Surface wave propagation in sandy layer overlying a liquid saturated porous half-space and lying under a uniform liquid layer

Dispersion of Rayleigh-type surface waves is studied in a sandy layer under a uniform layer of homogeneous liquid lying over liquid-saturated porous solid half-space. The frequency equation in the form of a ninth-order determinant is obtained and evaluated. Special cases have been deduced and dispersion curves for the phase velocity and wave number have been plotted for a particular model.     

Surface wave propagation in a double liquid layer over a liquid-saturated porous half-space

The frequency equation is derived for surface waves in a liquid-saturated porous half-space supporting a double layer, that of inhomogeneous and homogeneous liquids. Asymptotic approximations of Bessel functions are used for long and short wavelength cases. Certain other problems are discussed as special cases. Velocity ratio (phase and group velocity) is obtained as a function of wavenumber and the results are shown graphically.     

Effect of fluid viscosity on wave propagation in a cylindrical bore in micropolar elastic medium

Wave propagation in a cylindrical bore filled with viscous liquid and situated in a micropolar elastic medium of infinite extent is studied. Frequency equation for surface wave propagation near the surface of the cylindrical bore is obtained and the effect of viscosity and micropolarity on dispersion curves is observed. The earlier problems of Biot and of Banerji and Sengupta have been reduced as a special case of our problem.     

温度对水饱和孔隙介质压缩波速度的影响

温度作用使孔隙介质密度、弹性模量等参数发生改变,从而影响声波传播性质。文章基于变形体能量守恒定律,考虑热机耦合和两相介质热耦合,推导水饱和孔隙介质的热传导方程;考虑孔隙水和固相孔隙介质存在的三种耦合性,基于热作用下应力应变关系分析,建立了热机耦合声波传播模型;设计温度变化沉积物样品声学测量实验,当温度由2℃增加到27℃时,压缩波速度平均增大88m·s^-1运用热机耦合声波传播模型解释了实验测量结果的上升趋势,获得理论计算值与测量值相对偏差范围为-3．03％～1．19％。     

On propagation of shear waves in a multilayer medium including a fluid-saturated porous stratum

Summary The propagation of SH-type waves in a double surface layered medium with an intermediate transverse-isotropic fluid-saturated porous stratum has been examined. The top-most layer is assumed to be impermeable, elastic, homogeneous and isotropic, whereas the lower half-space is a nonhomogeneous one. The dispersion equation has been derived using the Biot's theory for the porous layer and the theory of elasticity for both the upper and the subjacent half-space.The corresponding dispersion equation for the simplified case where the dissipation caused by the relative fluid flow has been omitted has also been obtained. The numerical results obtained for this simplified case have been shown graphically.With 5 Figures     

Rayleigh surface wave propagation in an orthotropic rotating magneto-thermoelastic medium subjected to gravity and initial stress

Abstract

The prime objective of the present article is to analyze the effects of rotation and initial stress on the propagation of Rayleigh surface waves in a homogeneous, orthotropic magneto-thermoelastic half space subjected to gravity field. The frequency equations in closed form are derived and the amplitude ratios of surface displacements, temperature change during the Rayleigh wave propagation on the surface of half space have been computed analytically. The highlights of this study are the effects of different parameters (rotation, magnetic field, initial stress, and gravity) on the velocity of Rayleigh waves. Variation in phase velocity of Rayleigh waves against a wave number is shown graphically. Some particular cases have been deduced. Also, the classical Rayleigh wave equation is obtained as a special case of the present study. Numerical example has been carried out and represented by the means of graphs. Impacts of various involved parameters appearing in the solutions are carefully analyzed. In fact, in the absence of various parameters, these equations are in agreement with the results for isotropic medium.     

流体-孔隙介质周期性粗糙界面超声波反射与透射特性研究

为了研究超声波在流体-孔隙介质周期性粗糙界面的传播特性,文章基于周期性锯齿粗糙界面的衍射模型分析孔隙介质开孔与闭孔状态下孔隙度对反射与透射的影响。通过孔隙介质比奥特(Biot)理论与光栅方程理论,得到包含各阶反射系数、透射系数的线性方程组,再利用傅里叶变换进行数值计算,得到孔隙度与流体-孔隙介质周期性粗糙界面反射系数、透射系数之间的关系。结果表明,由于界面的周期性,频率对反射与透射系数的影响没有呈现一定的规律。但孔隙度对反射与透射系数有显著影响,且由于孔隙介质状态的差异性,导致反射与透射系数在开孔与闭孔时变化趋势不同。     

浅海海底模型对低频声传播的影响

海底参数特性是影响浅海低频水声传播的重要因素。理论上需要知道海底所有深度的参数特性才能确定水声传播,这在实践中很不现实。如果在误差的允许范围内只需要知道某个深度以上的海底参数特性,而这个深度以下的海底参数特性可以忽略,这个深度就定义为海底最大深度。低频声波能够穿透海底更深,最大深度能够达到几十米深,对比较高频率只有几米深。海水声速剖面也能影响声波穿透海底深度,声速剖面为负梯度时海底最大深度比等声速要深。在低频声传播过程中,海底横波对声场影响也很大,尤其是在超低频100Hz以下,2002年5月的南海试验也证实了这一点。     

The similarity regime for natural convection in a vertical cylindrical well filled with an anisotropic porous medium

An integral method based on Lighthill’s analysis (Q J Mech Appl Math 6 (1953) 398–439) is carried out to study the similarity regime for penetration of convective heat transfer in a vertical cylindrical well filled with an anisotropic porous medium. The porous medium is anisotropic in permeability with its principal axes oriented in a direction that is oblique to the gravity vector. In the limit of the slenderness of the porous matrix, the penetration length of the convective flow and the heat-transfer rate are expressed in terms of the anisotropic properties of the porous medium, the modified Darcy–Rayleigh number and the aspect ratio of the geometrical configuration. A scale analysis is applied to predict the order of magnitudes involved in the similarity regime of the phenomenon. The conditions of existence of the similarity pattern is found to be dependent on the anisotropic parameters. It is demonstrated that both the anisotropic permeability ratio and the orientation angle of the principal axes have a strong influence on the heat-transfer rate and on the vertical penetration length into the well.     

粘性液体对管道中扭转导波传播特性的影响研究

对带有液体的圆柱/管中的波传播进行了研究。在流动为层流的假设下,研究了有粘性液体管道中扭转导波的位移模式和传播特性。分析了波的频散和衰减曲线,得到了粘性、密度等和第一阶扭转模态衰减的关系,确定了粘性液体对扭转导波的影响,为扭转导波在损伤检测中应用做了一些理论工作。数值计算结果与某文献中实验结果符合较好,一定程度上证明了液体中的层流假设,说明了第一阶扭转模态在损伤探测中的优势。     

Shear waves in a fluid saturated elastic plate

In the present context, we consider the propagation of shear waves in the transverse isotropic fluid saturated porous plate. The frequency spectrum for SH-modes in the plate has been studied. It is observed that the frequency of the propagation is damped due to the two-phase character of the porous medium. The dimensionless phase velocities of the shear waves have also been calculated and presented graphically. It is interesting to note that the frequency and phase velocity of shear waves in porous media differ significantly in comparison to that in isotropic elastic media.     

A finite element solution of acoustic propagation in rigid porous media

This paper deals with the acoustical behaviour of a rigid porous material. A finite element method to compute both the response to an harmonic excitation and the free vibrations of a three‐dimensional finite multilayer system consisting of a free fluid and a rigid porous material is considered. The finite element used is the lowest order face element introduced by Raviart and Thomas, that eliminates the spurious or circulation modes with no physical meaning. For the porous medium a Darcy's like model and the Allard–Champoux model are taken into account. The numerical results show that the finite element method allows us to compute the response curve for the coupled system and the complex eigenfrequencies. Some of them have a small imaginary part but there are also overdamped modes. Copyright © 2004 John Wiley & Sons, Ltd.     

The onset of Brinkman ferroconvection in an anisotropic porous medium

Onset of ferroconvection in an anisotropic porous layer heated from below is investigated theoretically using modified Brinkman extended-Darcy equation with fluid viscosity different from effective viscosity. The isothermal bounding surfaces of a porous layer are considered to be either free or rigid-paramagnetic/ferromagnetic. The eigenvalue problem is solved exactly for free boundaries, while for realistic rigid-paramagnetic or rigid-ferromagnetic boundaries the critical stability parameters are obtained numerically using the Galerkin method. It is seen that the stability of the system depends on the nature of boundaries and rigid-paramagnetic boundaries are found to be preferred to the ferromagnetic ones as well as free boundaries in controlling ferroconvection in an anisotropic porous layer. It is observed that increase in the value of thermal anisotropy parameter and viscosity ratio is to delay the onset of ferroconvection, while increase in the value of mechanical anisotropy parameter and magnetic number is to hasten the onset of ferroconvection. Moreover, increasing the value of thermal anisotropy parameter and decreasing the value of mechanical anisotropy parameter is to narrow the convection cells.     

A new features on S-waves propagation in a nonhomogeneous anisotropic incompressible medium under influence of gravity field and initial stress with and without electromagnetic field and rotation

The present article is concerned with the investigation of the propagation of shear waves in a nonhomogeneous anisotropic incompressible medium under the effect of the electromagnetic field, gravity field, rotation, and initial stress taking into account a comparison between presence and absence of magnetic field, initial stress, and rotation. Analytical analysis reveals that the velocity of propagation of the shear waves depends upon the direction of propagation, the anisotropy, magnetic field, rotation, gravity field, nonhomogeneity of the medium, and the initial stress. The frequency equation that determines the velocity of the shear waves has been obtained. Some special cases are also deduced from the present investigation. In fact, these equations are an agreement with the corresponding classical results when the medium is isotropic. Numerical results have been given and illustrated graphically in each case considered. The results indicate that the effects of gravity field, initial stress, magnetic field, electric field, anisotropy, and rotation are very pronounced. Also, the absence of initial stress, magnetic field, and rotation tends to increasing of the S-waves velocity compared with presence of them.     

Coupling heat conduction and water–steam flow in a saturated porous medium

This paper is devoted to the simulation of water forced evaporation in a porous saturated medium in a 3D‐axisymmetric domain by resolution of partial differential algebraic equations (PDAE) that are encountered in different engineering applications. The goal of this paper is an attempt to present effective realizations, in order to determine the minimal duration of burning for prehistoric occupations. This multidisciplinary work includes scientists in Mathematics, Physics and Archaeology. The model proposed here couples the heat conduction in a water saturated soil with the water steam flow in the medium. We propose an efficient and robust global numerical method, based on a method of lines and differential algebraic equations (DAE) solvers, combined with a Newton method using a powerful sparse linear solver. After a brief overview of classes for numerical techniques applied for moving boundary problems, the Apparent Heat Capacity method (AHC) is used, and in order to validate our codes, a comparison with experiments is done. Copyright © 2010 John Wiley & Sons, Ltd.     

A 3-D,symmetric, finite element formulation of the Biot equations with application to acoustic wave propagation through an elastic porous medium

A weak solution of the coupled, acoustic-elastic, wave propagation problem for a flexible porous material is proposed for a 3-D continuum. Symmetry in the matrix equations; with respect to both volume, i.e. ‘porous frame’–‘pore fluid’, and surface, i.e. ‘porous frame/pore fluid’–‘non-porous media’, fluid–structure interaction; is ensured with only five unknowns per node; fluid pore pressure, fluid-displacement potential and three Cartesian components of the porous frame displacement field. Taking Biot's general theory as starting point, the discretized form of the equations is derived from a weighted residual statement, using a standard Galerkin approximation and iso-parametric interpolation of the dependent variables. The coupling integrals appearing along the boundary of the porous medium are derived for a number of different surface conditions. The primary application of the proposed symmetric 3-D finite element formulation is modelling of noise transmission in typical transportation vehicles, such as aircraft, cars, etc., where porous materials are used for both temperature and noise insulation purposes. As an example of an application of the implemented finite elements, the noise transmission through a double panel with porous filling and different boundary conditions at the two panel boundaries are analysed. © 1998 John Wiley & Sons, Ltd.     

The investigation of transient wave propagation in a dipping layered medium overlaying a half space

Abstract

The responses of transient wave propagation in a single dipping layered medium overlaying a half space was investigated in this study. To obtain the responses, a point source located in the dipping layered medium was assumed, and in order to make the results more consistent with real situations, the time functions for source mechanism, such as parabolic ramp function and triangular time function, were considered in this research. Finally, the famous mathematical tool with physical significance, the generalized ray theory [4], was employed to solve the foregoing problem, and the ray paths and responses for the distinct locations on the surface were then obtained and shown in sketches. It was found from the obtained results that the responses decay with the distance from the focus just as expected.     

温度对大鼠肝脏中剪切波与频散特性影响研究

剪切波相速度和衰减的频散特性的准确测量具有重要的意义。温度变化可能会对生物软组织的力学特性产生影响,为了研究温度的变化对剪切波相速度和衰减频散特性测量的影响,以大鼠肝脏为研究对象,基于声辐射力的剪切波成像的方法,通过离体实验来获取大鼠肝脏内部不同温度下的剪切波相速度和衰减频散特性曲线。实验结果发现,随着温度的升高,剪切波相速度逐渐减少,衰减频散逐渐增大,特别是在较高的频段(270~380 Hz)的变化更为显著。结果表明温度是测量大鼠肝脏中剪切波相速度和衰减频散特性中不可忽略的因素,这对今后的动物实验研究以及疾病评估提供了实验参考,具有重要的意义。