Guided waves in a transversely isotropic cylinder immersed in a fluid

Propagation of flexural guided waves in a fluid-loaded transversely isotropic cylinder is studied. Numerical results are presented for a cobalt cylinder immersed in water. The phase velocities are not significantly affected except for several modes in which the energy leakage occurs into the fluid over certain frequency ranges. Attenuation spectra for the leaking modes are plotted.     

A numerical investigation of the acoustic mode waves in a deviated borehole penetrating a transversely isotropic formation

A 2.5-dimensional method in frequency wave-number domain is developed to investigate the mode waves in a deviated borehole penetrating a transversely isotropic formation. The phase velocity dispersion characteristics of the fast and slow flexural mode waves excited by a dipole source are computed accurately at various deviation angles for both hard and soft formations. The sensitivities of the flexural mode waves to all elastic constants in a transversely isotropic formation are calculated. Numerical results show that, for a soft formation, the fast flexural mode wave is dominated by c66 at high deviation angles and low frequencies, while the slow flexural mode wave is dominated by c44 at the same conditions. Waveforms in time domain are also presented to support the conclusions.     

Theoretical investigation on cross-flow heat exchangers with axial dispersion in one fluid

The axial dispersion model for cross-flow heat exchangers is investigated to predict steady state thermal performance more accurately. This model takes flow maldistribution and backmixing into account and is simple and effective in describing their effect on the temperature effectiveness of a heat exchanger. An exact solution together with its asymptotic form for high dispersive Péclet numbers is obtained. The analysis shows that the temperature effectiveness deterioration caused by axial dispersion is significant for the dispersive Péclet number P_e < 20, particularly when the thermal capacity rate ratio is close to one. The P₁, P₂-charts are presented, which are useful for the design of compact cross-flow heat exchangers.     

横向各向同性地层快速各向异性反演方法

斯通利波的频散特性常用于反演横向各向同性地层的各向异性。该文重点对斯通利波频散曲线随井孔和地层弹性模量相关参数的变化规律进行了探讨,提出了频散曲线的快速插值计算方法,经过误差分析验证了插值频散计算的可行性。据此提出了通过对参数大间隔取值建立理论频散数值表,插值计算不同各向异性参数的频散曲线,对比波形频散快速反演横向各向同性地层各向异性的方法。基于实轴积分法计算的横向各向同性地层井孔声场分别进行了插值频散快速反演和传统方法反演,对比结果证实了该文提出的快速反演方法的准确高效性,并且对数据加噪后验证了快速反演方法的抗噪性。     

Localized bending waves in a transversely isotropic plate

The problem of bending waves localized near the free edge of a transversely isotropic plate is investigated using the Ambartsumian higher-order plate theory which takes account of the transverse shears generated by flexural deformation. Unlike the first-order Reissner-Mindlin theory, which also takes account of transverse shears, Ambartsumian's analysis does not demand that plane normal cross-sections remain plane during bending. Within this analysis the existence of localized bending waves in transversely isotropic plates is established, and solutions of the dispersion equation obtained for different values of the elastic parameters.The analysis of frequencies of localized bending waves shows that for thick plates the effect of anisotropy can be considerable. For the particular case of vibrations of a narrow plate, from the long wave approximation a new beam vibration equation of the Timoshenko type is obtained for a transversally isotropic plate.     

Wave dispersion and attenuation in viscoelastic isotropic media containing multiphase flow and its application

In this paper,we introduce the complex modulus to express the viscoelasticity of a medium.According to the correspondence principle,the Biot-Squirt(BISQ)equations in the steady-state case are presented for the space-frequency domain described by solid displacements and fluid pressure in a homogeneous viscoelastic medium.The effective bulk modulus of a multiphase flow is computed by the Voigt formula,and the characteristic squirt-flow length is revised for the gas-included case.We then build a viscoelastic BISQ model containing a multiphase flow.Through using this model,wave dispersion and attenuation are studied in a medium with low porosity and low permeability.Furthermore,this model is applied to observed interwell seismic data.Analysis of these data reveals that the viscoelastic parameter tanδ is not a constant.Thus,we present a linear frequency-dependent function in the interwell seismic frequency range to express tanδ.This improves the fit between the observed data and theoretical results.     

Including dispersion and attenuation directly in the time domain for wave propagation in isotropic media

When sound propagates in a lossy fluid, causality dictates that in most cases the presence of attenuation is accompanied by dispersion. The ability to incorporate attenuation and its causal companion, dispersion, directly in the time domain has received little attention. Szabo [J. Acoust. Soc. Am. 96, 491-500 (1994)] showed that attenuation and dispersion in a linear medium can be accounted for in the linear wave equation by the inclusion of a causal convolutional propagation operator that includes both phenomena. Szabo's work was restricted to media with a power-law attenuation. Waters et al. [J. Acoust. Soc. Am. 108, 2114-2119 (2000)] showed that Szabo's approach could be used in a broader class of media. Direct application of Szabo's formalism is still lacking. To evaluate the concept of the causal convolutional propagation operator as introduced by Szabo, the operator is applied to pulse propagation in an isotropic lossy medium directly in the time domain. The generalized linear wave equation containing the operator is solved via a finite-difference-time-domain scheme. Two functional forms for the attenuation often encountered in acoustics are examined. It is shown that the presence of the operator correctly incorporates both, attenuation and dispersion.     

Photoelastic investigation of interfacial fracture between orthotropic and isotropic materials

Static and dynamic fracture of interfaces between orthotropic and isotropic materials were studied using photoelasticity. In this study, a bi-material specimen made of PSM-1^® and Scotchply^® 1002, a unidirectional glass fiber reinforced epoxy composite, was used. Two fiber orientations, fibers parallel to the interface (α=0°) and fibers perpendicular to the interface (α=90°) were considered. Center crack bi-material specimens having different crack lengths were loaded quasi-statically and the full-field isochromatics were recorded using a digital camera. The complex stress intensity factor corresponding to each crack length was calculated from the isochromatics and the values were compared to that obtained from boundary collocation method. Dynamic interfacial fracture was studied with an edge crack bi-material geometry for the two different fiber orientations. The isochromatics around the propagating crack were recorded using a digital high-speed camera. The fracture parameters such as crack speed, complex stress intensity factor and energy release rate were extracted from the isochromatics using the asymptotic stress field equations. The complex stress intensity factor obtained from the static experiments was in close agreement with that calculated using the boundary collocation method. The results also indicated that the fiber orientation with respect to the interface influences the fracture parameters for stationary and propagating cracks.     

Transient wave propagation in a semi-infinite,transversely isotropic rod

In this study the response in a transversely isotropic, semi-infinite elastic rod is found to an input on its end that is time dependent. The solution follows closely the method developed by Skalak for isotropic rods which uses integral transforms to solve the governing equations. The solution differs from that of Skalak, apart from material properties, in that in this study mixed-mixed conditions are assumed for the end of the rod. The responses are found at a “distant” station and are expressed in terms of the axial and tangential strains.     

Effective permittivity of a fiber-reinforced composite with transversely isotropic constituents

Simple closed-form expressions for effective permittivity of fiber-reinforced composites with transversely isotropic constituents are found using asymptotic homogenization. Circular cylindrical fibers are distributed in a square array. The analysis considers four orientations of constituents transverse symmetry axis relative to fibers direction. Local problems defined on a periodic square unit cell are solved by means of complex potential theory using Weierstrassian and Natanzon's functions, assuming that the contrast of permittivities is small. Derived closed-form formulas are compared with finite element calculations and, in the isotropic case, with standard mixture rules and classical bounds, obtaining excellent results even when contrast is large.     

Wave-induced fluid flow in random porous media: attenuation and dispersion of elastic waves

A detailed analysis of the relationship between elastic waves in inhomogeneous, porous media and the effect of wave-induced fluid flow is presented. Based on the results of the poroelastic first-order statistical smoothing approximation applied to Biot's equations of poroelasticity, a model for elastic wave attenuation and dispersion due to wave-induced fluid flow in 3-D randomly inhomogeneous poroelastic media is developed. Attenuation and dispersion depend on linear combinations of the spatial correlations of the fluctuating poroelastic parameters. The observed frequency dependence is typical for a relaxation phenomenon. Further, the analytic properties of attenuation and dispersion are analyzed. It is shown that the low-frequency asymptote of the attenuation coefficient of a plane compressional wave is proportional to the square of frequency. At high frequencies the attenuation coefficient becomes proportional to the square root of frequency. A comparison with the 1-D theory shows that attenuation is of the same order but slightly larger in 3-D random media. Several modeling choices of the approach including the effect of cross correlations between fluid and solid phase properties are demonstrated. The potential application of the results to real porous materials is discussed.     

Theoretical investigation of the sound attenuation of membrane-type acoustic metamaterials

Membrane-type acoustic metamaterials have been recently shown to exhibit good performance of sound attenuation in a low frequency range. An analytical approach for the fast calculation of sound transmission loss of the membrane-type acoustic metamaterials is presented here. The discussion indicate that the first transmission loss valley and the transmission loss peak depend strongly on the attaching mass, while the second transmission loss valley is mainly influenced by the membrane properties. The effects of membrane tension and mass position on the transmission loss and characteristic frequencies are also discussed in detail.     

Acoustic waves generated by a laser point pulse in a transversely isotropic cylinder

A three-dimensional (3D) model is presented to predict the acoustic waves generated by a laser point pulse in a transversely isotropic cylinder. The Fourier series expansion and the two-dimensional Fourier transform are introduced to calculate the 3D transient response under either the ablation or the thermoelastic generation. The presented physical model and the numerical inverse scheme are applied to a fiber reinforced composite cylinder with a strong anisotropy. Experimental radial displacements of the cylinder surface are detected by the laser ultrasonic technique and analyzed by the ray trajectories for both generation regimes. Corresponding theoretical displacements are obtained numerically and compared to the experimental signals. Good agreement is found between theoretical and experimental results. The focusing effects that anisotropy gives rise to are observed in both theory and experiment under either regime.     

Modeling the quasicompressional wave field of a rectangular transducer in a transversely isotropic solid

A fast model for simulating the transient quasicompressional wave field of a rectangular ultrasonic transducer directly coupled to a transversely isotropic elastic half-space of general orientation is developed. The so-called two-tier asymptotic approach and the uniform stationary phase method are used to derive the high-frequency asymptotics of time-harmonic displacements. Then, transient fields are modeled by means of harmonic synthesis. In geometrical regions, the formulas involve elementary and inside boundary layers, well-known special functions (Fresnel integral and generalized Fresnel integral), and are applicable in the radiating near field. The asymptotics elucidate the physics in terms of various arrivals and give explicit dependence of the radiated waves upon model parameters. The asymptotic code is tested against a direct numerical solution. It is at least a thousand times faster but describes accurately both arrival times and amplitudes of various pulses radiated by the transducer.     

Transient elastic waves in a transversely isotropic laminate impacted by axisymmetric load

A method of reverberation-ray matrix has been extended to the investigation of the field of wave propagation in a transversely isotropic laminate. By using the decomposition in a local coordinate system, any complicated waves can be separated into a departing part and an arriving part, which are expressed in the local scattering matrix at structural interface. Together with the local phase matrix, we obtain a certain wave transmitting from a layer to the neighboring one. Thus, the wave propagation in the whole laminate can be described when assembling the local information with global phase and global permutation matrices. This method is perfectly suitable for evaluating the transient waves involving a large number of generalized-rays. In this paper, the method is applied to laminate made of transversely isotropic material. Numerical results show the influence of the change of thickness and elastic constants of the layers on the wave propagation in laminate.     

平面波在横向各向同性均匀介质中的传播

导出均匀各向异性介质当中具有横向各向同性性质的一类介质中平面波的严格解,给出了慢度曲面的三维分布图形,研究了属于这类介质的单向纤维增强复合材料中声波的传播规律。平面波的特征用慢度矢量、波矢量、偏振矢量和群速度等物理量来刻画.由于引入了描述介质各向异性特性的方向矢量,各物理量最终以与座标系无关的形式来表达,因而具有普遍的适用性。     

Perfect fluid in a static isotropic universe

Solutions of the Einstein field equations for a perfect fluid in a static isotropic gravitational field are obtained. The solution given by Melnick and Tavensky is corrected.     

Asymmetric and axisymmetric vibrations of finite transversely isotropic circular cylinders

This paper presents an approach for obtaining the exact frequency equations of axisymmetric and asymmetric free vibrations of transversely isotropic circular cylinders. The solution method is based on the three dimensional theory of linear elasticity and uses potential functions. Using this approach, the frequency spectra and vibration mode shapes are plotted for a number of transversely isotropic cylinders. The proposed approach introduces a number of merits compared to earlier approximate and exact solution methods. First, unlike numerically complicated series methods that provide approximate solutions, the proposed approach is exact. Second, combination of scalar functions employed for representing the displacement field is consistent with the physics of the problem. One scalar potential function has been considered for each component of the wave field inside the elastic cylinder. As a result, the solution is systematically divided into coupled and decoupled equations. In addition, by using this approach, there is no need to guess the final of the solution a priori. These merits make the proposed approach suitable for other vibration problems of anisotropic materials.     

用改进的传输线算法计算水平层状横向同性地层中海洋可控源电磁响应

利用二维Fourier变换与电磁场分解技术将层状横向同性地层中Maxwell方程转化成两个独立的关于横磁(TM)波和横电(TE)波的传输线方程; 借助传输线理论与叠加原理, 仅利用电流源传输线Green函数得到TM波和TE波的解, 改进传输线算法, 建立横向同性地层中频率-波数域电流源电场和磁场并矢Green函数的新算法与新的解析表达式, 提高海洋可控源电磁响应数值模拟效率. 在此基础上, 利用传输线Green函数的基本解以及边界条件, 推导出广义反射系数与振幅递推公式, 得到各个地层中传输线Green函数的解析解; 然后利用Fourier逆变换与Bessel公式将海洋可控源电磁响应表示为Sommerfeld形式的积分, 借助三次样条插值与Lommel积分公式快速计算其数值解. 通过数值模拟结果考察工作频率以及地层各向异性电阻率变化等对海洋电磁响应的影响. 关键词： 传输线法 横向同性地层 海洋可控源电磁 Sommerfeld积分