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.

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.

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.

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.

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.

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.

Simulation applied to working frequency selection in large-scale vi- brating screen＇s design

The working frequency selection of the ZK30525 vibrating screen was studied using ANSYS. Integrating the dynamic performance simulation analysis of the vibrating screen structure, the variation laws of beams＇ vibration displacements changing with different exciting frequencies were researched. These beams include six beams, with one discharging beam and one in-material beam. Results indicate that vibration displacements in the middle of these beams increase with the augmenta- tion of exciting frequency. When exciting frequency exceeds a certain value, there exists a flat change region for vibration displacement. According to vibrator characteristics, the vibrating screen＇s working frequency should be selected in the flat change region, and be far away from modal frequencies. The study provides theoretical guidance for the reasonable working frequency selection of the large-scale vibrating screen.

A Semi-Analytical Method for the PDFs of A Ship Rolling in Random Oblique Waves

The PDFs(probability density functions) and probability of a ship rolling under the random parametric and forced excitations were studied by a semi-analytical method. The rolling motion equation of the ship in random oblique waves was established. The righting arm obtained by the numerical simulation was approximately fitted by an analytical function. The irregular waves were decomposed into two Gauss stationary random processes, and the CARMA(2, 1) model was used to fit the spectral density function of parametric and forced excitations. The stochastic energy envelope averaging method was used to solve the PDFs and the probability. The validity of the semi-analytical method was verified by the Monte Carlo method. The C11 ship was taken as an example, and the influences of the system parameters on the PDFs and probability were analyzed. The results show that the probability of ship rolling is affected by the characteristic wave height, wave length, and the heading angle. In order to provide proper advice for the ship’s manoeuvring, the parametric excitations should be considered appropriately when the ship navigates in the oblique seas.

Time-domain analysis for vibration and sound radiation of submerged spherical shell excited by force

The vibration and sound radiation of a submerged spherical shell are studied in the time-domain by Laplace transform method, where a CW pulse force acts at the apex of the shell. The numerical results for the case of long pulse show that the different vibrational modes and the resonant or beat radiated sound are excited for different carrier-frequencies, but litle sound is radiated for some vibrational modes. For the case of short pulse the waveforms of the pulse become widened and deformed, when the pulse propagates between apexes of the shell. Then, the Doubly Asymptotic Approximations (DAA2) and Kirchhoff's Retarded Potential Formulate (KRPF)are used to solve the same problem. It is shown that the results of DAA2 and KRPF method have a good agreement with the results of Laplace transform method.

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.

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.

Approximation of structural damping and input excitation force

Structural dynamic characteristics are the most significant parameters that play a decisive role in structural damage assessment. The more sensitive parameter to the damage is the damping behavior of the structure. The complexity of structural damping mechanisms has made this parameter to be one of the ongoing research topics. Despite all the difficulties in the modeling of damping, there are some approaches like as linear and nonlinear models which are described as the energy dissipation throughout viscous, material or structural hysteretic and frictional damping mechanisms. In the presence of a mathematical model of the damping mechanisms, it is possible to estimate the damping ratio from the theoretical comparison of the damped and un-damped systems. On the other hand, solving the inverse problem of the input force estimation and its distribution to each SDOFs, from the measured structural responses plays an important role in structural identification process. In this paper model-based damping approximation method and a modelless structural input estimation are considered. The effectiveness of proposed methods has been carded out through analytical and numerical simulation of the lumped mass system and the results are compared with reference data. Consequently, high convergence of the comparison results illustrates the satisfactory of proposed approximation methods.

Investigation on the Forced Response of a Radial Turbine under Aerodynamic Excitations

Rotor blades in a radial turbine with nozzle guide vanes typically experience harmonic aerodynamic excitations due to the rotor stator interaction. Dynamic stresses induced by the harmonic excitations can result in high cycle fatigue(HCF) of the blades. A reliable prediction method for forced response issue is essential to avoid the HCF problem. In this work, the forced response mechanisms were investigated based on a fluid structure interaction(FSI) method. Aerodynamic excitations were obtained by three-dimensional unsteady computational fluid dynamics(CFD) simulation with phase shifted periodic boundary conditions. The first two harmonic pressures were determined as the primary components of the excitation and applied to finite element(FE) model to conduct the computational structural dynamics(CSD) simulation. The computed results from the harmonic forced response analysis show good agreement with the predictions of Singh's advanced frequency evaluation(SAFE) diagram. Moreover, the mode superposition method used in FE simulation offers an efficient way to provide quantitative assessments of mode response levels and resonant strength.

Vibration power flow in infinite stiffened-plate with force excitation applied on plate

The formula of the vibration response and power flow in beam-stiffened plate with force excitation applied on.the plate, have been obtained by using the Steepest Descent Integral method. The characteristics of the power flow have been studied through computer simulation.It is shown that the stiffener acts as an extra lineal excitation applied on the plate and changes the characteristics of the power flow of the infinite plate greatly The greater the stiffness and the smaller the distance between the exciting point and the stiffener is, the greater the induence is. Lastly, experiments have been carried out by using the dualaccelerometer measurement technique that based on cross spectrum, and the test data agree well with the theoretical results

Iterative Rankine HOBEM analysis of hull-form effects in forward-speed diffraction problem

A time-domain numerical algorithm based on the higher-order boundary element method and the iterative time-marching scheme is proposed for seakeeping analysis. The ship waves generated by a hull advancing at a constant forward speed in incident waves and the resultant diffraction forces acting on the hull are computed to investigate the hull-form effects on the hydrodynamic forces. A rectangular computational domain travelling at ship＇s speed is considered. An artificial damping beach for satisfying the radiation condition is installed at the outer portion of the free surface except the downstream side. An iterative time-marching scheme is employed for updating both kinematic and dynamic free-surface boundary conditions for numerical accuracy and stability. The boundary integral equation is solved by distributing higher-order boundary elements over the wetted body surface and the free surface. The hull-form effects on the naval hydrodynamics are investigated by comparing three different Wigley models. Finally, the corresponding unsteady wave patterns and the wave profiles around the hulls are illustrated and discussed.

Wave radiation and diffraction by a floating rectangular structure with an opening at its bottom in oblique seas

The radiation and the diffraction of linear waves by a rectangular structure with an opening at its bottom floating in oblique seas of finite depth are investigated. Analytical expressions for the radiated potentials and the diffracted potential are obtained by use of the method of separation of variables and the eigenfunction expansion method, with the unknown coefficients being determined by the boundary conditions and the matching requirement on the interface. The hydrodynamic coefficients and the wave excitation forces are verified using the symmetry properties of coupled hydrodynamic coefficients and one specific example investigated previously. By use of the present analytical-numerical solution, the influences of the angle of incidence, the width of the opening on the wave forces and the hydrodynamic coefficients are investigated. It is also found that in the oblique sea the external excitation frequency that can lead to the resonance of a rectangular tank depends on the wave direction and the wave number of the incident wave.

An iterative Rankine boundary element method for wave diffraction of a ship with forward speed

A 3-D time-domain seakeeping analysis tool has been newly developed by using a higher-order boundary element method with the Rankine source as the kernel function. An iterative time-marching scheme for updating both kinematic and dynamic free-surface boundary conditions is adopted for achieving numerical accuracy and stability. A rectangular computational domain moving with the mean speed of ship is introduced. A damping beach at the outer portion of the truncated free surface is installed for satisfying the radiation condition. After numerical convergence checked, the diffraction unsteady problem of a Wigley hull traveling with a constant forward speed in waves is studied. Extensive results including wave exciting forces, wave patterns and pressure distributions on the hull are presented to validate the efficiency and accuracy of the proposed 3-D time-domain iterative Rankine BEM approach. Computed results are compared to be in good agreement with the corresponding experimental data and other published numerical solutions.

Scattering of water waves by a wave energy device consisting of a pair of co-axial cylinders in a uniform water having finite channel width

We consider a device which consists of a floating structure over a cylindrical plate placed at a finite height from the impermeable ocean floor.This paper developes the interaction of linear water waves with such a device.The whole fluid domain is divided into a number of sub-domains and boundary value problems are formulated for each identified sub-domain.The channel multipoles,separation of variables and matched eigenfunction expansion methods allow us to solve boundary value problems for the diffracted velocity potentials in each sub-domain.We investigate the wave forces exerted on the proposed device.Consequently,the effects of the various parameters,e.g.,drafts,radii,the gap between the cylinders and mainly channel width of the device on the wave forces exerted by the cylinders are presented graphically.We observe a small oscillation nature near the peak value of the exciting force for the particular value of channel width w=2.4m.The peak value of the exciting forces occurs near the wavenumber kr 1=1.0 for different width of the channel walls.The obtained results are compared with some available results,and it shows a good agreement between the obtained and available results.