Longitudinal vibration characteristics of a tapered pipe pile considering the vertical support of surrounding soil and construction disturbance

This research is concentrated on the longitudinal vibration of a tapered pipe pile considering the vertical support of the surrounding soil and construction disturbance.First,the pile-soil system is partitioned into finite segments in the vertical direction and the Voigt model is applied to simulate the vertical support of the surrounding soil acting on the pile segment.The surrounding soil is divided into finite ring-shaped zones in the radial direction to consider the construction disturbance.Then,the shear complex stiffness at the pile-soil interface is derived by solving the dynamic equilibrium equation for the soil from the outermost to innermost zone.The displacement impedance at the top of an arbitrary pile segment is obtained by solving the dynamic equilibrium equation for the pile and is combined with the vertical support of the surrounding soil to derive the displacement impedance at the bottom of the upper adjacent segment.Further,the displacement impedance at the pile head is obtained based on the impedance function transfer technique.Finally,the reliability of the proposed solution is verified,followed by a sensitivity analysis concerning the coupling effect of the pile parameters,construction disturbance and the vertical support of the surrounding soil on the displacement impedance of the pile.

A vertical track nonlinear energy sink

Eliminating the effects of gravity and designing nonlinear energy sinks(NESs)that suppress vibration in the vertical direction is a challenging task with numerous damping requirements.In this paper,the dynamic design of a vertical track nonlinear energy sink(VTNES)with zero linear stiffness in the vertical direction is proposed and realized for the first time.The motion differential equations of the VTNES coupled with a linear oscillator(LO)are established.With the strong nonlinearity considered of the VTNES,the steady-state response of the system is analyzed with the harmonic balance method(HBM),and the accuracy of the HBM is verified numerically.On this basis,the VTNES prototype is manufactured,and its nonlinear stiffness is identified.The damping effect and dynamic characteristics of the VTNES are studied theoretically and experimentally.The results show that the VTNES has better damping effects when strong modulation responses(SMRs)occur.Moreover,even for small-amplitude vibration,the VTNES also has a good vibration suppression effect.To sum up,in order to suppress the vertical vibration,an NES is designed and developed,which can suppress the vertical vibration within certain ranges of the resonance frequency and the vibration intensity.

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.

Active Low-frequency Vertical Vibration Isolation System for Precision Measurements

Low-fi＇equency vertical vibration isolation systems play important roles in precision measurements to reduce seismic and environmental vibration noise. Several types of active vibration isolation systems have been developed. However, few researches focus on how to optimize the test mass install position in order to improve the vibration transmissibility. An active low-frequency vertical vibration isolation system based on an earlier instrument, the Super Spring, is designed and implemented. The system, which is simple and compact, consists of two stages： a parallelogram-shaped linkage to ensure vertical motion, and a simple spring-mass system. The theoretical analysis of the vibration isolation system is presented, including terms erroneously ignored before. By carefully choosing the mechanical parameters according to the above analysis and using feedback control, the resonance frequency of the system is reduced from 2.3 to 0.03 Hz, a reduction by a factor of more than 75. The vibration isolation system is installed as an inertial reference in an absolute gravimeter, where it improved the scatter of the absolute gravity values by a factor of 5. The experimental results verifies the improved performance of the isolation system, making it particularly suitable for precision experiments. The improved vertical vibration isolation system can be used as a prototype for designing high-performance active vertical isolation systems. An improved theoretical model of this active vibration isolation system with beam-pivot configuration is proposed, providing fundamental guidelines for vibration isolator design and assembling.

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.

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.

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.

THE DESIGN AND ANALYSIS OF VIBRATION STRUCTURE OF VERTICAL DYNAMIC BALANCING MACHINE

A new type of vibration structure (i.e. supporting system, called swing frame cus- tomarily) of vertical dynamic balancing machine has been designed, which is based on an analysis for the swing frame of a traditional double-plane vertical dynamic balancing machine. The static unbalance and couple unbalance can be e?ectively separated by using the new dynamic balancing machine with the new swing frame. By building the dynamics model, the advantages of the new structure are discussed in detail. The modal and harmonic response are analyzed by using the ANSYS7.0. By comparing the ?nite element modal analysis with the experimental modal analy- sis, the natural frequencies and vibration modes are found. There are many spring boards in the new swing frame. Their sti?nesses are di?erent and assorted with each other. Furthermore, there are three sensors on the measuring points. Therefore, the new dynamic balancing machine can measure static unbalance and coupling unbalance directly, and the interaction between them is faint. The result shows that the new vertical dynamic balancing machine is suitable for inertial measurement of ?ying objects, and can overcome the shortcomings of traditional double-plane vertical dynamic balancing machines, which the e?ect of plane-separation is inferior. The vertical dynamic balancing machine with the new vibration structure can ?nd wide application in the future. The modelling and analysis of the new vibration structure will provide theoretical basis and practical experience for designing new-type vertical dynamic balancing machines.

Finite Element Modelling of Car Seat with Hyperelastic and Viscoelastic Foam Material Properties to Assess Vertical Vibration in Terms of Acceleration

Primary objective of automobile seats is to offer adequate level of safety and comfort to the seated human occupant, primarily against vibration. Ideally, any sort of automotive seat is constructed by mechanical framework, cushion, backrest and headrest. The frame structures are made of metallic alloys, while the cushion, backrest and headrest are made of polyurethane foam material. During the design phase of automotive seat, the greatest challenge is to assign realistic material properties to foam material;as it is non-linear in nature and exhibit hysteresis at low level stress. In this research paper, a car seat has been modelled in finite element environment by implementing both hyperelastic and viscoelastic material properties to polyurethane foam. The car seat has been excited with the loads due to car acceleration and human object and the effects of vibration in terms of vertical acceleration at different locations have been measured. The aims of this simulation study are to establish a car seat with the foam material properties as accurately as possible and provide a finite element set up of car seat to monitor the vertical acceleration responses in a reasonable way. The RMS acceleration values for headrest, backrest and cushion have been found to be 0.91 mm/sec2, 0.54 mm/sec2 and 0.47 mm/sec2, respectively, which showed that the car seat foam can effectively be modelled through combined hyperelastic and viscoelastic material formulations. The simulation outputs have been validated through real life testing data, which clearly indicates that this computerized simulation technique is capable of anticipating the acceleration responses at different car seat segments in a justified way.

Characteristics of wheel-rail vibration of the vertical section in high-speed railways

In order to analyze the characteristics of wheel-rail vibration of the vertical section in a high-speed railway, a vehicle-line dynamics model is established using the dynamics software SIMPACK. Through this model, the paper analyzes the influence of vertical section parameters, including vertical section slope and vertical curve radius, on wheel-rail dynamics interaction and the acting region of wheel-rail vibration. In addition, the characteristics of wheel- rail vibration of the vertical section under different velocities are investigated. The results show that the variation of wheel load is not sensitive to the vertical section slope but is greatly affected by the vertical curve radius. It was also observed that the smaller the vertical curve radius is, the more severe the interaction between the wheel and rail be- comes. Furthermore, the acting region of wheel-rail vibration expands with the vertical curve radius increasing. On another note, it is necessary to match the slope and vertical curve radius reasonably, on account of the influence of operation speed on the characteristics of wheel-rail vibration. This is especially important at the design stage of vertical sec- tions for lines of different grades.

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.

Random Vibration Analysis of Urban Underground Tunnels Under Vertical Earthquake Excitations Based on Mass–Damper–Spring Model

In this paper, the verticalseismic effects on tunnels are studied based on a classic mass–damper–spring model. An analyticaldiscrete modelof urban underground tunnels subjected to verticalearthquake excitations is proposed by considering the first verticalvibration mode. Taking a light railproject in Tianjin as an example, this study uses the proposed discrete modelto analyze the displacements of tunneland soilunder verticalearthquake excitations. The soildisplacement responses at different tunnellocations are analyzed with linear random vibration theory.The computationalcost is greatly reduced using the proposed model. It can be seen that different from the case of horizontalearthquakes, the displacement responses under verticalearthquake excitations keep growing after seismic acceleration reaches its peak for a short duration, and then,they begin to decay. The soils at different positions around the tunnels have large relative displacement under verticalearthquake excitations. Moreover, a finite-element modelis also established for displacement responses using ABAQUS.The comparison with the results of the finite-element modelshows that the results of the proposed discrete modelare available.

NEW TYPE OF VIBRATION STRUCTURE OF VERTICAL DYNAMIC BALANCING MACHINE

A new type of vibration structure of vertical dynamic balancing machine isdesigned, which is based on the analysis for swing frame of a traditional vertical dynamic balancingmachine. The static unbalance and couple unbalance can be separated effectively by using the newmachine with the new swing frame. By building the dynamics model, the advantages of the newstructure are discussed in detail. The modal and harmonic response are analyzed by using theANSYS7.0. By comparing the finite element modal analysis with the experimental modal analysis, thenatural frequencies and vibration modes are found out. There are many spring boards in the new swingframe. Their stiffness is different and assort with each other. Furthermore, there are threesensors on the measurement points. Therefore, the new dynamic balancing machine can measure thestatic unbalance and couple unbalance directly, and the influence between them is faint. The newstructure has the function of belt-strain compensation to improve the measurement precision. Thepractical result indicates that the new vertical dynamic balancing machine is suitable for inertialmeasurement of flying objects, and can overcome the shortcomings of traditional double-planevertical dynamic balancing machines. The vertical dynamic balancing machine with the new vibrationstructure can be widely used in the future applications. The modeling and analysis of the newvibration structure provide theoretic instruction and practical experience for designing new type ofvertical dynamic balancing machines. Based on the design principles such as stiffness-matching,frequency-adjacence and strain-compensation and so on, various new type of vibration structures canbe designed.

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.

Vertical Vibration Isolation Using Displacement Feedback Control

A vertical active vibration isolation system using the displacement feedback force,a method widely used in gravitational and other experiments,is reanalyzed in detail.We find that more effective vibration isolation could be obtained if the feedback variable is proportional to the relative displacement between the platform and the foundation other than the absolute displacement of the platform itself The physical meaning is first recognized by introducing the concept of quasi-fixed reference system,this is significant for improving the isolation ratio of an active isolation system.

Vibration Control of Vertical Turbine Pump by Optimization of Vane Pitch Tolerances of an Impeller Using Statistical Techniques

The objective of the study is to find the tolerance on vane pitch dimensions of a Vertical Turbine(VT)pump impeller.For this purpose,the study is divided into two parts viz.to find the critical hydraulic eccentricity of a VT pump impeller by way of numerical simulations and design of experiments to find the vane pitch tolerance using critical hydraulic eccentricity.The effect of impeller vane pitch deviations on hydraulic unbalance is examined for a vertical turbine pump using Design of Experiments(DOE).A suitable orthogonal matrix has been selected with vane pitch at different axial locations of an impeller as the control factors.Hydraulic eccentricity,which is the output of the DOE experiments is analyzed using S/N ratio,ANOM and regression analysis to find the significant control factor effecting the hydraulic unbalance and hence vibrations.The vane pitch deviation at outlet and inlet of impeller shroud geometry are found to be the most critical factor affecting the pump vibrations.

THE MEASUREMENT AND STUDY OF BLASTING VIBRATION AFFECTING IN SITU CAST CONCRETE LINING OF VERTICAL SHAFT

Vertical shaft is main form of drivage in deep mineral depoist. They also serve as the entrance into and the exit from the underground mine. The main problems in shaft and tunnel engineering is to solve the contradiction between drivage and lining. The measurement of blasting vibration affecting concrete lining strength of vertical shaft is carried out in experiment and theory in this paper.