Vertical Vibration of Moving Strip in Rolling Process Based on Beam Theory

The shape and thickness qualities of strip are influenced by the vibration of rolling mill. At present, the researches on the vibration of rolling mill are mainly the vertical vibration and torsional vibration of single stand mill, the study on the vibration of tandem rolling mill is rare. For the vibration of tandem rolling mill, the key problem is the vibration of the moving strip between stands. In this paper, considering the dynamic of moving strip and rolling theory, the vertical vibration of moving strip in the rolling process was proposed. Take the moving strip between the two mills of tandem rolling mill in the rolling process as subject investigated, according to the theory of moving beam, the vertical vibration model of moving strip in the rolling process was established. The partial differential equation was discretized by Galerkin truncation method. The natural frequency and stability of the moving strip were investigated and the numerical simulation in time domain was made. Simulation results show that, the natural frequency was strongly influenced by the rolling velocity and tension. With increasing of the rolling velocity, the first three natural frequencies decrease, the fourth natural frequency increases; with increasing of the unit tension, when the rolling velocity is high and low, respectively, the low order dimensionless natural frequency gradually decreases and increases, respectively. According to the stability of moving strip, the critical speed was determined, and the matching relationship of the tension and rolling velocity was also determined. This model can be used to study the stability of moving strip, improve the quality of strip and develop new rolling technology from the aspect of dynamics.

Vertical vibration of a large diameter pipe pile considering transverse inertia effect of pile

Considering the transverse inertia effect of pile, the vertical soil layer is studied. The wave propagations in the outer and inner soil dynamic response of a large diameter pipe pile in viscoelastic are simulated by three-dimensional elastodynamic theory and those in the pile are simulated by Rayleigh-Love rod theory. The vertical and radial displacements of the outer and inner soil are obtained by utilizing Laplace transform technique and differentiation on the governing equations of soils. Then, based on the continuous conditions between the pile and soils, the displacements of the pile are derived. The frequency domain velocity admittance and time domain velocity response of the pile top are also presented. The solution is compared to a classical rod model solution to verify the validity. The influences of the radii and Poisson ratio of pile on the transverse inertia effect of pile are analyzed. The parametric study shows that Poisson ratio and outer radius of pile have significant influence on the transverse inertia effect of large diameter pipe piles, while the inner radius has little effect.

A Simplified Nonlinear Model of Vertical Vortex-Induced Force on Box Decks for Predicting Stable Amplitudes of Vortex-Induced Vibrations

Wind-tunnel tests of a large-scale sectional model with synchronous measurements of force and vibration responses were carried out to investigate the nonlinear behaviors of vertical vortex-induced forces （VIFs） on three typical box decks （i.e., fully closed box, centrally slotted box, and semi-closed box）. The mechanisms of the onset, development, and self-limiting phenomenon of the vertical vortex-induced vibration （VlV） were also explored by analyzing the energy evolution of different vertical VIF components and their contributions to the vertical VIV responses. The results show that the nonlinear components of the vertical VIF often differ from deck to deck; the most important components of the vertical VIF, governing the stable amplitudes of the vertical VIV responses, are the linear and cubic components of velocity contained in the self-excited aerodynamic damping forces. The former provides a constant negative damping ratio to the vibration system and is thus the essential power driving the development of the VIV amplitude, while the latter provides a positive damping ratio proportional to the square of the vibration velocity and is actually the inherent factor making the VIV amplitude self-limiting. On these bases, a universal simplified nonlinear mathematical model of the vertical VIF on box decks of bridges is presented and verified in this paper; it can be used to predict the stable amplitudes of the vertical VIV of long-span bridges with satisfactory accuracy.

Axisymmetrical analytical solution for vertical vibration of end-bearing pile in saturated viscoelastic soil layer

Based on elasticity and the theory of saturated porous media, and regarding the pile and the soil as a single phase elastic and a saturated viscoelastic media, respectively, the dynamical behavior of vertical vibration of an end-bearing pile in a saturated viscoelastic soil layer is investigated in the frequency domain using the Helmholtz decomposition and variable separation method. The axisymmetrical analytical solutions for vertical vibrations of the pile in a saturated viscoelastic soil layer are obtained, and the analytical expression of the dynamical complex stiffness of the pile top is presented. Responses of dynamic stiffness factor and equivalent damping of pile top with respect to the frequency are shown in figures using a numerical method. Effects of the saturated soil parameters, modulus ratio of the pile to soil, slenderness ratio of pile and pile＇s Poisson ratio, etc. on the stiffness factor and damping are examined. It is shown that, due to the effect of the transversal deformation of the pile and the radial force of the saturated viscoelastic soil acting on the pile, the dynamic stiffness factor and the damping derived from the axisymmetrical solution are greatly different from those derived from the classical Euler-Bernoulli rod model, especially at some specific excitation frequencies. Therefore, there are limitations on applicability of the Euler-Bernoulli rod model in analyzing verticai vibration of the pile. More accurate analysis should be based on a three-dimensional model.

Vertical vibration of a floating pile in a saturated viscoelastic soil layer overlaying bedrock

An axisymmetrical analytical solution is developed to investigate the vertical time-harmonic vibration of a floating pile in a saturated viscoelastic soil layer overlaying bedrock. The soil is described by porous medium model established by Boer, while the pile is described by a beam vibration theory. By using separation theory of differential operator and variables to solve the dynamic governing equations for the soil, the fundamental solutions for the soil reactions on side and bottom of the pile are obtained. The dynamic impedance of the pile head is then derived by solving the vibration equation for the pile according to the compatibility condition between the pile and the soil. The proposed model is validated by comparing special cases of our model with the existing results. Numerical examples are presented to analyze the vibration characteristics of the pile.

PERFORMANCE OF ULTRA-LOW FREQUENCY PASSIVE VERTICAL VIBRATION ISOLATION SYSTEM WITH REVERSE PENDULUM

A novel long period passive vertical vibration isolatorconstructed by mounting reverse pendu- lums on two pairs of torsionsprings is presented. By theoretical analysis and numericalcalculation, it is shown that the isolator can achieve much longerresonant period due to gravitational positive feedback and is smallerin size than the current torsion spring isolators with the samegeometric parameters.

Analysis on vertical steering vibration of drum shearer cutting part

The impact of the load on the shearer is mainly transmitted through cutting part.In this paper,in order to get the vertical steering vibration characteristics of the cutting part of the drum shearer,the working condition of coal mining machine is simplified.A simplified vertical steering model and the simplified vibration model of the whole cutting part of shearer are established.The vertical steering vibration process of the cutting unit is simplified into a single freedom and one forced vibration system under harmonic excitation.The dynamic response of the cutting part under sine excitation is obtained by using Matlab/Simulink for modeling and simulation.The influence of the support rigidity and damping of the high oil cylinder on the vertical steering vibration characteristics of the cutting part is analyzed.The results show that the damping of the cylinder can reduce the vibration of the system and the stability of the swing process of cutting the part is improved.

Vertical vibrations of elastic foundation resting on saturated half-space

This paper is mainly concerned with the dynamic response of an elastic foundation of finite height bounded to the surface of a saturated half-space. The foundation is subjected to time-harmonic vertical loadings. First, the transform solutions for the governing equations of the saturated media are obtained. Then, based on the assumption that the contact between the foundation and the half-space is fully relaxed and the halfspace is completely pervious or impervious, this dynamic mixed boundary-value problem can lead to dual integral equations, which can be further reduced to the Predhohn integral equations of the second kind and solved by numerical procedures. In the numerical extortples, the dynamic colnpliances, displacements and pore pressure are developed for a wide range of frequencies and material/geometrical properties of the saturated soil-foundation system. In most of the cases, the dynamic behavior of an elastic foundation resting on the saturated media significantly differs from that of a rigid disc on the saturated half-space. The solutions obtained can be used to study a variety of wave propagation problems and dynamic soil-structure interactions.

VERTICAL VIBRATION ANALYSIS OF AXISYMMETRIC SATURATED SOIL

Based on Biot＇s dynamic consolidation equations, by means of Laplace-Hankel transform technology, the integral solutions of stress and displacement in saturated soil with subjacent rock-stratum under axisymmetric arbitrary excitations were derived. Influence of the reflected wave generated by the boundary was revealed. Numerical results indicate that the vibration frequency has some effect on the vertical displacement of satu rated soil. The vertical displacement at the surface of saturated soil lags in phase with the load. Furthermore, the dynamic permeability coefficient of saturated soil has significant effect on the vertical displacement at the initial stage of load applied, but when the load becomes stable, the effect is inapparent.

Application of dynamic vibration absorber for vertical vibration control of corrugated rolling mill

A variable mass tuned particle absorber is designed for the nonlinear vertical vibration control of the corrugated rolling mill in the composite plate rolling process.Considering the nonlinear damping and nonlinear stiffness between the corrugated interface,a three-degree-of-freedom nonlinear vertical vibration mathematical model of corrugated rolling mill based on dynamic vibration absorber control is established.The multi-scale method is used to solve the amplitude–frequency characteristic curve equation of the installed dynamic vibration absorber(DVA)system.The effects of stiffness coefficient and damping coefficient on the amplitude–frequency characteristic curve are analyzed.The expressions of the dynamic developed factor of the corrugated roll are derived,and the influence laws of mass ratio,frequency ratio and damping ratio on the dynamic amplification factor are analyzed.The optimal parameters of the DVA are obtained by adaptive genetic algorithm.The control effect of the DVA on the nonlinear vertical vibration is studied by numerical simulation.The feasibility of the designed dynamic absorber is verified through experiments.The results show that the designed dynamic absorber can effectively suppress the vertical vibration of the corrugated roller.

Vibration analysis of maglev three-span rigid frame bridge considering magnetic force

The dynamic interaction between the maglev vehicle and the three-span rigid frame bridge is discussed. With the consideration of magnetic force, the interaction model is developed. Numerical simulations are performed to study the dynamic characteristics of the bridge during vehicle movement along the bridge. The results show that a reasonable value of the linear stiffness ratio of columns to beams is between 2. 0 and 3.0. The dynamic responses of the bridge are aggravated with the decrease in bending rigidity and the increase in vehicle speed and the span ratio of the bridge. It is suggested that a definite way is to control impact coefficients and acceleration in the dynamic design of the bridge. It is unsuitable to adopt the moving load model and the moving mass model in the design. The proposed results can serve in the design of high-speed maglev three-span rigid frame bridges.

Effects of wheelset vibration on initiation and evolution of rail short-pitch corrugation

The initiation and evolution of short-pitch corrugation in Beijing metro line 4 was studied from the viewpoint of wheelset vibration.A three-dimensional elastic model was set up.Numerical simulations were undertaken with this model to analyze the corrugation by the wheelset vertical vibration and torsional vibration.Based on numerical results,the relation between rail corrugation and wheelset vibration,and the relation between the position of electromotor and wheelset vibration were indicated.It is found that avoiding the wheelset-rail resonance is one method of controlling the rail short-pitch corrugation and solving the vibration and noise problem in metro lines.

Research and application on three-dimensional seismic and vibration isolation for building

This paper presents the study of a three-dimensional(3D) isolation system.Firstly,the authors investigated the effects of an innovative 3D isolator,which was composed of a connecting plate,a rubber pad for vibration isolation in the vertical direction and a horizontal rubber bearing for seismic isolation in both horizontal directions.Secondly,the authors designed such a vibration isolation system and installed it underneath two specific residential buildings which were built directly over an existing subway communication hub platform in Beijing.These buildings required good performance vibration and seismic isolation system to reduce the impact from the running of nearby subway trains.Finally,in situ tests were conducted for both the isolated and the non-isolated buildings for the purpose of comparison.The test results showed that the maximum acceleration response level of the isolated superstructure is reduced by 10% as compared to that of the platform.The maximum attenuation of vibration reaches up to 25 dB.The 3D system explored in this paper is very effective in control and suppression of building vibration induced by earthquakes or running of trains.

Experimental study and analysis on the rising motion of grains in a vertically-vibrated pipe

Previous experimental investigations have shown that when a narrow pipe is inserted into a granular bed and is vibrated vertically but the granular bed is kept still, the grains in the bed can enter the pipe and rise against gravity along the pipe and finally stabilized at a certain height. The growth velocity and final stable height of the grain column inside the pipe can be controlled by varying the vibration conditions. In this paper, we discuss those experimental findings. We establish a mathematic relation between the grain column height（h） and time（t）, and by using the relation we discuss the change of the growth velocity（ dh/ dt） and acceleration（ d^2h/ dt^2） with t and h, respectively. We also analyze the mechanism of the rising motion of the grains during vibration. Furthermore, we derive a theoretical expression for describing the final stable height（h st）, which shows that the main factors influencing the height are vibration strength（Γ）, bulk density of grains,inner diameter of the pipe, and vibration frequency, and that h st increases nonlinearly in the presence of air and linearly in a vacuum environment with increasing Γ.

Vibration Analysis of Continuous Maglev Guideway Considering the Magnetic Levitation System

The dynamic interaction between moving vehicles and two-span continuous guideway was discussed. With the consideration of the magnetic levitation system, the maglev vehicle/guideway dynamic interaction model was developed. Numerical simulation was performed to understand dynamic characteristics of the guideway used in practice. The results show that vehicle speed, span length and primary frequency of the guideway have an important influence on the dynamic responses of the guideway and there is no distinct trend towards resonance vibration when fl equals 1.0. The definite way is to control the impact coefficient and acceleration of the guideway. The conclusions can serve the design of high speed maglev guideway.

Analytical model of vertical vibrations in piles for different tip boundary conditions:parametric study and applications

In this paper,a model named fictitious soil pile was introduced to solve the boundary coupled problem at the pile tip.In the model,the soil column between pile tip and bedrock was treated as a fictitious pile,which has the same properties as the local soil.The tip of the fictitious soil pile was assumed to rest on a rigid rock and no tip movement was allowed.In combination with the plane strain theory,the analytical solutions of vertical vibration response of piles in a frequency domain and the corresponding semi-analytical solutions in a time domain were obtained using the Laplace transforms and inverse Fourier transforms.A parametric study of pile response at the pile tip and head showed that the thickness and layering of the stratum between pile tip and bedrock have a significant influence on the complex impedances.Finally,two applications of the analytical model were presented.One is to identify the defects of the pile shaft,in which the proposed model was proved to be accurate to identify the location as well as the length of pile defects.Another application of the model is to identify the sediment thickness under the pile tip.The results showed that the sediment can lead to the decrease of the pile stiffness and increase of the damping,especially when the pile is under a low frequency load.

Fuel efficient model predictive control strategies for a group of connected vehicles incorporating vertical vibration

This paper presents a decentralized fuel efficient model predictive control(MPC) strategy for a group of connected vehicles incorporating vertical vibration. To capture the vehicle vibration dynamics, the dynamics of the suspension system is integrated with the longitudinal dynamics of the vehicle. Furthermore, a MPC framework with finite time horizon is formulated to calculate the optimal velocity profile that compromises fuel economy, mobility and ride comfort for every individual vehicle with the safety and physical constraints considered. In the MPC framework, the target velocity is calculated using signal phase and timing(SPAT)information to reduce the number of stoppage at red lights, and the vertical acceleration is calculated parallel to the calculation of the fuel consumption. The MPC optimal problem is solved with fast-MPC approach which enhances the computational efficiency via exploiting the structure of the control system and approximate methods. Simulation studies are conducted over different SPATs and connectivity penetration rates and the results validate the advantages of the proposed control architecture.

Vibration characteristics of multi-parametric excitations and multi-frequency external excitations of rolling mill under entry thickness fuctuation of strip

A dynamic rolling force model with multi-parametric excitations and multi-frequency external excitations caused by entry thickness fuctuation of strip was established.Based on the dynamic rolling force,a nonlinear vertical vibration model with multi-parametric excitations and multi-frequency external excitations was established.The method of multiple scales was used to solve the amplitude-frequency characteristic equation of primary resonance of the nonlinear vibration system of a rolling mill.The transition set and the topology structure of systematic global bifurcation were obtained by using the singularity theory.Finally,primary resonance characteristics of the system under entry thickness fuctuation of strip were analyzed by using actual parameters of the rolling mill.The global bifurcation curves with the change of amplitude and frequency of entry thickness fuctuation of strip were obtained by using numerical simulation,and many dynamic behaviors were found such as single-cycle motion,multi-cycle motion and chaotic motion,which can provide a theoretical reference for further restraining the vibration of a rolling mill.

Vertical vibration characteristics of seated human bodies and a biodynamic model with two degrees of freedom

Understanding the vibration characteristics of a seated human body is critical for evaluation and improvement of ride comfort of various passenger vehicles. There have been very little publications about the vibration characteristics of a seated Chinese human body. By using wide-band white noise excitations and a homemade seat sensor, vertical vibration tests were carried out on 28 volunteers. Apparent masses were obtained for each volunteer at a frequency range of 1-20 Hz for various excitation le-vels. A biodynamic model, which has two degrees of freedom in parallel and includes a frame mass, was chosen to describe the vertical vibration characteristics of the seated human body. The model parameters were identified by means of a Gauss-Newton method with an error function defined in terms of both real and imaginary parts of the apparent mass against frequency. Based on the averaged data of the mass-normalized apparent mass from experiments, the model parameters and corresponding modal parameters were obtained for seated Chinese people at ages of 20-25 with standard weight. The apparent masses predicted by the biodynamic model with identified parameters agree very well with those obtained from experiments. Statistical analysis demonstrates the influence of volunteer’s height and weight on the model parameters for a seated human body.

Structural relaxation and avalanche dynamics of particle piles under vertical vibration

Granular matter can exhibit solid or liquid behavior,which contains complex physical mechanisms.In this work,we experimentally investigated the structural relaxation and avalanche dynamics of particle piles under vertical vibration.The influence of vibration parameters on the avalanche process was studied.The morphological features of avalanches were recorded and classified using high-speed camera.The effects of vibration parameters and particle properties on the relaxation mode are obtained.It is found that the evolution of particle pile height with time can be described by an exponential decay function.The relaxation rate and avalanche characteristics of four types of particles with different sizes are discussed.At the same acceleration level,for two larger particles,a smaller amplitude(A=0.025 mm)leads to a faster relaxation rate,while for two smaller particles,a large amplitude(A=0.500 mm)leads to a faster relaxation rate.The analogy powder surface tension is introduced to address the cohesion and flowability evolution of particles under vibration.