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.

Effect of Coupled Torsional and Transverse Vibrations of the Marine Propulsion Shaft System

In this study,the coupled torsional-transverse vibration of a propeller shaft system owing to the misalignment caused by the shaft rotation was investigated.The proposed numerical model is based on the modified version of the Jeffcott rotor model.The equation of motion describing the harmonic vibrations of the system was obtained using the Euler-Lagrange equations for the associated energy functional.Experiments considering different rotation speeds and axial loads acting on the propulsion shaft system were performed to verify the numerical model.The effects of system parameters such as shaft length and diameter,stiffness and damping coefficients,and cross-section eccentricity were also studied.The cross-section eccentricity increased the displacement response,yet coupled vibrations were not initially observed.With the increase in the eccentricity,the interaction between two vibration modes became apparent,and the agreement between numerical predictions and experimental measurements improved.Given the results,the modified version of the Jeffcott rotor model can represent the coupled torsional-transverse vibration of propulsion shaft systems.

Longitudinal vibration of pile in layered soil based on Rayleigh-Love rod theory and fictitious soil-pile model

The dynamic response of pile in layered soil is theoretically investigated when considering the transverse inertia effect.Firstly, the fictitious soil-pile model is employed to simulate the dynamic interaction between the pile and the soil layers beneath pile toe. The dynamic interactions of adjacent soil layers along the vertical direction are simplified as distributed Voigt models.Meanwhile, the pile and fictitious soil-pile are assumed to be viscoelastic Rayleigh-Love rods, and both the radial and vertical displacement continuity conditions at the soil-pile interface are taken into consideration. On this basis, the analytical solution for dynamic response at the pile head is derived in the frequency domain and the corresponding quasi-analytical solution in the time domain is then obtained by means of the convolution theorem. Following this, the accuracy and parameter value of the hypothetical boundaries for soil-layer interfaces are discussed. Comparisons with published solution and measured data are carried out to verify the rationality of the present solution. Parametric analyses are further conducted by using the present solution to investigate the relationships between the transverse inertia effects and soil-pile parameters.

INVESTIGATION OF SIMULATION EXPERIMENT ON ACTIVE CONTROL OF TORSIONAL VIBRATION IN A TURBOGENERATOR SHAFT SYSTEM

According to the theoretical analysis and calculation on the base ofcontinuous mass system, the simulation experimental investigation on active control of torsionalvibration in a turbogenerator shaft system is conducted. A test installation with the excitation ofgenerator motor and multi-stepped shaft system is established to simulate the torsional vibration ofa turbogenerator rotor shaft system, and to examine the active control strategy presented. Someuseful results are reached in the experimental study.

Forced Axial and Torsional Vibrations of a Shaft Line Using the Transfer Matrix Method Related to Solution Coefficients

This present paper deals with a mathematical description of linear axial and torsional vibrations. The normal and tangential stress tensor components produced by axial-torsional deformations and vibrations in the propeller and intermediate shafts, under the influence of propeller-induced static and variable hydrodynamic excitations are also studied. The transfer matrix method related to the constant coefficients of differential equation solutions is used. The advantage of the latter as compared with a well-known method of transfer matrix associated with state vector is the possibility of reducing the number of multiplied matrices when adjacent shaft segments have the same material properties and diameters. The results show that there is no risk of buckling and confirm that the strength of the shaft line depends on the value of the static tangential stresses which is the most important component of the stress tensor.

DESIGN AND ANALYSIS OF NOVEL ACTIVE ACTUATOR TO CONTROL LOW FREQUENCY VIBRATIONS OF SHAFT SYSTEM

Aiming at providing with high-load capability in active vibration control of large-scale rotor system, a new type of active actuator to simultaneously reduce the dangers of low frequency flexural and torsional vibrations is designed. The actuator employs electro-hydraulic system and can provide a high and circumferential load. To initialize new research, the characteristics of various kinds of active actuators to control rotor shaft vibration are briefly introduced. The purpose of this paper is to introduce the preliminary results via presenting the structure, functions and operating principles, in particular, the working process of the electro-hydraulic system of the new actuator which includes a set of high speed electromagnetic valves and a series of sloping cone-shaped openings, and presenting the transmission relationships among the control parameters from control signals into the valves to active load onto shaft. The course of the work is dynamic, and a series of spatial forces and moments are put on the shaft to get an external resultant force to reduce excitations that induce vibration of shafts. By checking states of vibration, the actuator can control the impulse width and the interval of injection time for applying different control force to a vibration shaft in two circumference directions through the regulating action of a set of combination directional control valves. The results from simulating analysis and experiment show evidence of that this design can satisfy the case of active process of decreasing of flexural and torsional vibrations.

ON THE REPEATED NATURAL FREQUENCIES FOR TORSIONAL VIBRATION OF SHAFTS

To investigate the repeated frequency condition (RFC) for torsional vibration of shafts' system, the transfer matrix method was adopted. Firstly, the transfer relationship from the boundary to engaging disks of double shafts' system (DSS) was constructed. Secondly, the RFC of DSS was deduced out and the methods to select mode shape were presented. Finally, the relationship was extended to multilevel transmission system (MTS), and the RFC of this system was explored. The conclusions is this: 1) the necessary RFC requires the existence of joint engaging couple (JEC); 2) for DSS, the sufficient is the number of boundary transfer factors (f(B)) larger than 2; 3) the whale system can be split into independent groups, the total multiplicity is the sum of independent solution number of every group, the latter is the number of independent f(B), = 0 inside the group minus 1.

Theoretical analysis of nonlinear vibration characteristics of gear pair with shafts

The circumferential vibration of a gear pair is a parametric excitation caused by nonlinear tooth stiffness,which fluctuates with meshing.In addition,the vibration characteristics of the gear pair become complicated owing to the tooth profile error and backlash.It is considered that the circumferential vibration of the gear pair is affected by the torsional vibration of the shafts.It is important to understand quantitatively the vibration characteristics of the gear system considering the shafts.Therefore,the purpose of this research was to clarify the nonlinear vibration characteristics of a gear pair considering the influence of the shafts using theoretical methods.To achieve this objective,calculations were performed using equations of motion in which the circumferential vibration of the gear pair and the torsional vibration of the shafts were coupled.The nonlinear tooth stiffness was represented by a sine wave.The influence of tooth separation was considered by defining a nonlinear function using backlash and the tooth profile error.For the numerical calculations,both stable and unstable periodic solutions were obtained by using the shooting method.The effect of the shafts on the gear system vibration were clarified by comparing the results in the cases in which the shaft was not considered,one shaft was considered,and both shafts were considered.

Longitudinal Vibration Analysis of Elastically Coupled Nanorods System with General Boundary Supports

In this paper,an accurate series solution for the longitudinal vibration analysis of elastically coupled nanorods system is established,in which artificial springs are introduced to simulate such general coupling and boundary conditions.Energy formulation is derived for the description of axial dynamics of multiple coupled nanorods based on Eringen nonlocal elasticity.For each nanorod component,its longitudinal vibration displacement function is invariantly assumed as the superposition of Fourier series and boundary smoothed supplementary polynomials,with the aim to make all the spatial differential sufficiently continuous across each rod.All the unknown coefficients are determined in conjunction with Rayleigh-Ritz procedure to solve a standard eigenvalue matrix.Numerical results are presented for the particular cases of twonanorod and three-nanorod systems to demonstrate the correctness and effectiveness of the proposed model.Excellent agreements can be repeatedly observed in comparison with those from other approaches available in literature.Based on the model established,influence of elastic boundary and coupling conditions on the longitudinal modal characteristics of multiple nanorods system is investigated and addressed.This work can provide an efficient energy-based modeling framework for longitudinal vibration analysis of elastically connected nanorod system with complicated boundary conditions.

Experimental study on integral axial squeeze film damper to suppress longitudinal vibration of propulsion shafting

This paper aims at investigating the effectiveness of squeeze oil film in suppressing the longitudinal vibration of propulsion shaft systems through a novel integral axial squeeze film damper(IASFD).After designing the IASFD,a propulsion shafting test rig for the longitudinal vibration control is built.Longitudinal vibration control experiments of the propulsion shafting are carried out under different magnitude and frequency of the excitation force.The results show that both IASFD elastic support and IASFD elastic damping support have excellent vibration attenuation characteristics,and can effectively suppress the longitudinal vibration of the shaft system in a wide frequency range.However,IASFD elastic damping support has a more significant vibration reduction effect than the other supports,and increasing the damping of the system has obvious effect on reducing the shafting vibration.For an excitation force of 45 N,the maximum reduction of the vibration amplitude is 89.16%.Also,the vibration generated by the resonance phenomenon is also significantly reduced.

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.

AN ANALYTICAL SOLUTION TO LONGITUDINAL VIBRATION OF A PILE OF ARBITRARY SEGMENTS WITH VARIABLE MODULUS

The vibration problem of a pile of arbitrary segments withvariable modulus modules under ex- citing force is established, inwhich the influence of the soil under pile toe and the surroundingsis tak- en into account. With Laplace transforms, the transmitfunctions for velocity and displacement of pile are derived.Furthermore, in terms of the convolution theorem and inversed Laplacetransform, an analytical solution for the time domain response of apile subjected to semi-sine impulse is developed, which is thetheoretical basis of the sonic method in pile integrity testing. Basedon the solution, the vibration properties of pile with sharp orcontinuous modulus are studied. The validity of this approach isverified through field dynamic tests on some engineering piles. Itshows that the theoretical predic- tion ad the response of the pileare in good agreement.

Experimental study on vibration suppression of gear shaft misalignment with ISFD

Misalignment faults in gear systems lead to violent vibration and noise, shortening the life of equipment. The aim of this work is the demonstration of vibration suppression of parallel-misaligned gear shafts using an integral squeeze film damper(ISFD). Using a first grade spur gear in engineering for reference, an open first-grade spur gear system is built and the vibration characteristics of the gear system with rigid supports and ISFD elastic damping supports are studied under different degrees of misalignment. The experimental results show that ISFD supports have excellent damping and vibration attenuation characteristics, which have improved control of the gear system vibration in horizontal, vertical and axial directions under different degrees of misalignment. This work shows that an ISFD structure can effectively suppress vibration of characteristic frequency components and resonance modulation frequency components. The test results provide evidence for the application of ISFD in vibration control of gear shaft misalignment faults in engineering.

Analytical analysis for vibration of longitudinally moving plate submerged in infinite liquid domain

The vibration of a longitudinally moving rectangular plate submersed in an infinite liquid domain is studied analytically with the Rayleigh-Ritz method. The liquid is assumed to be incompressible, inviscid, and irrotational, and the velocity potential is used to describe the fluid velocity in the whole liquid field. The classical thin plate theory is used to derive mechanical energies of the traveling plate. As derivative of transverse displacement with respect to time in the compatibility condition equation exists, an exponential function is introduced to depict the dynamic deformation of the moving plate. It is shown that this exponential function works well with the Rayleigh- Ritz method. A convergence study shows a quick convergence speed for the immersed moving plate. Furthermore, the parametric study is carried out to demonstrate the effect of system parameters including the moving speed, the plate location, the liquid depth, the plate-liquid ratio, and the boundary condition. Results show that the above system parameters have significant influence on the vibration characteristics of the immersed moving plate. To extend the study, the method of added virtual mass incremental （AVMI） factor is used. The results show good agreement with those from the Rayleigh-Ritz method.

Transient Model for Shafting Vibration of Hydro Turbine Generating Sets

The shafting vibration is closely related to the rotational angular speed.The angular speed of hydro turbine generating sets(HTGS)is rapidly change in fault transient,it maybe reduce the shafting damage.By means of energy analysis,the differential equation of shafting vibration for the HTGS is derived,in which include the equation of generator rotor and hydro turbine runner,it can be applied to transient analysis.Shafting model is transformed into first order differential equation groups,and is combined with the motion equation of HTGS to build integrated model.Various additional forces of shafting are taken as input inspire in proposed model,the generality of model is good.At last,the shafting vibration in emergency stop transient is simulated.

Longitudinal Vibration Analysis of Marine Riser During Installation and Hangoff in Ultra Deepwater

This paper is concerned with the problem of longitudinal vibration of a 3,000 m long disconnected drilling riser during installation and hangoff operation.The natural frequency,amplitude of vibration displacement and vibration force of longitudinal vibration have been determined with consideration of the damping effect of the sea water.Results show the natural frequency of riser under these two situations are both decrease with the increase of water depth.The natural frequency of riser in installation operation is bigger than that in hangoff operation.The vibration displacement in hangoff configuration is bigger than that in installation while the vibration force in hangoff configuration is smaller than that in installation configuration.Under the condition of resonance,the vibration displacement increase along riser from top end to the bottom end while the vibration force increase along riser from riser bottom end to the top end.

A Note on Stability of Longitudinal Vibrations of an Inhomogeneous Beam

In this paper, we have considered an inhomogeneous beam with a damping distributed along the length of the beam. The beam is clamped at both ends and is assumed to vibrate longitudinally. We have estimated the total energy of the system at any time t. By constructing suitable Lyapunov functional, it is established directly that the energy of this system decays exponentially.

TORSIONAL OSCILLATION CHARACTERISTICS OF ROTARY SHAFTS BASED ON TORSION AND BENDING COUPLED VIBRATION

The torsional oscillation characteristics on the bending and torsioh coupled vibration of rotary shaft system were investigated using the elasto-dynamic theory and other mathematic methods, such as difference approach, Fourier transform, and wavelet transform. It is concluded that mass eccentricity and other exciting modalities affect the bending and torsion coupled vibration of rotary shafts. Torsional vibration caused by bending vibration features linearity along with the change of amplitude of bending vibration. Meanwhile, energy spectrum concentrates on high frequency area with the wavelet analysis.

Influence of Track Irregularity on Longitudinal Vibration of Wheelset and Correlation Performance

Longitudinal vibration of wheelset with respect to bogie frame often exists with a high acceleration magnitude and relative high frequency. First, a simplified model with a single wheelset moving at a constant speed on a tangential track with irregularity is used to investigate the longitudinal vibration dynamics. Computional results indicate that the longitudinal vibration frequency of the wheelset is most sensitive to the primary longitudinal stiffness and the mass of the wheelset. As to the locomotive model, the longitudinal vibration is concerned with cross-level irregularity and vertical profile irregularity. Meanwhile, a method to estimate the resonance speed is presented. Finally, a possible solution is brought forward to extend wheel-rail service life by eliminating longitudinal vibration of the wheelset. The solution is simply to arrang the primary vertical damper with a forward angle, so that its damping component can be applied to longimdinal direction.

Analysis of Transverse Vibration of a Longitudinally Moving Fabric

Fabric moves along running direction continuously in the processing of weaving,dyeing and finishing and its dynamic behavior is very complex.Running at a high speed,the fabric vibrates,which has great influence not only on the performance of machine,but also on the fabric itself.Analysis of transverse free vibration of a longitudinally moving fabric is put forward in this paper and the calculating formula of natural frequencies of the fabric is introduced accordingly.Meanwhile the effects of several parameters on the first order natural frequency are also discussed.