-consuming detailed models,the finite-element boundary-element models of the track,the wavenumber integrals for the soil and the three-dimensional finite-element models of the building.In addition,measurement examples are given for each part of the prediction,confirming that the methods provide reasonable results.As the prediction models are fast in calculation,many predictions can be done,for example to assess the environmental effect along a new railway line.The simple models have the additional advantage that the user needs to know only a minimum of parameters.So,the prediction is fast and user-friendly,but also theoretically and experimentally well-founded.

Experimental and numerical investigation of the impacts of rotor tip-rake on excitation forces of pump-jet propulsors

The tip-clearance flow in a pump-jet propulsor exerts great impacts on the fluctuating pressures and resultant unsteady forces,which are important sources of structural vibrations and radiated noise underwater.The blade geometry close to the tip is an important factor determining the vortex strength in the tip-clearance flow.In the open-water condition,the effects of raking the rotor tips on the duct-surface fluctuating pressures and the resultant unsteady forces acting on different components of the propulsor are investigated via physical model experiments and the numerical solution of Reynolds-averaged Navier-Stokes(RANS)equations coupled with the SST k-ωturbulence model.The measured and simulated results of hydrodynamic pressures are consistent to each other,and the simulated flows help better understand why the fluctuating pressures change with the tip geometry.The strong fluctuations of duct-surface pressures are caused by intensive tip separation vortices.The duct-surface pressure fluctuations are effectively reduced by using the rake distribution near the tip towards blade back side and,for the combination of the five-bladed rotor and the seven-bladed stator,the resultant unsteady horizontal(and vertical)forces acting on the duct and stator are also reduced;while increasing rake leads to negative effect on pressure fluctuations and unsteady horizontal(and vertical)forces acting on all the components of the propulsor.

Robust control of exciting force for vibration control system with multi-exciters

Due to the dynamical character of electromagnetic exciter and the coupling between structure and exciter(s),the actual output force acting on the structure is usually not equal to the exact value that is supposed to be,especially when multi-exciters are used as actuators to precisely actuate large flexible structure.It is necessary to consider these effects to ensure the force generated by each exciter is the same as required.In this paper,a robust control method is proposed for the multi-input and multi-output(MIMO)structural vibration control system to trace the target actuating force of each exciter.A special signal is designed and put into the coupled mul-ti-exciter-structure system,and the input and output signals of the system are used to build a dynamic model involving both the dynamical characters of the exciters and the structure using the subspace identification method.Considering the uncertainty factors of the multi-exciter/structure system,an H-infinity robust controller is designed to decouple the coupling between structure and exciters based on the identified system model.A MIMO vibration control system combined with a flexible plate and three electromagnetic exciters is adopted to demonstrate the proposed method,both numerical simulation and model experiments showing that the output force of each exciter can trace its target force accurately within the requested frequency band.

Study on the Sliding Displacement of a Sliding Structure Subjected to Multi directional Earthquake Excitation

Transient dynamic analysis is used to study the effect of the bidirectional interaction of friction on the response of sliding displacement of a sliding structure subjected to bidirectional earthquake ground motion. The analysis varies the parameters of amplitude ratio of earthquake excitation, the period of the superstructure, and the coefficient of friction in the sliding support. Numerical results show that the sliding structure is significantly influenced by the interaction of frictional forces. So the sliding displacement may be underestimated and the acceleration of the superstructure may be overrated if the bidirectional interaction of frictional forces is neglected.

Electron excitation from ground state to first excited state:Bohmian mechanics method

The excitation process of electrons from the ground state to the first excited state via the resonant laser pulse is investigated by the Bohmian mechanics method. It is found that the Bohmian particles far away from the nucleus are easier to be excited and are excited firstly, while the Bohmian particles in the ground state is subject to a strong quantum force at a certain moment, being excited, to the first excited state instantaneously. A detailed analysis for one of the trajectories is made, and finally we present the space and energy distribution of 2000 Bohmian particles at several typical instants and analyze their dynamical process at these moments.

Seismic response of the long-span steel truss arch bridge with the thrust under multidimensional excitation

Purpose–Under different ground motion excitation modes,the spatial coupling effect of seismic response for the arch bridge with thrust,seismic weak parts and the internal force components of the control section of main arch ribs are analyzed.Design/methodology/approach–Taking a 490 m deck type railway steel truss arch bridge as the background,the dynamic calculation model of the whole bridge was established by SAP2000 software.The seismic response analyses under one-,two-and three-dimension(1D,2D and 3D)uniform ground motion excitations were carried out.Findings–For the steel truss arch bridge composed of multiple arch ribs,any single direction ground motion excitation will cause large axial force in the chord of arch rib.The axial force caused by transverse and vertical ground motion excitation in the chord of arch crown area is 1.4–3.6 times of the corresponding axial force under longitudinal seismic excitation.The in-plane bending moment caused by the lower chord at the vault is 4.2–5.5 times of the corresponding bending moment under the longitudinal seismic excitation.For the bottom chord of arch rib,the arch foot is the weak part of earthquake resistance,but for the upper chord of arch rib,the arch foot,arch crown and the intersection of column and upper chord can all be the potential earthquake-resistant weak parts.The normal stress of the bottom chord of the arch rib under multidimensional excitation is mainly caused by the axial force,but the normal stress of the upper chord of the arch rib is caused by the axial force,in-plane and out of plane bending moment.Originality/value–The research provides specific suggestions for ground motion excitation mode and also provides reference information for the earthquake-resistant weak part and seismic design of long-span deck type railway steel truss arch bridges.

Multi-Excitation Fatigue Testing for Large Full-Scale Wind Turbine Blade

In order to solve the problem of insufficient exciting force of equipment for large full-scale wind turbine blade fatigue testing,the influence of gravity on the performance of excitation equipment and fatigue damage evaluation of the different positions of wind turbine blades are analyzed.With the multi-excitation loading in the horizontal direction,the actuator force of the excitation equipment does not need to overcome the gravity of the dynamic mass,which directly outputs the exciting force of the system vibration.The excitation efficiency of the equipment is 77%higher than that of the vertical load.The gravity moment of the horizontal loading mode is perpendicular to the loading direction.That is,the mean load in the flapwise direction is zero.The weight of excitation equipment could replace the tuning mass on the condition that the self-weight of equipment is reduced by the multi-excitation mode,which helps the excitation equipment play the comprehensive function of excitation equipment and tuning mass.At the same time,the gravity moment in the edgewise direction will be decreased by 17.0%22.5%under the multi-excitation horizontal loading mode.In the vertical loading mode,the gravity moment is the mean load,which only increases fatigue damage accumulation by 15.6%.By comparing the role of gravity in the excitation equipment and fatigue damage evaluation,the multi-excitation horizontal loading mode has more advantage to performance the exciting force than the contribution of gravity to the fatigue damage accumulation in the vertical loading mode.Through the fatigue testing of multi-excitation horizontal loading,the potential of excitation equipment is explored,and the problem of insufficient exciting force in large full-scale wind turbine blade fatigue testing will be solved.

变弯度导叶铰接位置对风扇振动特性的影响

针对变弯度导叶尾迹激励引起的转子叶片共振,基于谐响应模态叠加法对风扇转子进行强迫振动分析,研究了不同铰接位置的变弯度导叶对风扇气动性能及其振动特性的影响。结果表明,随着铰接位置向尾缘移动,风扇转子流量、压比和效率增加,稳定裕度降低,主要影响下游转子叶根部位的进气角度。在气动激励方面,随着铰接位置后移,转子叶片表面的压力幅值增大,相位变化剧烈,通过将非定常气动力转换到模态空间中,可以看到叶片所受模态气动力在铰接位置为35%C (C为轴向弦长)的情况下达到最大值,后呈现先减小后增加的规律,这与振动响应的变化规律一致。铰接位置对所关注的高阶局部模态的气动阻尼影响较小,最大差异为0.046%。在振动响应方面,转子叶片的振动应力随铰接位置剧烈改变,且为非单调变化。在设计位置处叶片的振动应力最小,在35%C处振动应力达到设计位置的15倍。对于本文所研究的模型及工况,最优铰接位置为45%C,与仅考虑气动性能的25%C不同。因此在变弯度导叶设计时,需要考虑其对叶片振动特性的影响。

机械设备用感应电机电磁力动态特性计算与研究

机械设备用感应电机的动态性能是不可忽略的设计要求。为抑制电机动态电磁振动和噪声水平,展开了对电机电磁力动态特性分析及相应削弱措施的研究。首先利用经典气隙谐波磁场理论,确定磁场中的谐波磁势和谐波磁导来源,由此再通过张量法计算电机径向电磁力,并对比主要谐波分量的幅值、极对数和频率特征。然后采用有限元仿真和傅里叶分解法,确定电磁力时空行波的基本特征,推断主要力波的谐波磁场产生来源。结果表明谐波径向力绝对幅值的变化很难影响其占基波的相对比值。最后建立磁性槽楔理想模型对比仿真,谐波电磁力的削弱程度与槽楔磁导率正相关,样机振动测试试验间接验证了磁性槽楔的优越性,为电机动态特性研究及优化设计提供理论依据。

非线性动态特性系数对汽轮机转子-轴承-密封系统运动特性的影响

为准确地反应汽流激振下汽轮机转子-轴承-密封系统的运动特性,推导了包含非线性动态特性(非线性刚度、阻尼)的转子运动微分方程,将数值模拟获得的非线性汽流激振力拟合成方程耦合到运动方程中,采用龙格-库塔法求解对应的运动方程,基于试验对比验证了考察非线性因素的必要性与运动微分方程的准确性。在此基础上,分析汽流激振力作用下不同非线性动态特性系数对转子运动特性与稳定性的影响。结果表明:系统中的非线性动态特性会改变转子不同类型的混沌运动区域与位移,使1/2、1/3、2/3工频的出现范围及幅值改变,密频现象增加;耦合热、动载荷后高负荷区域转子位移减小。对比Lyapunov指数,考虑非线性动态特性后其均值有所上升;合理的非线性刚度能够改善系统的稳定性,高非线性阻尼值能提高系统稳定性;耦合热、动载荷后的系统高负荷运行时更稳定。