谐和与有界噪声联合参激作用下的Visco-Elastic系统

研究了带visco＿elastic项的非线性系统,在谐和与有界噪声联合参激作用下的响应和稳定性问题· 用多尺度法分离了系统的快变项,并求出了系统的最大Liapunov指数和稳态概率密度函数,根据最大Liapunov指数可得系统解稳定的充分必要条件· 讨论了系统的visco＿elastic项对系统阻尼项和刚度项的贡献。

One-dimensional consolidation of visco-elastic aquitard due to withdrawal of deep-groundwater

One-dimensional consolidation of visco-elastic aquitard due to withdrawal of deep-groundwater was studied.Merchant model was used to simulate visco-elastic characteristic of aquitard.General solutions of the governing equation were obtained by applying Laplace transform with respect to time,and then the pore-pressure,strain and deformation of the aquitard could be calculated by Laplace inversion.A case was analyzed to validate the correctness of the present method.Finally,some consolidation properties of the problem were analyzed.Comparison of the average degree of consolidation defined by pore pressure with that defined by settlement shows that they are different and the maximum difference is 22.8%.The influences of parameters of Merchant model and the rate of the water level on the consolidation are great.The smaller the viscosity coefficient is,the later the rate of consolidation decreases.The rate of consolidation is decreased with the decrease of the rate of the water level fall.Therefore,the lagged effect of land subsidence should be considered in the actual project.

Visco-elastic Properties of VES Diverting Acid for Carbonate Reservoirs

Storage modulus and loss modulus is the main performance index of visco-elastic properties.In this paper the storage modulus and loss modulus of a new diverting acid and their influencing factors were systematically investigated.Besides,the constitutive equations of the diverting acid at different temperatures were elicited from shearing experiments,which show that the visco-elastic surfactant(VES)acid system is a non-Newtonian power law fluid at low temperature and a Newtonian fluid at high temperature.The storage modulus and loss modulus at different temperatures,pH,and VES content in the acid are critical for the design of acid stimulation for oil well,especially when the VES acid is used in this field only on trial and the basic data are in urgent needed for the design and construction of the acidification stimulation.

Heat and Mass Transfer in MHD Visco-Elastic Fluid Flow through a Porous Medium over a Stretching Sheet with Chemical Reaction

This paper presents the study of convective heat and mass transfer characteristics of an incompressible MHD visco-elastic fluid flow immersed in a porous medium over a stretching sheet with chemical reaction and thermal stratification effects. The resultant governing boundary layer equations are highly non-linear and coupled form of partial differential equations, and they have been solved by using fourth order Runge-Kutta integration scheme with Newton Raphson shooting method. Numerical computations are carried out for the non-dimensional physical parameters. Here a numerical has been carried out to study the effect of different physical parameters such as visco-elasticity, permeability of the porous medium, magnetic field, Grashof number, Schmidt number, heat source parameter and chemical reaction parameter on the flow, heat and mass transfer characteristics.

Vibration of Visco-Elastic Parallelogram Plate with Parabolic Thickness Variation

The main objective of the present investigation is to study the vibration of visco-elastic parallelogram plate whose thickness varies parabolically. It is assumed that the plate is clamped on all the four edges and that the thickness varies parabolically in one direction i.e. along length of the plate. Rayleigh-Ritz technique has been used to determine the frequency equation. A two terms deflection function has been used as a solution. For visco-elastic, the basic elastic and viscous elements are combined. We have taken Kelvin model for visco-elasticity that is the combination of the elastic and viscous elements in parallel. Here the elastic element means the spring and the viscous element means the dashpot. The assumption of small deflection and linear visco-elastic properties of “Kelvin” type are taken. We have calculated time period and deflection at various points for different values of skew angles, aspect ratio and taper constant, for the first two modes of vibration. Results are supported by tables. Alloy “Duralumin” is considered for all the material constants used in numerical

Effect of Non-Homogeneity on Thermally Induced Vibration of Orthotropic Visco-Elastic Rectangular Plate of Linearly Varying Thickness

The analysis presented here is to study the effect of non-homogeneity on thermally induced vibration of orthotropic visco-elastic rectangular plate of linearly varying thickness. Thermal vibrational behavior of non-homogeneous rectangular plates of variable thickness having clamped boundary conditions on all the four edges is studied. For non–homogeneity of the plate material, density is assumed to vary linearly in one direction. Using the method of separation of variables, the governing differential equation is solved. An approximate but quite convenient frequency equation is derived by using Rayleigh-Ritz technique with a two-term deflection function. Time period and deflection at different points for the first two modes of vibration are calculated for various values of temperature gradients, non- homogeneity constant, taper constant and aspect ratio. Comparison studies have been carried out with non-homogeneous visco-elastic rectangular plate to establish the accuracy and versatility.

ONE-DIMENSIONAL CONSOLIDATION OF LAYERED AND VISCO-ELASTIC SOILS UNDER ARBITRARY LOADING

Based on the layered visco-elastic soil model, according to the Terzaghi's one dimensional consolidation theory, by the method of Laplace transform and matrix transfer technique, the problems about the consolidation of layered and saturated visco-elastic soils under arbitrary loading were solved. Through deductions, the general solution, in the terms of layer thickness, the modulus and the coefficients of permeability and Laplacian transform's parameters was obtained. The strain and deformation of the layered and saturated visco-elastic soils under arbitrary loading can be calculated by Laplace inversion. According to the results of several numerical examples, the consolidation of visco-elastic soils logs behind that of elastic soils. The development of effective stress and the displacement is vibrant process under cyclic loading. Finally, an engineering case is studied and the results prove that the methods are very effective.

An analytic solution describing the visco-elastic deformation of coal pillars in room and pillar mine

Coal pillar deformation is typically nonlinear and time-dependent. The accurate prediction of this defor- mation has a vital importance for the successful implementation of mining techniques. These methods have proven very important as a way to excavate coal resources from under buildings, railways, or water bodies. Elastic and visco-elastic theory are employed with a Maxwell model to formulate an analytic solution for displacement of coal pillars in room and pillar mine. These results show that the visco-elastic solution adequately predicts the coal pillar deformation over time. We conclude that the visco-elastic solution can predict the coal pillar and roadway displacement from the measured geological parameters of the conditions in situ. Furthermore, this method would be useful for mine design, coal pillar support optimization, ground subsidence prediction, and coal pillar stability analysis.

Rheological Behaviour for Polymer Melts and Concentrated Solutions Part Ⅰ:A New Multiple Reptation Model to Predict the Nonlinear Visco-elasticity with Nagai Chain Constraints in Entangled Polymer Melts

An approach of stochastically statistical mechanics and a unified molecular theory of nonlinear viscoelasticity with constraints of Nagai chain entanglement for polymer melts have been proposed. A multimode model structure for a single polymer chain with n tail segments and N reversible entanglement sites on the test polymer chain is developed. Based on the above model structure and the mechanism of molecular flow by the dynamical reorganization of entanglement sites, the probability distribution function of the end-to-end vectr for a single polymer chain at entangled state and the viscoelastic free energy of deformation for polymer melts are calculated by using the method of the stochastically statistical mechanics. The four types of stress-strain relation and the memory function are derived from this thery. The above theoretical relations are verified by the experimentaf data for various polymer melts. These relations are found to be in good agreement with the experimental results

Rayleigh-type wave propagation in incompressible visco-elastic media under initial stress

Propagation of Rayleigh-type surface waves in an incompressible visco-elastic material over incompressible visco-elastic semi-infinite media under the effect of initial stresses is discussed. The dispersion equation is determined to study the effect of differ- ent types of parameters such as inhomogeneity, initial stress, wave number, phase velocity, damping factor, visco-elasticity, and incompressibility on the Rayleigh-type wave prop- agation. It is found that the affecting parameters have a significant effect on the wave propagation. Cardano＇s and Ferrari＇s methods are deployed to estimate the roots of dif- ferential equations associated with layer and semi-infinite media. The MATHEMATICA software is applied to explicate the effect of these parameters graphically.

Visco-elastic fluid flow past an infinite vertical porous plate in the presence of first-order chemical reaction

An analysis has been developed to study the unsteady free convection flow of an incompressible visco-elastic fluid on a continuously moving vertical porous plate in the presence of a first-order chemical reaction. The governing equations are solved numerically using an implicit finite difference technique. The obtained numerical solutions are compared with the analytical solutions. The velocity profiles are presented. A parametric analysis is performed to illustrate the influences of the visco-elastic parameter, the dimensionless chemical reaction parameter, and the plate moving velocity on the steady state velocity profiles, the time dependent friction coefficient, the Nusselt number, and the Sherwood number.

Thermal Effect on Free Vibration of Non-Homogeneous Orthotropic Visco-Elastic Rectangular Plate of Parabolically Varying Thickness

A simple model presented here is to study the thermal effect on vibration of non-homogeneous orthotropic visco-elastic rectangular plate of parabolically varying thickness having clamped boundary conditions on all the four edges. For non-homogeneity of the plate material, density is assumed to vary linearly in one direction. Using the separation of variables method, the governing differential equation has been solved for vibration of non-homogeneous orthotropic viscoelastic rectangular plate. An approximate frequency equation is derived by using Rayleigh-Ritz technique with a two-term deflection function. Results are calculated for time period and deflection at different points, for the first two modes of vibration, for various values of temperature gradients, non-homogeneity constant, taper constant and aspect ratio and shown by graphs.

Experimental study on visco-elastic constitutive relationship and its parameters for geogrids

Geogrids are used as reinforcement materials widely in geotechnical and civil engineering fields. In this paper, a series of comparative tests on creep behavior of specific geoOgrids are conducted in the laboratory under different combinations of loading levels and environmental temperature. Based on the test results,comparative analyses are made to study long-term behaviors of isochronous load-strain curves, creep curves and relaxation curves for the specified geogrids. Furthermore, a constitutive model based on theory of visco-elasticity and tests results is proposed for geogrids and a rational procedure is presented in detail for determining the relevant parameters of the proposed model. Finally, the effect of tests temperature on model parameter values is investigated.

A HYBRID FEM ALGORTHM FOR FLUID FLOW IN A VISCO-ELASTIC PIPE

A variational principle of hybrid FEM is proposed to solve the flow in a visco-elaslic pipe. As an example, the influence of an axisymmetrical stenosis on an artery vibrating flow with a single frequency is calculated.

HEMORRHEOLOGY, VISCO-ELASTICITY AND THIXOTROPY IN CEREBRAL THROMBOSIS

In this study, we used blood rheometer type HT-I to determine blood viscosity, plasma viscosity, hematocrit, blood red cell visco-elasticity and thixotropy in 70 cases with cerebral thrombosis, compared with normal control group in order to study the relationship between their alteration and cerebral thrombosis blood and plasma viscosity were higher in the patients than in normal control. Hysteresis loop analysis showed that the red blood cell’s visco-elasticity, thixotropy and deformity decrease.

The Equilibrium of Fractional Derivative and Second Derivative: The Mechanics of a Power-Law Visco-Elastic Solid

This paper investigates the equilibrium of fractional derivative and 2nd derivative, which occurs if the original function is damped (damping of a power-law viscoelastic solid with viscosities η of 0 ≤ η ≤ 1), where the fractional derivative corresponds to a force applied to the solid (e.g. an impact force), and the second derivative corresponds to acceleration of the solid’s centre of mass, and therefore to the inertial force. Consequently, the equilibrium satisfies the principle of the force equilibrium. Further-more, the paper provides a new definition of under- and overdamping that is not exclusively disjunctive, i.e. not either under- or over-damped as in a linear Voigt model, but rather exhibits damping phases co-existing consecutively as time progresses, separated not by critical damping, but rather by a transition phase. The three damping phases of a power-law viscoelastic solid—underdamping, transition and overdamping—are characterized by: underdamping—centre of mass oscillation about zero line;transition—centre of mass reciprocation without crossing the zero line;overdamping—power decay. The innovation of this new definition is critical for designing non-linear visco-elastic power-law dampers and fine-tuning the ratio of under- and overdamping, considering that three phases—underdamping, transition, and overdamping—co-exist consecutively if 0 < η < 0.401;two phases—transition and overdamping—co-exist consecutively if 0.401 < η < 0.578;and one phase— overdamping—exists exclusively if 0.578 < η < 1.

Heat and Mass Transfer in Visco-Elastic Fluid through Rotating Porous Channel with Hall Effect

This paper examined the hydromagnetic boundary layer flow of viscoelastic fluid with heat and mass transfer in a vertical channel with rotation and Hall current. A constant suction and injection is applied to the plates. A strong magnetic field is applied in the direction normal to the plates. The entire system rotates with uniform angular velocity (Ω), about the axis perpendicular to the plates. The governing equations are solved by perturbation technique to obtain an analytical result for velocity, temperature, concentration distributions and results are presented graphically for various values of viscoelastic parameter (K2), Prandtl number (Pr), Schmidt number (Sc), radiation parameter (R), heat generation parameter (Qh) and Hall parameter (m).

UNSTEADY FLOW OF NON-NEWTONIAN VISCO-ELASTIC FLUID IN DUAL-POROSITY MEDIA WITH THE FRACTIONAL DERIVATIVE

The fractional order derivative was introduced to the seepage flow research to establish the relaxation models of non-Newtonian viscoelastic fluids in dual porous media. The flow characteristics of non-Newtonian viscoelastic fluids through a dual porous medium were studied by using the Hankel transform, the discrete Laplace transform of sequential fractional derivatives and the generalized Mittag-Leffler function. Exact solutions were obtained for arbitrary fractional order derivative. The long-time and short-time asymptotic solutions for an infinite formation were also resulted. The pressure transient behavior of non-Newtonian viscoelastic fluids flow through an infinite dual porous media was studied by using Stehfest＇s inversion method of the numerical Laplace transform. It shows that the characteristics of the fluid flow are appreciably affected by the order of the fractional derivative.

Seismic wave propagating in Kelvin-Voigt homogeneous visco-elastic media

This paper studies, under a small disturbance, the responses of seismic transient wave in the visco-elastic media and the analytic solution of the corresponding third-order partial differential equation. A plane wave solution of Kelvin-Voigt homogeneous visco-elastic third-order partial differ-ential equation with a pulse source is obtained. By the principle of pulse stacking of particle vibration, the result is extended to the solution of Kelvin-Voigt homogeneous visco-elastic third-order partial differential equation with any source. The velocities of seismic wave propagating and the attenuation of seismic wave in Kelvin-Voigt homogeneous visco-elastic media are discussed. The velocities of seismic wave propagating and the coefficient of attenuation of seismic wave in Kelvin-Voigt homogeneous visco-elastic media are derived, expressed as functions of density of the media, elastic modulus and visco-elastic coefficient. These results can be applied in inversing lithology parameters in geophysical prospecting.

AN UNSTEADY SEEPAGE FLOW MODEL OF VISCO-ELASTIC POLYMER SOLUTION

With the consideration of the visco―elasticity, the adsorption effect andthe variation of rheological parameters, a seepage flow model of visco-elastic polymer solutions wasestablished. The model was numerically treated with the finite difference method. Then curves ofBottom Hole Pressure (BHP) and formation pressure were drawn. The influences of the relaxation time,the injection rate, the permeability reduction coefficient, the consistency coefficient and thepower-law exponent of the injected fluid on pressure performance were analyzed. This study showsthat it is necessary to consider the visco-elasticity of non-Newtonian fluid in analyzing ofpressure performance in the polymer flooding.