Natural vibration and critical velocity of translating Timoshenko beam with non-homogeneous boundaries

In most practical engineering applications,the translating belt wraps around two fixed wheels.The boundary conditions of the dynamic model are typically specified as simply supported or fixed boundaries.In this paper,non-homogeneous boundaries are introduced by the support wheels.Utilizing the translating belt as the mechanical prototype,the vibration characteristics of translating Timoshenko beam models with nonhomogeneous boundaries are investigated for the first time.The governing equations of Timoshenko beam are deduced by employing the generalized Hamilton's principle.The effects of parameters such as the radius of wheel and the length of belt on vibration characteristics including the equilibrium deformations,critical velocities,natural frequencies,and modes,are numerically calculated and analyzed.The numerical results indicate that the beam experiences deformation characterized by varying curvatures near the wheels.The radii of the wheels play a pivotal role in determining the change in trend of the relative difference between two beam models.Comparing the results unearths that the relative difference in equilibrium deformations between the two beam models is more pronounced with smaller-sized wheels.When the two wheels are of equal size,the critical velocities of both beam models reach their respective minima.In addition,the relative difference in natural frequencies between the two beam models exhibits nonlinear variation and can easily exceed 50%.Furthermore,as the axial velocities increase,the impact of non-homogeneous boundaries on modal shape of translating beam becomes more significant.Although dealing with non-homogeneous boundaries is challenging,beam models with non-homogeneous boundaries are more sensitive to parameters,and the differences between the two types of beams undergo some interesting variations under the influence of non-homogeneous boundaries.

The Outer-Performance Distortion of the Suspension Shock Absorber and Its Critical Velocity

On the basis of analysing the outer performance degradation of shock absorber on suspenson and from the relationship between outer and inner performances of the shock absorber, an internal relationship between the structure design and degradation of the shock absorber is discussed in the paper. From dynamic property, analysed the dynamic cause for degradation, the paper proposes a technical method of improving outer performance and a concept of critical velocity, and discusses what effects the critical velocity and the outer performance mance degradation has.

The Influence of the Imperfectness of Contact Conditions on the Critical Velocity of the Moving Load Acting in the Interior of the Cylinder Surrounded with Elastic Medium

The dynamics of the moving-with-constant-velocity internal pressure acting on the inner surface of the hollow circular cylinder surrounded by an infinite elastic medium is studied within the scope of the piecewise homogeneous body model by employing the exact field equations of the linear theory of elastodynamics.It is assumed that the internal pressure is point-located with respect to the cylinder axis and is axisymmetric in the circumferential direction.Moreover,it is assumed that shear-spring type imperfect contact conditions on the interface between the cylinder and surrounding elastic medium are satisfied.The focus is on the influence of the mentioned imperfectness on the critical velocity of the moving load and this is the main contribution and difference of the present paper the related other ones.The other difference of the present work from the related other ones is the study of the response of the interface stresses to the load moving velocity,distribution of these stresses with respect to the axial coordinates and to the time.At the same time,the present work contains detail analyses of the influence of problem parameters such as the ratio of modulus of elasticity,the ratio of the cylinder thickness to the cylinder radius,and the shear-spring type parameter which characterizes the degree of the contact imperfection on the values of the critical velocity and stress distribution.Corresponding numerical results are presented and discussed.In particular,it is established that the values of the critical velocity of the moving pressure decrease with the external radius of the cylinder under constant thickness of that.

Critical velocity of sandwich cylindrical shell under moving internal pressure

Critical velocity of an infinite long sandwich shell under moving internal pressure is studied using the sandwich shell theory and elastodynamics theory. Propagation of axisymmetric free harmonic waves in the sandwich shell is studied using the sandwich shell theory by considering compressibility and transverse shear deformation of the core, and transverse shear deformation of face sheets. Based on the elastodynamics theory, displacement components expanded by Legendre polynomials, and position-dependent elastic constants and densities are introduced into the equations of motion. Critical velocity is the minimum phase velocity on the desperation relation curve obtained by using the two methods. Numerical examples and the finite element （FE） simulations are presented. The results show that the two critical velocities agree well with each other, and two desperation relation curves agree well with each other when the wave number k is relatively small. However, two limit phase velocities approach to the shear wave velocities of the face sheet and the core respectively when k limits to infinite. The two methods are efficient in the investigation of wave propagation in a sandwich cylindrical shell when k is relatively small. The critical velocity predicted in the FE simulations agrees with theoretical prediction.

Critical velocity and dynamic respondency of pipe conveying fluid

Presents the calculation of critical velocity, natural frequency and dynamic respondency of fluid conveying pipe are calculated under different boundary conditions using finite element method, and the use of calculation results to design and research rocket pipes feeding fuel and watery turbine pipes conveying water etc.

Critical velocity in phosphorus exchange processes across the sediment-water interface

Sediments are ultimate sinks of nutrients in lakes that record the pollution history evolutionary processes, and anthropogenic activities of a lake. However, sediments are considered as inner sources of environmental factor changes such as the variation in hydrodynamic conditions because of the nutrients they release. How does this process happen？ This study investigates a typical nutrient phosphorus （P） exchange among sediment, suspended particle matter （SPM）, and water. Compared with numerical and experimental studies, this study confirms that the critical velocity that occurs at a lower flow rate state exists in the range of 7 to 15 crn/sec. Critical velocity below the critical flow rate promotes the migration of particulate phosphorus （PP） to the SPM. On the other hand, critical velocity above the critical flow rate promotes the release of PP in water.

Numerical and experimental study on the critical velocity and smoke maximum temperature in the connected area of branch tunnel

The objective of this study is to investigate critical velocity and smoke maximum temperature beneath the ceiling in the connected area of branch tunnel with varying fire locations.The fire sources were located in the divergent connected area of the branch tunnel,to imitate traffic accidents near the branch point.A 1/20 scale model branch tunnel was built including main line before branch,main line after branch,and ramp.Experimental tests and numerical simulations were performed to explore smoke movement characteristics with longitudinal ventilation.The results showed that the enlarged cross-sectional area in branch tunnel caused the shortening of the back-layering length,and a modified model of back-layering length was proposed.The higher tunnel height in this work affected the critical condition of large fire;it caused a larger transition point of dimensionless critical velocity.A revised model was proposed for the maximum temperature rise of tunnel fires in the connected area of branch tunnel.The critical velocity kept unchanged when the branch angle increased from 0°to 20°because there is little change in the longitudinal smoke temperature.As the local tunnel width of fire source was increased,the required critical velocity was increased while the local effective velocity kept nearly the same.

Critical Velocity of Short Floating Slab Track Using Alterable Element Method Considering Wheel-Rail Contact Loss

In actual line operation,the critical velocity is one of the key physical quantities of rail design owing to its great infuence on the riding comfort and safety of vehicles due to the wheel-rail contact loss caused by the abrupt change of rail foundation rigidity,rail wear,or abruptness irregularities on rail.In this study,the short floating slab track(SFST)structure is regarded as a double-layer system.The Euler beam and the rigid body model are adopted for the rail and the floating slab,respectively.and the dispersion equation and the theoretical critical velocity of the rail structure under ideal conditions are deduced.Besides,this st udy considers the implementation of the SFST in the vehicle-structure coupling system.The alterable element method is introduced for accurately simulating the change of the whee-rail contact state and coding a vehicle-structure dynamic analysis program(VSDAP)to calculate the critical velocity of rail structures from the dynamic response of vehicles and rail structures.The principle of its design at the beginning of the design is given on the basis of the theoretical value of the critical velocity and the simulation of the dynamic response,which can provide reference for practical engineering design.

Numerical Experiments on Critical Ventilation Velocity and Back-layer in Tunnel Fire

Full-scale numerical experiments were carried out on the vehicular fire in a long tunnel to study the critical ventilation velocity and back-layer distance with heat release rate of 5, 20 and 100 MW respectively. A computational fluid dynamics (CFD) model of fire-driven fluid flow FDS(Fire Dynamics Simulator) was used to solve numerically a form of the Navier-Stokes equations for fire. The results were compared with the expressions proposed in the literature. A modified equation for the critical ventilation velocity was given to better fit the experimental results. A bi-exponential model that well fitted the numerical experimental results was proposed to describe the relationship between back-layer distance and ventilation velocity.

A Novel Pre-control Method of Vehicle Dynamics Stability Based on Critical Stable Velocity during Transient Steering Maneuvering

The current research of direct yaw moment control（DYC） system focus on the design of target yaw moment and the distribution of wheel brake force. The differential braking intervention can effectively improve the lateral stability of the vehicle, however, the effect of DYC can be improved a step further by applying the control of vehicle longitudinal velocity. In this paper, the relationship between the vehicle longitudinal velocity and lateral stability is studied, and the simulation results show that a decrease of 5 km/h of longitudinal velocity at a particular situation can bring 100° increasing of stable steering upper limit. A critical stable velocity considering the effect of steering and yaw rate measurement is defined to evaluate the risk of losing steer-ability or stability. A novel velocity pre-control method is proposed by using a hierarchical pre-control logic and is integrated with the traditional DYC system. The control algorithm is verified through a hardware in-the-loop simulation system. Double lane change（DLC） test results on both high friction coefficient（μ） and low μ roads show that by using the pre-control method, the steering effort in DLC test can be reduced by 38% and 51% and the peak value of brake pressure control can be reduced by 20% and 12% respectively on high μ and low μ roads, the lateral stability is also improved. This research proposes a novel DYC system with lighter control effort and better control effect.

Experimental study of the critical sand starting velocity of gas-watersand flow in an inclined pipe

The purpose of this paper is to study the critical sand starting velocity and transformation law of flow pattern based on gas-water-sand three-phase flow in an inclined pipe.Firstly,the indoor simulation experiment system of gas-water-sand three-phase flow was used to test the conversion law of flow pattern based upon the different gas void fraction.Secondly,the influence of slug bubbles on sand migration was investigated according to distinctive hole deviation angles,gas void fraction and sand concentration.Finally,the critical sand starting velocity was tested based on dissimilar hole deviation angles,gas void fraction,sand concentration and sand particle size,and then the influence of the abovementioned key parameters on the sand starting velocity was debated based on the force analysis of the sand particles.The experimental results illustrated that when the gas void fraction was less than 5%,it was bubbly flow.When it increased from 5%to 30%,the bubbly flow and slug flow coexisted.When it was between 30%and 50%,the slug flow and agitated flow coexisted.When it reached 50%,it was agitated flow.Providing that the hole deviation angle was 90°,the phenomenon of overall migration and wavelike migration on the surface of sand bed was observed.On the contrary,the phenomenon of rolling and jumping migration was recognized.The critical sand starting velocity was positively correlated with the hole deviation angle and sand particle size,but negatively associated with the gas void fraction and sand concentration.This research can provide a certain reference for sand-starting production in the field of petroleum engineering.

Aerodynamic unstable critical wind velocity for three-dimensionalopen cable-membrane structures

The aerodynamic unstable critical wind velocity for three-dimensional open cable-membrane structures is investigated. The geometric nonlinearity is introduced into the dynamic equilibrium equations of structures. The disturbances on the structural surface caused by the air flow are simulated by a vortex layer with infinite thickness in the structures. The unsteady Bernoulli equation and the circulation theorem are applied in order to express the aerodynamic pressure as the function of the vortex density. The vortex density is then obtained with the vortex lattice method considering the coupling boundary condition. From the analytical expressions of the unstable critical wind velocities, numerical results and some useful conclusions are obtained. It is found that the initial curvature of open cable-membrane structures has clear influence on the critical wind velocities of the structures.

A new model for predicting the critical liquid-carrying velocity in inclined gas wells

Based on the assumption of gas-liquid stratified flow pattern in inclined gas wells,considering the influence of wettability and surface tension on the circumferential distribution of liquid film along the wellbore wall,the influence of the change of the gas-liquid interface configuration on the potential energy,kinetic energy and surface free energy of the two-phase system per unit length of the tube is investigated,and a new model for calculating the gas-liquid distribution at critical conditions is developed by using the principle of minimum energy.Considering the influence of the inclination angle,the calculation model of interfacial friction factor is established,and finally closed the governing equations.The interface shape is more vulnerable to wettability and surface tension at a low liquid holdup,resulting in a curved interface configuration.The interface is more curved when the smaller is the pipe diameter,or the smaller the liquid holdup,or the smaller the deviation angle,or the greater gas velocity,or the greater the gas density.The critical liquid-carrying velocity increases nonlinearly and then decreases with the increase of inclination angle.The inclination corresponding to the maximum critical liquid-carrying velocity increases with the increase of the diameter of the wellbore,and it is also affected by the fluid properties of the gas phase and liquid phase.The mean relative errors for critical liquid-carrying velocity and critical pressure gradient are 1.19%and 3.02%,respectively,and the misclassification rate is 2.38%in the field trial,implying the new model can provide a valid judgement on the liquid loading in inclined gas wells.

Numerical study on critical flow velocity of ice slurry in the pipe of ice source heat pump system

The traditional evaporator of water source heat pump system is easy to freeze when the water source temperature is too low in winter.A novel ice source heat pump system is proposed,which can use low temperature surface water to supply heat to buildings.One of the key problems for safe transportation is velocity range of ice slurry in ice outlet pipeline.In order to study the critical flow velocity of ice slurry in the pipe,an Euler model of horizontal straight pipe and 90°elbow pipe were established by Fluent software.The influence of five factors on the critical flow velocity of two kinds of pipes,including initial ice packing fraction,ice particle size,pipe diameter,length of straight pipe and radius curvature of elbow was studied.It found that the initial ice content should be controlled from 10%to 15%.The inlet flow rate was 20%higher than the critical flow rate under the most unfavorable condition.Ice particle size was less than 0.2 mm.The total length of ice discharge pipeline was less than 50 m.Curvature radius of the bend should be met the minimum requirements of the specification of the pipe used.

High Velocity Impact Experiment on Ti/CFRP/Ti Sandwich Structure

Aircraft laminated composite components often suffer a variety of high velocity impacts with large quantity of energy,which usually affects aircraft behavior and would incur component damages,even disastrous consequences.Therefore,one investigates the impact resistance of a new type of composite material,Ti/CFRP/Ti sandwich structure,and launches impact tests by using an air gun test system.Then one acquires the critical breakthrough rate of the structure and analyzes the damages.The results show that the main failure mode of the front titanium sheet is shear plugging and brittle fracture of adhesive layer with fiber breakage,while the back titanium sheet is severely ripped.The rear damage is worse than the front one.Compared with traditional CFRP laminates,the critical breakthrough rate of Ti/CFRP/Ti sandwich structure is improved by 69.9% when suffered the impact of a bearing ball with 2mm radius.

On the energy conservation and critical velocities for the propagation of a "steady-shock" wave in a bar made of cellular material

The propagation of shock waves in a cellular bar is systematically studied in the framework of continuum solids by adopting two idealized material models, viz. the dynamic rigid, perfectly plastic, locking （D-R-PP-L） model and the dynamic rigid, linear hardening plastic, locking （D-R-LHP-L） model, both considering the effects of strain-rate on the material properties. The shock wave speed relevant to these two models is derived. Consider the case of a bar made of one of such material with initial length L 0 and initial velocity v i impinging onto a rigid target. The variations of the stress, strain, particle velocity, specific internal energy across the shock wave and the cease distance of shock wave are all determined analytically. In particular the ＂energy conservation condition＂ and the ＂kinematic existence condition＂ as proposed by Tan et al. （2005） is re-examined, showing that the ＂energy conservation condition＂ and the consequent ＂critical velocity＂, i.e. the shock can only be generated and sustained in R-PP-L bars when the impact velocity is above this critical velocity, is incorrect. Instead, with elastic deformation, strain-hardening and strain-rate sensitivity of the cellular materials being considered, it is appropriate to redefine a first and a second critical impact velocity for the existence and propagation of shock waves in cellular solids. Starting from the basic relations for shock wave propagating in D-R-LHP-L cellular materials, a new method for inversely determining the dynamic stress-strain curve for cellular materials is proposed. By using e.g. a combination of Taylor bar and Hopkinson pressure bar impact experimental technique, the dynamic stress-strain curve of aluminum foam could bedetermined. Finally, it is demonstrated that this new formulation of shock theory in this one-dimensional stress state can be generalized to shocks in a one-dimensional strain state, i.e. for the case of plate impact on cellular materials, by simply making proper replacements of the elastic and plastic constants.

Research on the Critical Conditions for Clay Particle Release During Saline Aquifer Freshening Process

Water sensitivity phenomenon occurs during saline aquifer freshening process in seawater intrusion area, and clay particles released in the phenomenon can damage the infiltration capacity of the aquifer. In order to find out the factors and mechanisms for clay particle release, laboratory column infiltration experiments simulating saline aquifer freshening process were designed to measure the critical conditions(critical flow velocity, critical salt concentration and critical ionic strength) and force analysis for clay particle according to DLVO electric double layer theory was employed to illustrate the mechanisms for particle release. The research results showed that critical flow velocity for clay particle release is influenced by salt concentration of injecting solution. When salt concentration of injecting solution is very high, clay particles are not released, indicating that there does not exist a critical flow velocity in this situation. As salt concentration of injecting solution decreases, particles start to be released. The critical salt concentration for clay particle release is 0.052 mol L-1 in our work, which was determined by a constant-flux experiment for stepwise displacement of high concentration Na Cl solution. The critical ionic strength for clay particle release decreases as Ca2+ molar content percentage of the mixed solution of Na Cl and Ca Cl2 increases following the first-order exponential decay equation y = 0.0391e-0.266 x + 0.0015.

Dynamic modeling of fluid-conveying pipes restrained by a retaining clip

Although most pipes are restrained by retaining clips in aircraft,the influence of the clip parameters on the vibration of the fluid-conveying pipe has not been revealed.By considering the clip width,a new dynamic model of a fluid-conveying pipe restrained by an intermediate clip is established in this paper.To demonstrate the necessity of the proposed model,a half pipe model is established by modeling the clip as one end.By comparing the two models,it is found that the half pipe model overestimates the critical velocity and may estimate the dynamical behavior of the pipe incorrectly.In addition,with the increase in the clip stiffness,the conversion processes of the first two modes of the pipe are shown.Furthermore,by ignoring the width of the clip,the effect of the flow velocity on the accuracy of a concentrated restraint clip model is presented.When the flow velocity is close to the critical velocity,the accuracy of the concentrated restraint clip model significantly reduces,especially when the width of the clip is large.In general,the contribution of this paper is to establish a dynamic model of the fluid-conveying pipe which can describe the influence of the clip parameters,and to demonstrate the necessity of this model.

Non-symmetric distributions of solids deposition for solid-water stratified flow in deviated tubing strings

Dynamic performance on solids flow with water in deviated tubing is essential for the reliability of pump and normal operation of horizontal and directional wells.Compared with coal-water flow in vertical tubing and sand-oil flow with high production in deviated tubing,solids deposition with water shows obvious non-symmetric distributions in deviated tubing from simulations and experiments.The mathematical model of two phase flow was developed under coupling conditions of deviated tubing,low flow rate and viscosity based on the kinetic theory of granular flow and first-order discrete scheme.The results show that solid-water stratified flow in deviated tubing can be divided into two zones of suspension bed and the moving bed throughout the flow field.The solid flowing velocity with water is negative and particles slide down at the bottom of moving bed zone.The process of solids flow with water in deviated tubing will produce pressure loss and consume the kinetic energy.The thickness of deposited layer and the flowing velocity of solids flow downward with water at the moving bed zone enhance with the decreased inlet flow rate and the increased particle size,tubing inside diameter(ID)and inclination angle.Solids are easier into suspension from the upper part of moving bed zone to suspension bed zone and more solid particles flow with water towards the tubing outlet with the increase of inlet flowing velocity.The decision is made to reduce the screen width,tubing ID and inclination angle to maintain to be greater than critical deposition velocity in order to prevent solids settling.And it provides the theoretical basis and technical reserves for solid control and offers an effective approach to enhance tubing cleaning in deviated strings.

基于流固耦合方法的两自由度水翼流激振动特性研究

The flutter of a hydrofoil can cause structural damage and failure,which is a dangerous situation that must be avoided.In this work,based on computational fluid dynamics and structural finite element methods,a co-simulation framework for the flow-induced vibration of hydrofoil was established to realize fluid-structure interaction.Numerical simulation research was conducted on the flow-induced vibration characteristics of rigid hydrofoil with 2-DOF under uniform flow,and the heave and pitch vibration responses of hydrofoil were simulated.The purpose is to capture the instability of hydrofoil vibration and evaluate the influence of natural frequency ratio and inertia radius on vibration state to avoid the generation of flutter.The results indicate that when the inflow velocity increases to a certain critical value,the hydrofoil will enter the flutter critical state without amplitude attenuation.The attack angle of a hydrofoil has a significant impact on the vibration amplitude of heave and pitch.Additionally,the natural frequency ratio and inertia radius of the hydrofoil significantly affect the critical velocity of the flutter.Adjusting the natural frequency ratio by reducing the vertical stiffness or increasing the pitch stiffness can move the vibration from a critical state to a convergent state.