Dynamic Characteristics of Functionally Graded Timoshenko Beams by Improved Differential Quadrature Method

This study proposes an effective method to enhance the accuracy of the Differential Quadrature Method(DQM)for calculating the dynamic characteristics of functionally graded beams by improving the form of discrete node distribution.Firstly,based on the first-order shear deformation theory,the governing equation of free vibration of a functionally graded beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam axial displacement,transverse displacement,and cross-sectional rotation angle by considering the effects of shear deformation and rotational inertia of the beam cross-section.Then,ignoring the shear deformation of the beam section and only considering the effect of the rotational inertia of the section,the governing equation of the beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam transverse displacement.Based on the differential quadrature method theory,the eigenvalue problem of ordinary differential equations is transformed into the eigenvalue problem of standard generalized algebraic equations.Finally,the first several natural frequencies of the beam can be calculated.The feasibility and accuracy of the improved DQM are verified using the finite element method(FEM)and combined with the results of relevant literature.

Analysis of mesoscopic mechanical dynamic characteristics of ballast bed with under sleeper pads

The meso-dynamical behaviour of a high-speed rail ballast bed with under sleeper pads(USPs)was studied.The geometrically irregular refined discrete element model of the ballast particles was constructed using 3D scanning techniques,and the 3D dynamic model of the rail-sleeper-ballast bed was constructed using the coupled discrete element method-multiflexible-body dynamics(DEM-MFBD)approach.We analyse the meso-mechanical dynamics of the ballast bed with USPs under dynamic load on a train and verify the correctness of the model in laboratory tests.It is shown that the deformation of the USPs increases the contact area between the sleeper and the ballast particles,and subsequently the number of contacts between them.As the depth of the granular ballast bed increases,the contact area becomes larger,and the contact force between the ballast particles gradually decreases.Under the action of the elastic USPs,the contact forces between ballast particles are reduced and the overall vibration level of the ballast bed can be reduced.The settlement of the granular ballast bed occurs mainly at the shallow position of the sleeper bottom,and the installation of the elastic USPs can be effective in reducing the stress on the ballast particles and the settlement of the ballast bed.

Dynamic stiffness characteristics of aero-engine elastic support structure and its effects on rotor systems:mechanism and numerical and experimental studies

The support structure of a rotor system is subject to vibration excitation,which results in the stiffness of the support structure varying with the excitation frequency(i.e.,the dynamic stiffness).However,the dynamic stiffness and its effect mechanism have been rarely incorporated in open studies of the rotor system.Therefore,this study theoretically reveals the effect mechanism of dynamic stiffness on the rotor system.Then,the numerical study and experimental verification are conducted on the dynamic stiffness characteristics of a squirrel cage,which is a common support structure for aero-engine.Moreover,the static stiffness experiment is also performed for comparison.Finally,a rotor system model considering the dynamic stiffness of the support structure is presented.The presented rotor model is used to validate the results of the theoretical analysis.The results illustrate that the dynamic stiffness reduces the critical speed of the rotor system and may lead to a new resonance.

Dynamic mechanical characteristics of NdFeB in electromagnetic brake

With the continuous development of artillery,the disadvantages of hydraulic recoil brakes gradually appear.At the same time,the appearance of high-performance Nd Fe B permanent magnet makes it possible to apply electromagnetic braking technology to recoil mechanism.In this paper,prototype tests of a certain artillery were carried out to verify the feasibility of the electromagnetic brake(EMB)and obtain the electromagnetic braking force.Due to the brittleness of Nd Fe B,in order to eliminate the worry about the safety of EMB,SHPB experiments of Nd Fe B were carried out.Then,based on the assumption of uniform crack distribution,the law of crack propagation and damage accumulation was described theoretically,and the damage constitutive model suitable for brittle materials was proposed by combining the Zhu-Wang-Tang(ZWT)equation.Finally,the numerical simulation model of the artillery prototype was established and through calculation,the dynamic mechanical characteristics of Nd Fe B in the prototype were analyzed.The calculation results show that the strength of Nd Fe B can meet the requirements of the use in the working process.From the perspective of damage factor,the damage value of the permanent magnet on the far right is larger,and the damage value of the inner ring gradually decreases to the outer ring.

Liquefaction susceptibility and deformation characteristics of saturated coral sandy soils subjected to cyclic loadings-a critical review

Coral sandy soils widely exist in coral island reefs and seashores in tropical and subtropical regions.Due to the unique marine depositional environment of coral sandy soils,the engineering characteristics and responses of these soils subjected to monotonic and cyclic loadings have been a subject of intense interest among the geotechnical and earthquake engineering communities.This paper critically reviews the progress of experimental investigations on the undrained behavior of coral sandy soils under monotonic and cyclic loadings over the last three decades.The focus of coverage includes the contractive-dilative behavior,the pattern of excess pore-water pressure(EPWP)generation and the liquefaction mechanism and liquefaction resistance,the small-strain shear modulus and strain-dependent shear modulus and damping,the cyclic softening feature,and the anisotropic characteristics of undrained responses of saturated coral sandy soils.In particular,the advances made in the past decades are reviewed from the following aspects:(1)the characterization of factors that impact the mechanism and patterns of EPWP build-up;(2)the identification of liquefaction triggering in terms of the apparent viscosity and the average flow coefficient;(3)the establishment of the invariable form of strain-based,stress-based,or energy-based EPWP ratio formulas and the unique relationship between the new proxy of liquefaction resistance and the number of cycles required to reach liquefaction;(4)the establishment of the invariable form of the predictive formulas of small strain modulus and strain-dependent shear modulus;and(5)the investigation on the effects of stress-induced anisotropy on liquefaction susceptibility and dynamic deformation characteristics.Insights gained through the critical review of these advances in the past decades offer a perspective for future research to further resolve the fundamental issues concerning the liquefaction mechanism and responses of coral sandy sites subjected to cyclic loadings associated with seismic events in marine environments.

Research on dynamic characteristics of arc under electrode relative motion

The relative motion of the electrodes is a typical feature of sliding electrical contact systems.The system fault caused by the arc is the key problem that restricts the service life of the sliding electrical contact system.In this paper,an arcing experimental platform that can accurately control the relative speed and distance of electrodes is built,and the influence of different electrode speeds and electrode distances on arc motion characteristics is explored.It is found that there are three different modes of arc root motion:single arc root motion mode,single and double arc roots alternating motion mode,and multiple arc roots motion mode.The physical process and influence mechanism of different arc root motion modes are further studied,and the corresponding relationship between arc root motion modes and electrode speed is revealed.In addition,to further explore the distribution characteristics of arc temperature and its influencing factors,an arc magnetohydrodynamic model under the relative motion of electrodes is established,and the variation law of arc temperature under the effect of different electrode speeds and electrode distances is summarized.Finally,the influence mechanism of electrode speed and electrode distance on arc temperature,arc root distance,and arc root speed is clarified.The research results enrich the research system of arc dynamic characteristics in the field of sliding electrical contact,and provide theoretical support for restraining arc erosion and improving the service life of the sliding electrical contact system.

Physical modeling of long-term dynamic characteristics of the subgrade for medium-low-speed maglevs

To investigate the dynamic characteristics and long-term dynamic stability of the new subgrade structure of medium-low-speed(MLS)maglevs,cyclic vibration tests were performed under natural and rainfall conditions,and the dynamic response of the subgrade structure was monitored.The dynamic response attenuation characteristics along the depth direction of the subgrade were compared,and the distribution characteristics of the dynamic stress on the surface of the subgrade along the longitudinal direction of the line were analyzed.The critical dynamic stress and cumulative deformation were used as indicators to evaluate the long-term dynamic stability of the subgrade.Results show that water has a certain effect on the dynamic characteristics of the subgrade,and the dynamic stress and acceleration increase with the water content.With the dowel steel structure set between the rail-bearing beams,stress concentration at the end of the loaded beam can be prevented,and the diffusion distance of the dynamic stress along the longitudinal direction increases.The dynamic stress measured in the subgrade bed range is less than 1/5 of the critical dynamic stress.The postconstruction settlement of the subgrade after similarity ratio conversion is 3.94 mm and 7.72 mm under natural and rainfall conditions,respectively,and both values are less than the 30 mm limit,indicating that the MLS maglev subgrade structure has good long-term dynamic stability.

Dynamic response characteristics of a circular lined tunnel under anisotropy frost heave of overlying soil at the tunnel portal section in cold regions

The rapid development of traffic engineering in cold regions and its consequent problems need to be considered.In this paper,the dynamic response characteristics of the tunnel portal section in cold regions with harmonic load acting on the lining were studied in the frequency domain.The lining is in close contact with the frozen soil,and there is relative movement between the frozen and unfrozen soil due to the phase change.The analytical solution of the vibration of tunnel portal section caused by the harmonic load acting on the lining was derived under the consideration of the anisotropy frost heave of overlying soil.Based on the continuity conditions and boundary conditions,the undetermined coefficients were obtained,and the analytical solutions for different medium displacements and stresses of the cold-region tunnel system were acquired.The vertical pressure coefficient was equivalently simplified as a variable that could be used to replace the thickness of the overlying soil above the tunnel.The analysis of the parameter model shows that the change of the medium parameters(lining,frozen,and unfrozen soil)affects the circumferential stresses,the radial displacements and their peak frequencies of the soil.For example,the increase of density ratio of tunnel lining to frozen soil decreases the radial stresses of the frozen and unfrozen soil;the increase of volumetric frost heaving strain of the frozen soil increases the radial displacements of the frozen surface and decreases the stability of the frozen surface;the increasing of thickness of the frozen soil significantly reduces the radial displacement of unfrozen soil at dimensionless radius η=4.5 compared with that of frozen soil at η=1.5.

Dynamic physical characteristics of DC arc on arcing horn for HVDC grounding electrode line

The dynamic physical characteristics of a DC arc on an arcing horn for a high voltage direct current(HVDC)grounding electrode line are significantly different from those of the switching device arc,secondary arc,AC fault arc and pantograph-catenary arc.In this work,an experimental platform for the DC arc on the arcing horn was built,and mechanisms of the arc column short circuit and arc root movement were studied.This work further analyzes the characteristics and mechanisms of the arc motion when wind speed and direction,magnetic field and the expansion angle of the electrode are varied.Arc root movement is more likely to occur at the upper electrode.There is a competitive relationship between arc expansion and the transferring effect.The effect of wind on the arc column is greater than the effect on the arc root.The magnetic field has a significant driving effect on both the arc column and the arc root.The research results provide a comprehensive experimental basis for forther probing the method of DC arc suppression,and the improvement of the arcing horn.

Dynamic simulation analysis of molten salt reactor-coupled air-steam combined cycle power generation system

A nonlinear dynamic simulation model based on coordinated control of speed and flow rate for the molten salt reactor and combined cycle systems is proposed here to ensure the coordination and stability between the molten salt reactor and power system.This model considers the impact of thermal properties of fluid variation on accuracy and has been validated with Simulink.This study reveals the capability of the control system to compensate for anomalous situations and maintain shaft stability in the event of perturbations occurring in high-temperature molten salt tank outlet parameters.Meanwhile,the control system’s impact on the system’s dynamic characteristics under molten salt disturbance is also analyzed.The results reveal that after the disturbance occurs,the controlled system benefits from the action of the control,and the overshoot and disturbance amplitude are positively correlated,while the system power and frequency eventually return to the initial values.This simulation model provides a basis for utilizing molten salt reactors for power generation and maintaining grid stability.

Review on Dynamic Modeling and Vibration Characteristics of Rotating Cracked Blades

As one of the most important parts in the engine,the structure and state of the rotating blade directly affect the normal performance of the aeroengine.In order to monitor engine crack failure and ensure flight safety,it is necessary to carry out research on the dynamic modeling of the cracked blade and breathing crack-induced vibration mechanisms.This paper summarizes the current research status on the dynamics of cracked blade,and the related topics mainly include four aspects:crack propagation path,mechanical model of open and breathing cracks,dynamic modeling methods of cracked blades such as lumped mass model,semi-analytical model and finite element model,and dynamic characteristics of cracked blades.The review will provide valuable references for future studies on dynamics and fault diagnosis of cracked blade in aeroengine.

Spalling characteristics of high-temperature treated granitic rock at different strain rates

The dynamic spalling characteristics of rock are important for stability analysis in rock engineering.This paper presented an experimental investigation on the dynamic spalling characteristics of granite with different temperatures and strain rates.A series of dynamic spalling tests with different impact velocities were conducted on thermally treated granite at different temperatures.The dynamic spalling strengths of granite with different temperatures and strain rates were determined.A model was proposed to correlate the dynamic spalling strength of granite,high temperature and strain rate.The results show that the spalling strength of granite decreases with increasing temperature.Moreover,the spalling strength of granite with a higher strain rate is larger than that with a lower strain rate.The proposed model can describe the relationship among dynamic spalling strength of granite,high temperature and strain rate.

Research of transient rotor dynamic characteristic of magnetic liquid double suspension bearing in double collision state

During the operation of magnetic liquid double suspension bearing(MLDSB),due to rotor resonance,assembly error and other factor,the vibration amplitude of the rotor in resonance state exceeds the original design clearance,resulting in the collision damage between the rotor and the stator,the rotor and the casing.This paper presents a method to simulate the influence of different factors on the dynamic characteristics of 5 degrees of freedom(DOF)rotor based on the dynamic model of MLDSB.Firstly,according to the second Lagrange equation,the dynamic equation of 5 DOF rotor is derived,and the mathematical model is established.Then,based on 5 DOF rotor dynamic equation,the rotor transient dynamic equation under collision state is obtained,and the rotor transient collision dynamic simulation model is established.Finally,the key influencing factors of rotor dynamic characteristics are extracted,and the influence mapping relationship of rotor displacement,axis locus and stress distribution under different factors is simulated by using ANSYS Workbench software.The experimental results show that this method can effectively reflect the influence of various factors on the dynamic characteristics of the rotor.This method can provide theoretical reference for the design and control of MLDSB.

Effects of Floating Ring Bearing Manufacturing Tolerance Clearances on the Dynamic Characteristics for Turbocharger

The inner and outer oil film dynamic characteristic coefficients of floating ring bearings（FRBs） change due to the manufacturing tolerance of the floating ring, journal and intermediate, which leads to high-speed turbocharger＇s vibration too large and even causes nonlinear vibration accident. However, the investigation of floating ring bearing manufacturing tolerance clearance on the rotordynamic characteristics is less at present. In order to study the influence law of inner and outer clearance on turbocharger vibration, the rotor dynamic motion equations of turbocharger supported in FRBs are derived by analyzing the size relations between floating ring, journal and intermediate for the inner and outer oil film clearances, the time transient response analysis for combination of FRBs clearance are developed. A realistic turbocharger is taken as a research object, the FE model of the turbocharger with FRBs is modeled. Under the conditions of four kinds of limit state bearing clearances for inner and outer oil film, the nonlinear transient analyses are performed based on the established FE dynamic models of the nonlinear rotor-FRBs system applied incentive combinations of gravity and unbalance force, respectively. From the waterfall, the simulation results show that the speed for the appearance of fractional frequency is not identical and the amplitude magnitude is different under the four kinds of bearing manufacturing tolerance limit clearances, and fractional frequency does not appear in the turbocharger and the amplitude is minimum under the ODMin/IDMax bearing manufacturing tolerance clearances. The turbocharger vibration is reduced by controlling the manufacturing tolerance clearance combinations of FRBs, which is helpful for the dynamic design and production-manufacturing of high-speed turbocharger.

Theoretical Analysis and Numerical Simulation of the Static and Dynamic Characteristics of Hydrostatic Guides Based on Progressive Mengen Flow Controller

The oil film thickness of oil hydrostatic guide with constant pressure supply based on capillary restrictor is greatly affected by load, and this kind of hydrostatic guide is usually applied to the machine tools with moderate load. The static and dynamic characteristics of the guide have been studied by using some theoretical, numerical and experimental approaches, and some methods and measures have been proposed to improve its performances. The hydrostatic guide based on progressive mengen（PM） flow controller is especially suitable for the heavy numerical control（NC） machine tools. However, few literatures about the research on the static and dynamic characteristics of the hydrostatic guides based on PM flow controller are reported. In this paper, the formulae are derived for analyzing the static and dynamic characteristics of hydrostatic guides with rectangle pockets and PM flow controller according to the theory of hydrostatic bearing. On the basis of the analysis of hydrostatic bearing with circular pocket, some equations are derived for solving the static pressure, volume pressure and squeezing pressure which influence the dynamic characteristics of hydrostatic guides with rectangle pocket. The function and the influencing factors of three pressures are clarified. The formulae of amplitude-frequency characteristics and dynamic stiffness of the hydrostatic guide system are derived. With the help of software MATLAB, programs are coded with C＋＋ language to simulate numerically the static and dynamic characteristics of the hydrostatic guide based on PM flow controller. The simulation results indicate that the sensitive oil volume between the outlet of the PM flow controller and the guide pocket has the greatest influence on the characteristics of the guide, and it should be reduced as small as possible when the field working condition is met. Choosing the oil with a greater viscosity is also helpful in improving the dynamic performance of hydrostatic guides. The research work has instructing significance for analyzing and designing the guide with PM flow controller.

Dynamic characteristics of a novel damped outrigger system

This paper presents exact analytical solutions for a novel damped outrigger system, in which viscous dampers are vertically installed between perimeter columns and the core of a high-rise building. An improved analytical model is developed by modeling the effect of the damped outrigger as a general rotational spring acting on a Bernoulli-Euler beam. The equivalent rotational spring stiffness incorporating the combined effects of dampers and axial stiffness of perimeter columns is derived. The dynamic stiffness method(DSM) is applied to formulate the governing equation of the damped outrigger system. The accuracy and effi ciency are verifi ed in comparison with those obtained from compatibility equations and boundary equations. Parametric analysis of three non-dimensional factors is conducted to evaluate the infl uences of various factors, such as the stiffness ratio of the core to the beam, position of the damped outrigger, and the installed damping coeffi cient. Results show that the modal damping ratio is signifi cantly infl uenced by the stiffness ratio of the core to the column, and is more sensitive to damping than the position of the damped outrigger. The proposed analytical model in combination with DSM can be extended to the study of structures with more outriggers.

Dynamic Characteristics of Multi-degrees of Freedom System Rotor-bearing System with Coupling Faults of Rub-impact and Crack

Extensive studies on rotor systems with single or coupled multiple faults have been carried out. However these studies are limited to single-span rotor systems. A finite element model for a complex rotor-bearing system with coupled faults is presented. The dynamic responses of the rotor-bearing system are obtained by using the rotor dynamics theory and the modern nonlinear dynamics theory in connection with the continuation-shooting algorithm（commonly used for obtaining a periodic solution for a nonlinear system） for a range of rub-impact clearances and crack depths. The stability and Hopf instability of the periodic motion of the rotor-bearing system with coupled faults are analyzed by using the procedure described. The results indicate that the finite element method is an effective way for determining the dynamic responses of such complex rotor-bearing systems. Further for a rotor system with rub-impact and crack faults, the influences of the clearances are significantly different for different rub-impact stiffness. On the contrary, the influence of crack depths is rather small. The instability speeds of the rotor-bearing system increase due to the presence of the crack fault. The results obtained using the new finite element model, presented for computation and analysis of dynamic responses of the rotor-bearing systems with coupled faults, are in accordance with measurements in experiment. The formulations given can be used for diagnosis of faults, vibration control, and safe and stable operations of real rotor-bearing systems.

RESEARCH OF THE DYNAMIC CHARACTERISTICS ON A NEW HYDRAULIC SYSTEM OF ELECTRO-HYDRAULIC HAMMER

A new typed hydraulic system of electro hydraulic hammer is researched and developed By means of power bond graphs the modeling and simulation to the dynamic characteristics of the new hydraulic system are performed The experimental research which is emphasized on the blowing stroke is also performed It is proved from the result of simulation and experiment that this new hydraulic system possesses such advantages as simplification of structure,flexibleness of operation and reliability of working Especially it possesses better dynamic characteristics

Model test on dynamic characteristics of invert and foundation soils of high-speed railway tunnel

A dynamic model test(CL = 4) at different velocities of train,namely different loading frequencies,is carried out to study the dynamic characteristics of a high-speed railway tunnel invert and its foundation soils.Not only are the accelerations,dynamic coefficients,dynamic stresses of the invert and foundation soils emphatically analyzed,their relationship with the velocity of the train are discussed in detail.Through laboratory testing,the attenuation of vibration propagating from up the rails is obtained and the calculation formula of the speed influence coefficient of the tunnel invert is preliminarily established.The depth of the foundation soils influenced by vibration is also determined in this study.It is shown that the responses of the tunnel invert and foundation soils to vibration are slightly increased with the velocity of the train;circumferential stresses in the bottom of the invert are tensile stresses and maximum stresses appear under the foot of the rails;the dynamic soil pressures of the foundation decrease quickly with the distance away from the tunnel invert and an exponential relationship exists between them.

Numerical simulation of dynamic characteristics of a cable-stayed aqueduct bridge

In this paper, a full-scale 3-D finite element model of the Jundushan cable-stayed aqueduct bridge is established with ANSYS Code. The shell, fluid, tension-only spar and beam elements are used for modeling the aqueduct deck, filled water, cables and support towers, respectively. A multi-element cable formulation is introduced to simulate the cable vibration. The dry （without water） and wet （with water） modes of the aqueduct bridge are both extracted and investigated in detail. The dry modes of the aqueduct bridge are basically similar to those of highway cable-stayed bridges. A dry mode may correspond to two types of wet modes, which are called the in-phase （with lower frequency） and out-of-phase （with higher frequency） modes. When the water-structure system vibrates in the in-phase/out-of-phase modes, the aqueduct deck moves and water sloshes in the same/opposite phase-angle, and the sloshing water may take different surface-wave modes. The wet modes of the system reflect the properties of interaction among the deck, towers, cables and water. The in-phase wet frequency generally decreases as the water depth increases, and the out-of-phase wet frequency may increase or decrease as the water depth increases.