Vibration response of Euler-Bernoulli-damped beam with appendages subjected to a moving mass

This paper addresses the problem of a viscoelastic Euler-Bernoulli beam under the influence of a constant velocity moving mass and different types of appendages.Four types of boundary conditions are considered:pinned-pinned,fixed-pinned,fixed-free(or cantilever),and fixed-fixed.Appendages considered include lumped masses,dampers,and springs.The modal decomposition method is employed to derive the equation of motion of the beam,for which an analytical closed-form expression of the dynamic vibration response is generated.The proposed method enables the study of the effect of a single appendage or a combination of the three types of appendages on the non-dimensional dynamic response of the beam.Numerical examples are presented to illustrate the effects of these appendages and compare them to the reference cases of a beam with no appendages.The results demonstrate the importance of considering these parameters in the design of structures.The proposed method is compared to other techniques in the literature and found to be advantageous due to its direct approach.The method also offers a versatile tool for investigating various configurations,aiding in engineering design and structural analysis for which establishing a precise prediction of beam vibrations is crucial.

Analysis of vibration response characteristics of subway station and superstructure with hard combination

The vibration response and noise caused by subway trains can affect the safety and comfort of superstructures.To study the dynamic response characteristics of subway stations and superstructures under train loads with a hard combination,a numerical model is developed in this study.The indoor model test verified the accuracy of the numerical model.The influence laws of different hard combinations,train operating speeds and modes were studied and evaluated accordingly.The results show that the frequency corresponding to the peak vibration acceleration level of each floor of the superstructure property is concentrated at 10–20 Hz.The vibration response decreases in the high-frequency parts and increases in the lowfrequency parts with increasing distance from the source.Furthermore,the factors,such as train operating speed,operating mode,and hard combination type,will affect the vibration of the superstructure.The vibration response under the reversible operation of the train is greater than that of the unidirectional operation.The operating speed of the train is proportional to its vibration response.The vibration amplification area appears between the middle and the top of the superstructure at a higher train speed.Its vibration acceleration level will exceed the limit value of relevant regulations,and vibration-damping measures are required.Within the scope of application,this study provides some suggestions for constructing subway stations and superstructures.

Research on vibration response characteristics and evolution law of finishing rolling in hot strip mills

In this study,a comprehensive rolling mill vibration test program was designed,including specific test conditions and a test system.The analysis of measured signals reveals the vibration response characteristics and their evolution at different gauge points in the finishing mill.This is particularly evident during abnormal rolling,where the signals highlight the characteristics of abnormal responses and vibration intensities.Abnormal vibrations during the rolling process mainly occur when the strip thickness is less than 2.5 mm,and at the rolling speed-up stage,the strong abnormal vibration occurs at each measuring point on the F2 transmission side.The maximum vibration intensity of the backup roll’s bearing seat is 17 mm/s.As the rolling progresses,the stress on the bolts changes.The strip thickness is negatively correlated with the peak values of bite and tail-flick impacts.The vibration characteristics vary with the strip thickness and the process state.

Vibration response analysis of 2-DOF locally nonlinear systems based on the theory of modal superposition

Many important vibration phenomena which simultaneously contain quadratic nonlinear stiffness and damping exist in the complicated vibrating systems under practical circumstances. In this paper, we established a 2-degree-of-freedom (DOF) nonlinear vibration model for such a system, deduced the differential equations of motion which govern its dynamics, and worked out the solutions for the governing equations by the principle of superposition of nonlinear normal modes (NLNM) based on Shaw’s theory of invariant manifolds. We conducted numerical simulations with the established model, using superposition of nonlinear normal modes and direct numerical methods, respectively. The obtained results demonstrate the feasibility of the proposed method in that its calculated data varies in a similar tendency to that of the direct numerical solutions.

Nonlinear Modeling and Identification of Structural Joint by Response Control Vibration Test

Components of mechanical product are assembled by structural joints,such as bolting,riveting,welding,etc.Structural joints introduce nonlinearity to some engineering structures,and the nonlinearity need to be modeled precisely.To meet serious quality requirements,it is necessary to detect and identify nonlinearity of mechanical products for structural optimization.Modal test to acquire a dynamic response has been applied for decades,which provides reliable results for finite element(FE)model updating.Here response control vibration test for identification of nonlinearity is presented.A nonlinear system can be regarded as linearity for particular steady state response,and classical linear analysis tool is applicable to extract modal data for particular response.First,its applicability is illustrated by some numerical simulations.Subsequently,it is implemented on experimental setup with structural joints by shaking table.The stiffness and damping function dependent of relative displacement are fitted to describe its inherent nonlinearity.The spring and damping forces are identified by harmonic balance method(HBM)to predict output response.Based on the identified results,the procedure is recommended that it allows a reliable measurement of nonlinearity with a certain accuracy.

The bending vibration response and approximate calculation of elastic cylindrical shell

Useful structure characteristics of elastic cylindrical shells have led them to being widely applied in virtual projects,so it is important to conduct vibration research on the shells and find it’s a simpler corresponding compact calculation method. Utilising the input and transfer point mobility of a thin plate structure, a theoretical expression of the cylindrical shell’s bending vibration responsewas deduced and numerical simulations were done to simplify the theoretical expression within an acceptable error margin, greatly reducing the amount of computations. Furthermore, whole vibration response distributions of the cylindrical shell were analyzed. It was found thathe vibration energy propagates in helical form under mono-frequency excitation, while under bandwidth frequency excitation, it attenuates around in term of fluctuation.The axial attenuation rate of the vibration energy is larger than the circumferential attenuation rate.

Parametric characteristic of the random vibration response of nonlinear systems

Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of nonlinear engineering systems and structures that can be represented by a Volterra series model.In the present study,the random vibration of nonlinear systems is investigated using Volterra series.Analytical expressions were derived for the calculation of the output power spectral density（PSD） and input-output cross-PSD for nonlinear systems subjected to Gaussian excitation.Based on these expressions,it was revealed that both the output PSD and the input-output crossPSD can be expressed as polynomial functions of the nonlinear characteristic parameters or the input intensity.Numerical studies were carried out to verify the theoretical analysis result and to demonstrate the effectiveness of the derived relationship.The results reached in this study are of significance to the analysis and design of the nonlinear engineering systems and structures which can be represented by a Volterra series model.

Vibration Response and Stress Analysis of Planar Elastic Tube Bundle Induced by Fluid Flow

Flow?induced vibration plays a positive role on heat transfer enhancement. Meanwhile, it is also a negative factor for fatigue strength. Satisfying the fatigue strength is the primary prerequisite for heat transfer enhancement. This paper numerically studied the flow?induced vibration of planar elastic tube bundle based on a two?way fluid–structure interaction(FSI) calculation. The numerical calculation involved the unsteady, three?dimensional incompressible governing equations solved with finite volume approach and the dynamic balance equation of planar elastic tube bundle solved with finite element method combined with dynamic mesh scheme. The numerical approach was verified by comparing with the published experimental results. Then the vibration trajectory, deformation and stress contour of planar elastic tube bundle were all studied. Results show that the combined movement of planar elastic tube bundle represents the agitation from inside to outside. The vibration of out?of?plane is the main vibration form with the typically sinusoidal behavior because the magnitude of displacement along the out?of?plane direction is the 100 times than the value of in?plane direction. The dangerous point locates in the innermost tube where the equivalent stress can be utilized to study the multiaxial fatigue of planar elastic tube bundle due to the alternating stress concentration. In the velocity range of 0.2-3 m/s, it is inferred that the vibration amplitude plays a role on the stress response and the stress amplitude is susceptible to the fluid velocity. This research paves a way for studying the fatigue strength of planar elastic tube bundle by flow?induced vibration.

Numerical simulation of vibrational response characteristics of railway subgrades with insulation boards

This study presents a numerical method based on the surface temperature data and the ground temperature increase in Daqing for predicting temperature field distribution in the Binzhou Railway subgrade and analyzing the temporal and spatial distribution of freeze−thaw status of railway subgrade.The calibrated numerical method is applied to simulate the temperature field distribution and roadbed vibrational response of the railway subgrade with a thermal insulation layer at different seasons.The results show the following:(1)The thermal insulation layer can remarkably increase the soil temperature below it and maximum frost depth in the subgrade.(2)Thermal insulation can effectively reduce the subgrade vibration and protect it from frost damage.(3)Given that the strength requirements are met,the insulation layer should be buried as shallow as possible to effectively reduce the subgrade vibration response.The research findings provide theoretical support for the frost damage prevention of railway subgrades in seasonally frozen regions.

VIBRATION NUMERICAL ANALYSIS OF COUNTER-ROTATING TURBINE WITH WAKE-FLOW USING FLUID-STRUCTURE INTERACTION METHOD

The design of counter-rotating turbine is one of new techniques to improve the thrust-weight ratio of jet propulsion engines.Numerical analysis of a low pressure（LP）counter-rotating turbine rotor blade is presented by using ANSYS/CFX software.Interaction of aerodynamics and solid mechanics coupling in the computation is applied.In some rating of turbine,stress distribution and vibration characteristics of low pressure turbine（LPT）blade are computed.The wake aerodynamic forces and LPT blade vibration are transformed in frequency domain using fast Fourier transform（FFT）method.The results show that under wake aerodynamic force excitation,the first order modal vibration is more easily aroused and the higher order response cannot be ignored.Moreover,with different temperature fields,the vibration responses of blade are also different.

Identification of vibration loads on hydro generator by using hybrid genetic algorithm

Vibration dynamic characteristics have been a major issue in the modeling and mechanical analysis of large hydro generators. An algorithm is developed for identifying vibration dynamic characteristics by means of hybrid genetic algorithm. From the measured dynamic responses of a hydro generator, an appropriate estimation algorithm is needed to identify the loading parameters, including the main frequencies and amplitudes of vibrating forces. In order to identify parameters in an efficient and robust manner, an optimization method is proposed that combines genetic algorithm with simulated annealing and elitist strategy. The hybrid genetic algorithm is then used to tackle an ill-posed problem of parameter identification, in which the effectiveness of the proposed optimization method is confirmed by its comparison with actual observation data.

Numerical and test study on vertical vibration characteristics of pile group in slope soil topography

Topography effects on the vertical vibration responses of pile group are revealed though numerical analysis and model tests.First,a series of model tests with different topography of ground and bedrock are conducted.The results indicate that displacement amplitude of the pile head in sloping ground topography is larger than in horizontal ground.Differential displacement at various positions of the pile cap is observed in non-horizontal topography.Afterwards,a numerical algorithm is employed to further explore the essential response characteristics in group piles of different topography configurations,which has been verified by the test results.The lengths of the exposed and frictional segment,together with the thickness of the subsoil layer,are the dominant factors which cause non-axisymmetric vibration at the pile cap.

Matrix test measurements of ground-borne vibration induced by the heavy-duty trains on embankment and cutting tracks in a loess area

This paper presents a comparative analysis of ground vibration in three directions generated by a heavy-duty railway with various track sections.The vibration characteristics in the plane area were investigated by using matrix test measurements.Acceleration peak attenuation was faster within 25 m from the embankment,and the high-frequency vibration attenuates faster with increased distance.For the cutting section with multi-stage soil slope,decay rate of acceleration was relatively larger.The acceleration level of the plane region ranged to 82.2-89.1 dB by the single C80 train.Yet the acceleration level caused by the C80 trains running parallel after meeting showed a distinct increment.The increment of the cutting section was much larger compared with the embankment section,with the increment ranging from 1.2-2.5 dB.In terms of the cutting section,Y direction acceleration was dominant closer to the track.Within 10-30 m of the track,the Y direction acceleration(perpendicular to the rail)decreased rapidly and became comparable to the X direction(parallel to the rail)and Z direction.Additionally,the cutting case generated a higher level of vibration in all three directions compared to the embankment,but as the distance from track increased,the deviation between acceleration gradually decreased.

Research on vibration characteristics of L-shaped plate using a mobility power flow approach

L-shaped plates have become an important focuses in structural vibration research. To determine their vibration characteristics, this paper applied a mobility power flow method. Firstly, the L-shaped plate was divided into two substructures to simplify analysis. The coupled bending moment was then deduced by applying a continuous vibration property on the common edge. Next, the response on any point of the plate and the input and transmitted power flow formulas were calculated. Numerical simulations showed the distribution of the coupled bending moment and the response of the whole structure. The validity of this method was verified by the SEA approach.

Vibration and sound radiation of a rotating train wheel subject to a vertical harmonic wheel–rail force

The rapid development of high-speed railway networks requires advanced methods for analysing vibration and sound radiation characteristics of a fast rotating train wheel subject to a vertical harmonic wheel-rail force. In order to consider the rotation of the wheel and at the same time increase the computational efficiency, a procedure is adapted in this paper taking advantage of the axial symmetry of the wheel. In this procedure, a recently developed 2.5D finite element method, which can consider wheel rotation but only requires a 2D mesh over a cross section containing the wheel axis, is used to calculate the vibration response of the wheel. Then, the vibration response of the wheel is taken as acoustic boundary condition and the 2.5D acoustic boundary element method, which only requires a 1D mesh over the boundary of the above cross section, is utilised to calculate the sound radiation of the wheel. These 2.5D methods and relevant programs are validated by comparing results from this procedure with those from conventional 3D analyses using commercial software. The comparison also demonstrates that these 2.5D methods have a much higher computational efficiency. Using the 2.5D methods, we study the wheel rotation speed influences on the factors including the vertical receptance of the wheel at wheel-rail contact point, sound pressure level at a pre-defined standard measurement point, radiated sound power level, directivity of the radia- tion, and contribution of each part of the wheel. It can be concluded that the wheel rotation speed splits most peaks of the vertical receptance at the wheel-rail contact point, sound pressure levels at the field, and the sound power level of the wheel into two peaks. The directivity and power contribution of the wheel are also significantly changed by the wheel rotation speed. Therefore, the rotation of a train wheel should be taken into account when calculating its vibration and sound radiation.

Experimental Study on Response Performance of VIV of A Flexible Riser with Helical Strakes

Laboratory tests were conducted on a flexible riser with and without helical strakes. The aim of the present work is to further understand the response performance of the vortex induced vibration（VIV） for a riser with helical strakes. The experiment was accomplished in the towing tank and the relative current was simulated by towing a flexible riser in one direction. Based on the modal analysis method, the displacement responses can be obtained by the measured strain. The strakes with different heights are analyzed here, and the response parameters like strain response and displacement response are studied. The experimental results show that the in-line（IL） response is as important as the cross-flow（CF） response, however, many industrial analysis methods usually ignore the IL response due to VIV. The results also indicate that the response characteristics of a bare riser can be quite distinct from that of a riser with helical strakes, and the response performance depends on the geometry on the helical strakes closely. The fatigue damage is further discussed and the results show that the fatigue damage in the CF direction is of the same order as that in the IL direction for the bare riser. However, for the riser with helical strakes, the fatigue damage in the CF direction is much smaller than that in the IL direction.

Analysis on Pseudo Excitation of Random Vibration for Structure of Time Flight Counter

Traditional computing method is inefficient for getting key dynamical parameters of complicated structure.Pseudo Excitation Method（PEM）is an effective method for calculation of random vibration.Due to complicated and coupling random vibration in rocket or shuttle launching,the new staging white noise mathematical model is deduced according to the practical launch environment.This deduced model is applied for PEM to calculate the specific structure of Time of Flight Counter（ToFC）.The responses of power spectral density and the relevant dynamic characteristic parameters of ToFC are obtained in terms of the flight acceptance test level.Considering stiffness of fixture structure,the random vibration experiments are conducted in three directions to compare with the revised PEM.The experimental results show the structure can bear the random vibration caused by launch without any damage and key dynamical parameters of ToFC are obtained.The revised PEM is similar with random vibration experiment in dynamical parameters and responses are proved by comparative results.The maximum error is within 9%.The reasons of errors are analyzed to improve reliability of calculation.This research provides an effective method for solutions of computing dynamical characteristic parameters of complicated structure in the process of rocket or shuttle launching.

Vibration Control Induced by Ice of a Jacket Platform

Based on the self-excited vibration theory of ice, the vibration control technology of jacket platform is studied in this paper. The magnetorheological suspensions (MR) unit is chosen as the damper, the control objective function for vibration excited by ice is determined by instantaneous optimal control (IOC) method, and genetic algorithm (GA) is used to select the optimal control force. For the jacket platform of 40 m in height and a 3-floor deck, the vibration responses induced by ice have been calculated before and after control considering the different thickness and speed of ice. It is shown that the control method presented in this paper can reduce the vibration response by 30%, and it is feasible to adopt MR absorber and GA in the control of vibration induced by ice.

Research on two-dimensional fluid vibration axial transmission path model of axial piston pump

High speed and high pressure can enhance the vibration of axial piston pump. A fluid vibration transmission law of axial piston pump is studied in this paper. According to harmonic response analysis results, a transmission path analysis is used to establish a two-dimensional fluid vibration transmission path model in the vertical plane, which has characteristics of multi excitation sources, multi-path and multi-receptors. Model parameters are obtained by experimental and numerical analysis. Matlab is used to solve the model, and acceleration vibration response of three shells is got. To reduce the effect of mechanical vibration, the surface acceleration of pump is tested under low speed condition. Results show that the model can accurately reveal transmission law of fluid vibration and the accuracy is more than 90%. The research lays a foundation for exploring vibration transmission law and vibration control.

Comparison of nonlinear modeling methods for the composite rubber clamp

The cubic stiffness force model(CSFM)and Bouc-Wen model(BWM)are introduced and compared innovatively.The unknown coefficients of the nonlinear models are identified by the genetic algorithm combined with experiments.By fitting the identified nonlinear coefficients under different excitation amplitudes,the nonlinear vibration responses of the system are predicted.The results show that the accuracy of the BWM is higher than that of the CSFM,especially in the non-resonant region.However,the optimization time of the BWM is longer than that of the CSFM.