Axial Amplitude Research Articles

Estimation of shear rate change in vertically oscillating non-Newtonian fluids: Predictions on particle settling

This study investigates the effect of oscillatory motion on velocity and shear rate change within different non-Newtonian, slightly viscoelastic fluids oscillated in a vertical U-shaped circular pipe. An estimation to quantify the influence on particle settling in an oscillatory environment is also presented. Flow visualization using particle image velocimetry (PIV) technique was deployed to compare the two-dimensional velocity field in the vertical plane of the U-tube axis and the resulting shear rate change in three different non-Newtonian fluids. The experiments were performed in a 1.2 m high, 50 mm diameter transparent test section, at room temperature (21 ± 0.5 °C) and atmospheric pressure.A piston was driven at harmonic motion via a gas buffer, to provide the driving force for the test fluids at four different low frequencies ranging from 0.1 – 0.75 Hz and at three different piston oscillation amplitude ratios of A = a/D = 0.3, 0.4 and 0.5, where a is the displacement amplitude of the piston and D is the pipe diameter. Oscillatory Reynolds number (Reδ) based on Stokes layer thickness was used as the criteria for determining the specific flow regime. 36 different experimental cases were tested within the range of 2 < Reδ < 34, and all the experimental cases exhibited the laminar flow regime.The study reveals that the axial velocity amplitude along the pipe centerline increases with the increasing frequency and with increasing oscillation amplitude irrespective of the non-Newtonian fluid type. The thickness of the shear region decreases with the increase of frequency. The change of shear rate is maximum near the wall region of the pipe and that is achieved at the maximum position of the phase cycle, where the axial velocity also possesses its highest magnitude. The most viscous and the least elastic fluid have reported a maximum reduction of viscosity as an effect of the oscillatory motion and the viscosity reduction becomes insignificant when the non-Newtonian fluids become less viscous.

Extremely large-amplitude dynamics of cantilevers under coupled base excitation

Extremely large-amplitude nonlinear dynamics of a cantilever with a mass at the tip under coupled base excitations is examined for the first time. An exact model of the centreline rotation of the cantilever is developed capable of accurately predicting the cantilever dynamic response even at extremely large amplitudes; a nonlinear static finite element analysis is conducted to verify the accuracy of the proposed model at very large deflection amplitudes. The proposed model is based on the theory of Euler-Bernoulli and the internal damping model of Kelvin-Voigt; the centreline of the cantilever is assumed to remain inextensible. The proposed model for the cantilever centreline rotation is discretised via the Galerkin modal decomposition method while keeping all terms exact. Extensive numerical simulations are conducted to examine the primary and parametric resonance of the cantilever due to transverse and axial base excitations, respectively. It is shown that under the same axial and transverse amplitudes of excitation, the parametric resonance is much stronger than the primary resonance.

Influence of Eccentricity on Hydrodynamic Characteristics of Nuclear Reactor Coolant Pump under Different Cavitation Conditions

In order to study the influence of eccentricity on hydrodynamic characteristics of nuclear reactor coolant pump under different cavitation conditions, five different schemes were obtained by analyzing and optimizing the existing structural schemes. Based on the RNG k-ε model (Renormalization Group with k-epsilon turbulence models) and two-fluid two-phase flow model, the unsteady numerical analysis and test verification of different designed schemes are carried out by using the flow field software ANSYS CFX. The results of research show that different eccentricities will affect the nuclear reactor coolant pump’s head under different cavitation conditions, and the corresponding head in the scheme with the eccentricity of 5mm under the fracture cavitation condition is lower than that of the other schemes. When the impeller rotates at a certain angle from the initial position under critical and severe cavitation conditions, the radial force acting on the rotor system will fluctuate greatly. Under the condition of fracture cavitation, the radial force changed periodically and the resultant force value is small. Compared to the original scheme, the peak value of radial force is 6° clockwise after eccentricity of the impeller appeared. With the aggravation of cavitation condition, the axial force value of impeller decreases, but the corresponding amplitude of the impeller increases. Under critical and severe cavitation conditions, the maximum axial force amplitude of the nuclear reactor coolant pump appears in the two times blade frequency, and in the broken cavitation condition, the maximum axial force amplitude appears at the shaft frequency. When the eccentricity is 20 mm, the axial force fluctuates most under critical and severe cavitation conditions, and when the eccentricity is 10 mm, the corresponding axial force is smaller than that of the original scheme. When the eccentricity is 5 mm, the axial force on the impeller is the smallest, but the amplitude is the largest under the condition of fracture cavitation.

Nonlinear stability and optimization of thin nanocomposite multilayer organic solar cell using Bees Algorithm

Abstract This paper carries out the nonlinear stability of nanocomposite multilayer organic solar cell (NMOSC) subjected to axial compressive loads. The model of organic solar cell is assumed to consist five layers: Al, P3HT:PCBM, PEDOT:PSS, IOT and Glass. Based on the classical plate theory, the basic equations are established taking into account the effect of elastic foundations and initial imperfection. The approximation solutions are selected based on the boundary conditions of the four edges of NMOSC. The equation which indicates the relationship between axial compressive loads and deflection amplitude of NMOSC is obtained by using the Galerkin method. Bees Algorithm is applied to maximize the value of critical buckling load with nine variables including the thickness of five layers, the length and the width of NMOSC and two stiffness coefficients of elastic foundations. The numerical results show the effect of geometrical and material parameters, initial imperfection and elastic foundations on the nonlinear static stability and the critical buckling load of NMOSC. Optimal values of nine geometrical parameters of NMOSC are also determined.

Parametric Vibration and Numerical Validation of Axially Moving Viscoelastic Beams With Internal Resonance, Time and Spatial Dependent Tension, and Tension Dependent Speed

Abstract In this paper, the idea of an axially moving time-dependent beam model is briefly introduced. The nonlinear response of an axially moving beam is investigated. The effects of a time and spatial dependent tension depending on the external forces at the boundary and a tension dependent speed are highlighted, which gives a new model to study the parametric vibration of axially moving structures. This paper focuses on simultaneous resonant cases that are the principal parametric resonance of first mode and internal resonance of the first two modes. In general, the method of multiple scales can study nonlinear vibration of axially moving structures with homogeneous boundary conditions. Taking Kelvin viscoelastic constitutive relation into account, the inhomogeneous boundary conditions make the solvability conditions fail, which is also one of the highlights of this paper. In order to resolve this problem, the technique of the modified solvability conditions is employed. The influence of some parameters, such as material’s viscoelastic coefficients, viscous damping coefficients, and the axial tension fluctuation amplitudes, on the steady-state vibration responses is demonstrated by some numerical examples. Furthermore, the approximate analytical results are verified by using the differential quadrature method (DQM).

A Novel Axial Vibration Model of Multistage Pump Rotor System with Dynamic Force of Balance Disc

In this paper, a novel axial dynamic model including the transient force of balance disc is proposed to predict the vibration characteristics of multistage pump rotor system. To obtain the dynamic force, the rotating effect of the rotor system is considered and the Navier–Stokes equations are further simplified on the basis of the geometric structure and inner flow characteristic of the balance disc. In addition, based on finite element method and matrix operation, a novel axial motion model of rotor system is established. The efficient Newmark method is applied to describe the dynamic response of the coupled rotor system. The pressure distribution in axial clearance and the corresponding dynamic force present obvious nonlinear reduction as the axial gap increases from 0.2 mm to 1 mm. The inner chamber pressure is more sensitive to the inlet pressure than the rotating speed, especially when the axial gap is 0.2 mm. Moreover, the axial steady amplitude of the rotor system is directly proportional to the rotating speed and initial axial gap, while it is inversely proportional to the outer radius of the balance disc. In addition, the vibration frequencies for axial vibration are multiple even when the motion of the rotor system is regularly reciprocating. The transient force of the balance disc needs to be considered in the calculation of axial rotor dynamics for the multistage pump. The calculated results can provide references for the design of the balance disc and an axial vibration model of the multistage pump rotor system.

Axial Vibration Characteristic of Levitation Force for Radial-Type Superconducting Magnetic Bearing

Dynamic levitation behavior is crucial to the stable operation of superconducting magnetic bearing (SMB). In this article, we mainly focus on the axial vibration characteristic of levitation force for the radial-type SMB. The axial levitation force is calculated by using the H-formulation two-dimensional (2-D) axial-symmetry finite element model established in COMSOL. Also, experimental measurements of the levitation force are carried out under the field-cooling and zero-field cooling conditions. The comparisons show a good agreement and validate the modeling method. Based on the model, the dynamic levitation behaviors of radial-type SMB are investigated when the permanent magnet (PM) rotor vibrates axially. The influences of different axial vibration amplitude and period on the levitation behavior are mainly concerned and validated by experimental measurements. It is concluded that the levitation force will vary as a rule similar to the position variation of the PM rotor and the overall attenuation trend is similar to the trend of relaxation for the levitation force. Besides, the degree of attenuation increases obviously and is related to the vibration period and amplitude. The obtained results may be useful to the study of dynamic levitation behavior and the engineering applications of SMB.

Analytical and Numerical Study of a Pulsatile Flow in a Porous Tube

Lateral leakage is encountered in many biological and chemical applications such as renal flows and filtration processes. In this paper, we report a comprehensive analytical and numerical method to examine pulsatile flow in a porous-walled tube, with leakage flow rate or permeation coefficient prescribed. In the first scenario, the analytical results have been obtained when the leakage flow rate is small as compared to the axial flow rate. Numerical simulations using ansysFluent were performed for cases where both the pulsatile Reynolds number based on the amplitude of the axial velocity and the leakage ratio (ratio of leakage velocity amplitude to the mean axial velocity amplitude) were varied. The comparison between the analytical and the numerical results indicates that the analytical solution for the axial velocity had an increasing deviation from the numerical results with the increasing pulsatile Reynolds number, or increasing leakage ratio. Interestingly, the analytical radial velocity almost overlapped with its numerical counterpart, for all considered cases. In the second scenario where a permeation coefficient for the leakage is prescribed, an analytical solution was obtained. Importantly, the solution in the second scenario suggests the criteria based on the wall permeability for the application of the analytical method developed herein.

Nonlinear vibration of axially moving beams with internal resonance, speed-dependent tension, and tension-dependent speed

In this paper, a new nonlinear model of an axially accelerating viscoelastic beam is established. The effects of a speed-dependent tension (a time-dependent tension due to perturbation of the speed) and a tension-dependent speed (a time-dependent speed due to perturbation of the tension) are highlighted. However, there was one common characteristic in previous studies about parametric vibration of axially moving beams with time-dependent tensions and time-dependent speeds: Axial tension and axial speed are independent of each other. Another highlight is that the inhomogeneous boundary conditions arising from Kelvin viscoelastic constitutive relation are taken into account. The technique of the modified solvability conditions is employed to resolve the existing solvability conditions failure because of the inhomogeneous boundary conditions. The influences of material’s viscoelastic coefficients, axial speed fluctuation amplitude, axial tension fluctuation amplitude, and dependent and independent models on the steady-state vibration responses are demonstrated by some numerical examples. Furthermore, the approximate analytical results are verified by using the differential quadrature method.

Adaptive modeling of rock crack mechanism during drilling operation based on modified peridynamics

In this paper, an efficient adaptive model is developed to simulate the rock crack mechanism during drilling operation based on a three-dimensional modified peridynamics. The modified peridynamics equation defines the micro-bond force as the combination of a normal part, which comes from the tensile deformation, and a tangential part, which comes from the shear deformation. The bond break criterion is set to include both the tensile deformation and the shear deformation. By redefining the local damage criterion and the bit penetration criterion, this model iterates adaptively with crack propagation and drill bit penetration. Penetration rates under different drilling conditions are investigated, including weight on bit, rotary speed, axial vibration frequency and amplitude. This approach takes advantages of the peridynamics in solving discontinuity involved problems, and successfully applies peridynamics to drilling modeling. As a consequence, the damage propagation of rock is automatically captured. Another advantage of this approach comes from the application of the modified peridynamics, where the shear deformation and its related damage are considered separately in the constitutive relation. This is crucial for drilling modeling because the rotation of drill bit often introduces large amounts of tangential cracks. Finally, the proposed model is adaptive and quite efficient, thus, this approach can be used to model the complete drilling process with a large depth.

Liquefaction resistance of unsaturated sands: experimental evidence and theoretical interpretation

Cyclic undrained triaxial tests were carried out on saturated and unsaturated loose specimens of three fine-grained materials. The results confirm that, as the saturation degree decreases, liquefaction resistance sharply increases. In the interpretation of results, the first step was the assessment of the reliability of the use of the 5% strain amplitude criterion to define the attainment of liquefaction. With this aim, the tests were analysed assuming that the soil behaves as an equivalent viscous material. It is shown that the characteristic values of viscosity defining the start and completion of liquefaction depend on soil grading, increasing as the coefficient of uniformity increases. The equivalent viscosity corresponding to a condition of double strain axial amplitude of 5% is fairly constant for all soils. Then, starting from the observation of the relationship between the final volumetric strain and the initial degree of saturation, a theoretical interpretation of the tests is reported. It is shown that the behaviour of the tested sands can be interpreted quantifying the thermodynamic specific energy spent to reach liquefaction, considering the contribution of all phases (soil, water and air). The position of the liquefaction resistance curve depends on the volumetric component of such a specific energy.

A new algorithm for fatigue life assessment of automotive safety components based on the probabilistic approach: The case of the steering knuckle

In the present paper, the author has attempted to examine fatigue life of automotive safety components under axial variable amplitude loading conditions. To this end, the time components of stress tensor in the critical area of the knuckle and Liu-Zenner criterion were used to calculate the time history of equivalent stress. Then, the probability distribution function (PDF) of stress was extracted by applying the stress level counting technique. The Fourier curve fitting method was employed in order to formulate the PDF. Subsequently, the fatigue life of the component was estimated using the probabilistic approach. Finally, the results of the higher order of Fourier curve fitting and different counting ranges were compared with the experimental results. Thus, the best algorithm for precisely determining fatigue life of automotive components was obtained.

Reconstructed drill-bit motion for sonic drillstring dynamics

In tunnel excavation that integrates Resonant Sonic Head Drilling (RSHD) machine, one of the important stability problem to deal with is represented by the necessity to assign axial vibration amplitude induced by the RSHD to a resonant vibration mode. In general, a control law depends on system variables which are partially available for measurements. In drilling operation, the drillstring variables at the tip boundary aren’t easy, if not impossible, to be measured. The sonic drillstring infinite dimension dynamics, derived in this paper, will play an important role in PDE (Partial Derivative Equation) observer design for the drill bit motion. The well-posedness problem is addressed, and the designed PDE-observer stability is detailed using the resolvent method. The wave peak amplitude is determined from the resonant drillstring mode shape, and the system’s stability is analyzed around a practical frequency mode.

A New Geometrically Exact Model for Buckling and Postbuckling Statics and Dynamics of Beams

In this study, a new geometrically exact nonlinear model is developed for accurate analysis of buckling and postbuckling behavior of beams, for the first time. Three-dimensional nonlinear finite element analysis is conducted to verify the validity of the developed model even at very large postbuckling amplitudes. It is shown that the model commonly used in the literature for buckling analysis significantly underestimates the postbuckling amplitude. The proposed model is developed on the basis of the beam theory of Euler–Bernoulli, along with the assumption of centerline inextensibility, while taking into account the effect of initial imperfection. The Kelvin–Voigt model is utilized to model internal energy dissipation. To ensure accurate predictions in the postbuckling regime, the nonlinear terms in the equation of motion are kept exact with respect to the transverse motion, resulting in a geometrically exact model. It is shown that even a fifth-order truncated nonlinear model does not yield accurate results, highlighting the significant importance of keeping the terms exact with respect to the transverse motion. Using the verified geometrically exact model, the possibility of dynamic buckling is studied in detail. It is shown that dynamic buckling could occur at axial load variation amplitudes as small as 2.3% of the critical static buckling load.

The origin of self-excited oscillation of double-walled carbon nanotubes

The mechanism of self-excited oscillation of the inner tube in a double-walled carbon nanotube (DWCNT) is investigated with the aid of the molecular dynamics (MD) simulation. In the simulation, the outer tube is fixed, and the inner tube is free in terms of axial displacement and rotation. The MD results indicate that a van der Walls (vdW) energy barrier to axial oscillation exists in both commensurate and incommensurate DWCNTs, and this vdW energy barrier can be broken through at sufficient high temperatures or with sufficiently large rotational excitations. The max amplitude of axial oscillation of the inner tube can reach larger than half distance of the difference between the length of the inner and outer tubes when the temperature exceeds around 10 ∼ 100 K for the incommensurate tubes and around 500 ∼ 700 K for the commensurate tubes. Above the critical temperature, the rotational excitation cannot increase the axial oscillation amplitude of the inner tube, but below the critical temperature, a sufficiently large rotational excitation can trigger an axial oscillation with large amplitude for incommensurate DWCNTs. Our findings are therefore helpful to both the understanding of oscillation mechanism and the design of nano-devices at ultralow temperature.

Biomechanical test protocols to detect minor injury effects in intervertebral discs

Intervertebral discs (IVDs) maintain flexibility of the spine and bear mechanical load. Annulus fibrosus (AF) defects are associated with IVD degeneration and herniation which disrupt biomechanical function and can cause pain. AF puncture injuries can induce IVD degeneration but are needed to inject therapies. Identifying small AF defects with biomechanical testing can be difficult because IVDs have a complex, composite structure and nonlinear biomechanical properties that are dependent on AF fiber tension. It remains unclear how choice of biomechanical testing protocols affect the sensitivity of biomechanical properties to AF injuries. This study determined whether axial preload or magnitude of cyclic axial or torsional testing affected the ability to detect minor AF defects in rat caudal motion segments using ex vivo biomechanical testing. Intact and injured motion segments were subjected to a repeated measures study design with multiple biomechanical testing protocols that varied axial tension-compression force amplitude (±1.6 N, ±8.0 N, ±16.0 N), axial preload (−1.6 N, −8.0 N, −16.0 N, corresponding to −0.1 MPa, −0.5 MPa, and −1.0 MPa, respectively), and torsional rotation angle (±10°, ±15°, and ±20°). Biomechanical properties obtained from the lowest force testing conditions for axial tension-compression (±1.6 N), axial preload (−1.6 N), and angular rotation (±10°) exhibited the largest differences in biomechanical properties between intact and injured conditions. Biomechanical properties determined under low axial force or torsion amplitudes involve less AF fiber tension and were most sensitive to injury. Low force testing protocols are recommended for detecting minor structural AF defects and may enable more precise assessments of IVD injuries, healing or repair.

Pion-to-vacuum vector and axial vector amplitudes and weak decays of pions in a magnetic field

We propose a model-independent parametrization for the one-pion-to-vacuum matrix elements of the vector and axial vector hadronic currents in the presence of an external uniform magnetic field. It is shown that, in general, these hadronic matrix elements can be written in terms of several gauge covariant Lorentz structures and form factors. Within this framework we obtain a general expression for the weak decay ${\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\rightarrow}l{\overline{\ensuremath{\nu}}}_{l}$ and discuss the corresponding limits of strong and weak external magnetic fields.

Investigation on continuous pressure wave in a periodic transient flow using a three-dimensional CFD model

ABSTRACTThis paper explores continuous pressure wave characteristics and flow features in a periodic transient flow induced by a rotary pressure wave generator. A three-dimensional CFD model based on the realizable k-ϵ turbulence model is established to conduct the simulations. The results show that the turbulent kinetic energy evolution in the periodic transient flow is similar to that in an instantaneous transient flow. In addition, there exists an optimal frequency corresponding to the maximum wave amplitude, which is closely related to the fluid properties and system parameters. When the disturbance frequency is less than the optimal frequency, the pressure and velocity derivative satisfy a linear relation in all zones of the upstream pipe. In contrast, a linear zone away from the rotor is locally formed at regions where the linear relation is approximately valid. Correspondingly, a nonlinear zone is near the rotor where the linear relation is inapplicable. The disturbance frequency significantly affects the axial wave amplitude distribution.

Effects of Nozzle Exit Angle on the Pressure Characteristics of SRWJs Used for Deep-Hole Drilling

The self-resonating waterjet (SRWJ) has been applied in petroleum, natural gas, and mining engineering ever since its strong erosion ability in deep-hole drilling was recognized. Aiming at further improving the working efficiency of SRWJs, the effects of the exit angle of the organ-pipe nozzle on the axial pressure oscillations of the jet were experimentally studied. Six exit angles of θ = 0°, 30°, 45°, 60°, 75°, and 90° were employed in the experiment, and the axial pressure oscillation peak (Pmax) and amplitude (Pa) were used for characterizing the performance of SRWJs. It was found that the exit angle greatly affects the axial pressure oscillations, including the development trends against the standoff distance and the magnitudes of Pmax and Pa. Under testing with two inlet pressures, the exit angle of θ = 0° always resulted in the greatest Pmax and Pa within the range of the testing standoff distance. With the increase of standoff distance, both Pmax and Pa first increased and then decreased when the exit angle was 0°; while they kept decreasing when the exit angle was 30°, 45°, 60°, 75°, and 90°. Moreover, the exit angles of θ = 90° and 60°, corresponding to inlet pressures of Pi = 10 MPa and 20 MPa, led to both the minimum magnitudes of Pmax and Pa under the experimental conditions. The results also indicate that the exit angle affects the interactions between the nozzle lip and the jet and help provide information for improving the working efficiency of SRWJs in practical applications.

On the phase angle role in the shear response of ZK60 Mg alloys under multiaxial fatigue

Proportional and non-proportional multiaxial fatigue tests are conducted on the closed-die forged ZK60 extrusion. The shear strain amplitude was kept constant at 0.5% for all the tests, while two different axial strain amplitudes of 0.4% and 0.7% were considered. At the higher strain amplitude (0.7%) significant difference was observed between the torque amplitudes of proportional and non-proportional tests, whereas the axial load amplitude responses remained the same regardless of the phase angle shifts. It is likely that as the phase angle changes from 0-90, the twin volume fraction at the peak shear strain decreases resulting in higher torque responses. On the other hand, at the lower strain amplitude, i.e. 0.4%, where twinning is not active, phase angle does not show any effect on the shear response. An energy-based fatigue model is employed that effectively explains the different damage contributions by the axial and torsional loadings at different strain amplitudes, and accurately predicts the proportional and non-proportional multiaxial fatigue lives.