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.

LINEAR ULTRASONIC MOTOR USING LONGITUDINAL VIBRATION

A linear ultrasonic motor using longitudinal vibration of bar with varying section is proposed. The lin- ear ultrasonic motor has two varying section bars connected by semi-circumferential structure. Elliptical trajecto- ries of particles are formed on top of the semi-circumferential structure outer surface where a driving foot is locat- ed. And a mover is pushed to move linearly when the driving foot is pressed onto it. Finite element model of sta- tor is built and results of harmonic analysis verify its principle. Moreover, design requirements of the motor are analyzed through finite element analysis and the results of sensitive analysis provide an efficient way to design the type of linear ultrasonic motor. Prototype test shows that the motor can afford load of 10 N at the speed of 100 mm/s.

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.

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.

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.

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.

Longitudinal dynamic response of pile in layered soil based on virtual soil pile model

Taking the effect of finite soil layers below pile end into account,the longitudinal dynamic response of pile undergoing dynamic loading in layered soil was theoretically investigated.Firstly,finite soil layers below pile end are modeled as virtual soil pile whose cross-section area is the same as that of the pile and the soil layers surrounding the pile are described by the plane strain model.Then,by virtue of Laplace transform and impedance function transfer method,the analytical solution of longitudinal dynamic response at the pile head in frequency domain is yielded.Also,the semi-analytical solution in time domain undergoing half-cycle sine pulse at the pile head is obtained by means of inverse Laplace transform.Based on these solutions,a parametric study is conducted to analyze emphatically the effects of parameters of soil below pile end on velocity admittance and reflected wave signals at the pile head.Additionally,a comparison with other models with different supporting conditions from soil below pile end is performed to verify the model presented.

Interaction of In-wheel Permanent Magnet Synchronous Motor with Tire Dynamics

Drive wheel systems combined with the in-wheel permanent magnet synchronous motor（I-PMSM） and the tire are highly electromechanical-coupled. However, the deformation dynamics of this system, which may influence the system performance, is neglected in most existing literatures. For this reason, a deformable tire and a detailed I-PMSM are modeled using Matlab/Simulink. Furthermore, the influence of tire/road contact interface is accurately described by the non-linear relaxation length-based model and magic formula pragmatic model. The drive wheel model used in this paper is closer to that of a real tire in contrast to the rigid tire model which is widely used. Based on the near-precise model mentioned above, the sensitivity of the dynamic tire and I-PMSM parameters to the relative error of slip ratio estimation is analyzed. Additionally, the torsional and longitudinal vibrations of the drive wheel are presented both in time and frequency domains when a quarter vehicle is started under conditions of a specific torque curve, which includes an abrupt torque change from 30 N·m to 200 N·m. The parameters sensitivity on drive wheel vibrations is also studied, and the parameters include the mass distribution ratio of tire, the tire torsional stiffness, the tire damping coefficient, and the hysteresis band of the PMSM current control algorithm. Finally, different target torque curves are compared in the simulation, which shows that the estimation error of the slip ratio gets violent, and the longitudinal force includes more fluctuation components with the increasing change rate of the torque. This paper analyzes the influence of the drive wheel deformation on the vehicle dynamic control, and provides useful information regarding the electric vehicle traction control.

Free longitudinal vibrations of non-uniform rods

Free longitudinal vibrations of non-uniform rods are investigated by a proposed method, which results in a series solution. In a special case, with the proposed method an exact solution with a concise form can be obtained, which imply four types of profiles with variation in geometry or material properties. However, the WKB (Wentzel-Kramers-Brillouin) method leads to a series solution, which is a Taylor expansion of the results of the proposed method. For the arbitrary non-uniform rods, the comparison indicates that the WKB method is simpler, but the convergent speed of the series solution resulting from the pro-posed method is faster than that of the WKB method, which is also validated numerically using an exact solution of a kind of non-uniform rods with Kummer functions.

Determination of complex Young's modulus of viscoelastic bars using forced longitudinal vibration of slender rods

A method to identify complex Young＇s modulus of viscoelastic materials using forced longitudinal vibration of slender rods is proposed. The method differs from the beam one. Experimental tests were carried out at room temperature with different lengths in 108 mm, 100 mm, 90 ram, 83.5 mm, 80 ram, 74.5 mm, 70 mm for the polycarbonate bars, and the curves of ratios A2/A1 between two ends of a viscoelastic bar versus frequencies are obtained, furthermore, the corresponding 3 dB bandwidth and the storage and loss modulus can be calculated. Sufficient number of obtained complex Young＇s modulus at different frequency allows us to calculate other ones using the least square method. If the step of the tested frequency is 5 Hz, the maximum error of results can be less than 6%. By comparison with the measurement methods which the previous literature mentioned, this new method simplifies the calculation, and the physical meaning appears apparently and clearly.

Longitudinal vibrations of arbitrary non-uniform rods

Free and steady-state forced longitudinal vibrations of non-uniform rods are investi- gated by an iteration method, which results in a series solution. The series obtained are convergent and linearly independent. Its convergence is verified by convergence tests, its linear independence confirmed by the nonzero value of the corresponding Wronski determinant. Then, the solution obtained is an exact one reducible to a classical solution for the case of uniform rods. In order to verify the method, two examples are presented as an application of the proposed method. The results obtained are equivalent to the method in literature. In contrast to the proposed method ca- pable of dealing with arbitrary non-uniform rods in principle, the method in literature is confined to work on special cases.

Fluid Pump Using a Bar-shaped Piezoelectric Transducer

There are two kinds of piezoelectric pumps:check valve pumps and valve-less pumps.Whether to use a check valve or not depends upon the application occasion.To achieve large backpressure for higher flow rates,the pump with check valve is desirable.However,adding check valves implies more complex structure and higher probability of valve blocking,etc.In order to solve the problem,effective driving and transport mechanics with compact construction and reliable service are being sought.In this paper,using the second-order longitudinal vibration mode of a bar-shaped piezoelectric vibrator for driving fluid,a piezoelectric pump is successfully made.The proposed piezoelectric pump consists of coaxial cylindrical shells and a bar-shaped piezoelectric vibrator,which has a disk part and a cone part.The lead zirconium titanate ceramic rings fixed in the vibrator are polarized along the thickness direction.When the second-order longitudinal vibration of the vibrator along its axis is excited,the disk part of the vibrator changes periodically the volume of the chamber and the cone part acts as a pin valve,driving the fluid from the inlet port to the outlet port.Finite elements analysis on the proposed pump model is carried out to verify its operation principle and design by the commercial FEM software ANSYS.Components of the piezoelectric pump were manufactured,assembled,and tested for flow rate and backpressure to validate the concepts of the proposed pump and confirm the simulation results of modal and harmonic analyses.The test results show that the performance of the proposed piezoelectric pump is about 910 mL/min in flow rate with a highest pressure level of 1.5 kPa under 400 V peak-to-peak voltage and 51.7 kHz operating frequency.It is confirmed that this bar-shaped piezoelectric transducer can be effectively applied in fluid transferring mechanism of pump through this research.

Analytical and numerical investigation into the longitudinal vibration of uniform nanotubes

In recent years, prediction of the behaviors of micro and nanostructures is going to be a matter of increasing concern considering their developments and uses in various engineering fields. Since carbon nanotubes show the specific properties such as strength and special electrical behaviors, they have become the main subject in nanotechnology researches. On the grounds that the classical continuum theory cannot accurately predict the mechanical behavior of nanostructures, nonlocal elasticity theory is used to model the nanoscaled systems. In this paper, a nonlocal model for nanorods is developed, and it is used to model the carbon nanotubes with the aim of the investigating into their longitudinal vibration. Following the derivation of governing equation of nanorods and estimation of nondimensional frequencies, the effect of nonlocal parameter and the length of the nanotube on the obtained frequencies are studied. Furthermore, differential quadrature method, as a numerical solution technique, is used to study the effect of these parameters on estimated frequencies for both classical and nonlocal theories.

Segregation of Eucalyptus Lumbers for Finger-jointed Using Longitudinal Vibration

The variation in lumber quality within the supply of eucalypt is large. Effective segregation of the lumber according to "fitness for purpose " is fundamental to enabling the capture of greater value for the finger-jointed. This paper deals with the longitudinal vibration technique as a means of assessing modulus of elasticity (MOE) of solid and finger-jointed specimens made with Eucalyptus grandis × E. urophylla and E. grandis. Dynamic MOE was calculated from resonance frequencies obtained from longitudinal vibration. The dynamic MOE was well correlated to the static bending MOE for solid and finger-jointed lumber from the two eucalyptuses. Correlation coefficients were obtained for the regression of dynamic MOE on static bending MOE for solid and finger-jointed lumber, and were statistically significant. Although the correlation coefficient of finger-jointed was lower than that of solid lumber, the results indicated that the static bending MOE of finger-jointed was strongly correlated with the dynamic MOE of solid lumber, namely, the solid lumber with higher dynamic MOE can produce higher bending MOE finger-jointed. It can be concluded that the longitudinal vibration technique may be useful as a nondestructive method for segregating lumbers for finger-jointed.

Design and experiments of a small resonant inchworm piezoelectric robot

A small resonant inchworm piezoelectric robot with six driving feet which are set evenly along the circumference is proposed and tested.A bonded-type structure is adopted to realize a small size.The radial bending vibration mode and longitudinal vibration mode are excited at the same frequency.The superposition of these two vibration modes makes the driving feet produce elliptical motions.And the driving force can be generated by friction coupling between the driving foot and the operating plane.The structure of the robot is designed by finite element simulation.The geometric parameters are adjusted to make the resonant frequencies of the vibration modes as close as possible.The elliptical trajectories generated at the driving feet are discussed in detail.The vibration and motion characteristics of the prototype are tested,and the resonant frequencies of the radial bending mode and the longitudinal vibration mode are degenerated successfully.The optimal working frequency of the prototype is 21.5 kHz.The maximum speed of the prototype is 200 mm/s,and the displacement resolution is 0.71μm.The measured results show that the resonant inchworm piezoelectric robot can be used for fast and high-precision transportation in narrow space.