Flexural gravity wave motion over poroelastic bed

Using Biot’s consolidation theory, effect of poroelastic bed on flexural gravity wave motion is analyzed in both the cases of single-layer and two-layer fluids. The model for the flexural gravity waves is developed using linear water wave theory and small amplitude structural response in finite water depth. The effects of permeability and shear modulus of poroelastic bed and time period on flexural gravity wave motion are studied by analyzing the dispersion relation, phase speed, plate deflection, interface elevation and pressure distribution along water depth. Various results for surface gravity waves are analyzed as special cases. The study reveals that bed permeability retards the hydrodynamic pressure distribution along the water depth significantly compared to shear modulus whilst, floating plate deflection decreases significantly with change in shear modulus compared to permeability of the poroelastic bed. The present study can be generalized to analyze various wave–structure interaction problems over poroelastic bed.     

Effect of loosely bonded undulated boundary surfaces of doubly layered half-space on the propagation of torsional wave

This paper investigates the propagation of torsional wave in an initially stressed poroelastic layer with corrugated as well as loosely bonded boundary surfaces, sandwiched between a corrugated fiber-reinforced layer and a viscoelastic half-space under initial stress. The velocity equation has been obtained in closed form analytically and the substantial effect of affecting parameters on the phase velocity of torsional surface wave has been demonstrated numerically and graphically. Comparative study has been made to observe the effect of flatness parameter, reinforcement, viscoelasticity and porosity on the phase velocity, meticulously. Some particular cases have also been discussed and it is found that velocity equation is in well-agreement to the classical Love wave equation. Moreover, some remarkable observation has been made through numerical computation and graphical demonstration for fiber-reinforced layer of carbon fiber-epoxy resin, poroelastic layer of sandstone and a viscoelastic half-space.     

Parametric stress-concentration factors in greenstick bone fracture

The reported work is a part of an ongoing research program concerned with structural analysis of fractured long bone and methods of internal fixation. The stress-concentration factors for equine metacarpus bones containing greenstick fractures and “through” fractures (surgically repaired) were determined for the compression, flexural and torsional modes of loading based on whole bone (unfractured) strengths. The greenstick type of fracture was simulated with saw cuts at the mid-span of the bone, and the parameters varied were depth of fracture and orientation of fracture. All specimens consisted of fresh dead bone which had been placed in a freezer within 4 hr after expiration. The maximum stress-concentration factors for the simulated greenstick fractures studied were about 3.4 for compression, 4.3 for torsion and 16 for flexure. The stressconcentration factors for fractured bones surgically repaired with commercial plates were about 3.0 for compression, 2.7 for torsion and 6.1 for flexure.     

Experimental investigation of transient flexural waves in beams with discontinuities of cross section

There has been little experimental work on flexural wave propagation in general and on flexural wave propagation in beams with discontinuities of cross section in particular. Experimental data are obtained for various test beams subjected to eccentric longitudinal impact. The bending strain versus time results are presented for several positions along a uniform beam and finite beams (of circular cross section) with discontinuities of cross section. Bending strain histories are recorded at several positions before and after the discontinuity. The effect of reflections on the propagated flexural wave is illustrated. The dispersion of the traveling flexural wave caused several alternating peaks within the duration of the original positive input pulse. The importance of investigating discontinuities of cross section in structures subjected to impact loading is clearly manifested.     

Rayleigh Waves on an Exponentially Graded Poroelastic Half Space

In this paper we consider the propagation of seismic waves in isotropic poroelastic half spaces with continuously varying elastic properties, namely with an exponentially decaying depth profile. The present paper shows that the problem leads naturally to a bicubic equation. We obtain explicit inhomogeneous plane wave solutions in an exponential evanescent form with respect to the depth of half space. Further, these solutions are used to solve the boundary value problem of a Rayleigh surface wave and the secular equation is established. The results obtained theoretically are exemplified for numerical data and represented graphically for a representative poroelastic material.     

含电学边界的压电层合梁的非线性弯曲波

非线性科学己成为近代科学发展的一个重要标志,特别是非线性动力学和非线性波的研究对于解决自然科学各领域中遇到的复杂现象和问题有着极其重要的意义.本文研究了含电学边界条件的压电层合梁的非线性弯曲波传播特性.首先,考虑几何非线性效应和压电耦合效应,利用哈密顿原理建立了一维无限长矩形压电层合梁弯曲波的非线性方程.其次,采用Ja...     

Mathematical study on wave interaction with a composite poroelastic submerged breakwater

In this paper the problem of wave propagation over an adjoining-type of composite submerged poroelastic breakwater with different materials is investigated theoretically. A new analytical solution for describing the dynamic response of wave interaction with poroelastic structures is presented. A set of simultaneous equations is developed and numerically solved in order to produce a general solution for each region subject to matching boundary conditions. The present paper focuses on the changes of influence parameters such as different component widths of the composite breakwater, permeability coefficients, composite materials and configurations of breakwater on wave variations.     

An Asymptotic Model of Seismic Reflection from a Permeable Layer

Analysis of compression wave propagation in a poroelastic medium predicts a peak of reflection from a high-permeability layer in the low-frequency end of the spectrum. An explicit formula expresses the resonant frequency through the elastic moduli of the solid skeleton, the permeability of the reservoir rock, the fluid viscosity and compressibility, and the reservoir thickness. This result is obtained through a low-frequency asymptotic analysis of Biot’s model of poroelasticity. A review of the derivation of the main equations from the Hooke’s law, momentum and mass balance equations, and Darcy’s law suggests an alternative new physical interpretation of some coefficients of the classical poroelasticity. The velocity of wave propagation, the attenuation factor, and the wave number are expressed in the form of power series with respect to a small dimensionless parameter. The absolute value of this parameter is equal to the product of the kinematic reservoir fluid mobility and the wave frequency. Retaining only the leading terms of the series leads to explicit and relatively simple expressions for the reflection and transmission coefficients for a planar wave crossing an interface between two permeable media, as well as wave reflection from a thin highly permeable layer (a lens). Practical applications of the obtained asymptotic formulae are seismic modeling, inversion, and attribute analysis.     

Ultrasound propagation in cancellous bone

Wave propagation in fluid-saturated cancellous bone is studied on the basis of two approaches: The thermodynamic-consistent Theory of Porous Media (TPM) and Biot’s theory. Phase velocities in the low-frequency range, calculated with the Biot-Gassmann relations, Wyllie’s equation and the TPM, are demonstrating that a simple, so-called hybrid biphasic TPM model is able to capture the main acoustical effects in cancellous bones. Furthermore, an extension towards high-frequency wave propagation is discussed on the basis of the constitutive relations for the momentum exchange of the fluid and the solid phases. Further numerical results show that, in the high-frequency (ultrasound) range a viscous correction as well as an added mass effect (tortuosity) needs to be taken into account to explain experimentally obtained results.     

地震波倾斜入射下两相饱和土层响应数值模拟

基于Biot两相饱和多孔介质理论建立了频域内饱和土层的刚度矩阵,对从基岩倾斜入射地震波下饱和土层的波动响应进行了数值研究,入射波采取修正的Kanai-Tajimi谱。通过土层地表面处的水平以及竖直放大系数研究了在不同工况条件下土层的波动响应,研究结果表明,土层的波动响应在入射角接近临界入射角时达到峰值;土层的波动响应随着基岩埋深基以及土层阻尼比的增大显著减小;而土层与基岩的波速比对土层的波动响应的影响存在临界波速比,使土层响应达到极值。对于含有夹层的地质环境,研究了波动响应沿深度的分布,通过与均质土层下响应对比,显示非均质夹层能显著减小土层地表处的波动响应,尤其软夹层能较好地阻止入射波向上的传播。     

成层饱和介质平面波斜入射问题的一维化时域方法

地震波斜入射下自由场的输入是大型结构抗震分析中亟待解决的问题之一,尤其是成层饱和多孔介质自由场问题,由于问题的复杂性,目前研究甚少. 本文基于Biot提出的饱和多孔介质动力方程,建立了一种新的求解平面波斜入射下基岩上覆饱和多孔介质成层场地自由场分析的一维化时域计算方法. 该方法首先根据Snell定律将饱和多孔介质二维空间问题转化为一维时域问题,通过对深度方向的有限元离散,得到饱和多孔介质波动问题的一维化有限元方程,然后采用单相弹性介质精确人工边界条件模拟基岩半空间的波动辐射和输入特征,通过考虑基岩与饱和多孔介质间透水或不透水边界条件以及不同饱和多孔介质交界面边界条件,形成基岩上覆成层饱和介质系统的整体有限元方程,最后采用中心差分法与Newmark平均加速度近似格式相结合的方法对时间进行离散,得到节点的动力时程的显式表达. 典型场地的地震反应分析表明,本文方法的计算结果与传递矩阵法结合傅里叶变换的计算结果完全吻合,证明了其有效性.      

Rayleigh-type wave propagation through liquid layer over corrugated substrate

The propagation of the Rayleigh-type wave in a fluid layer overlying a corrugated substrate is studied. The corrugated substrate is considered as a fluid saturated poroelastic substrate and a quadratically heterogeneous isotropic elastic substrate in Case I and Case II, respectively. Closed form expressions of dispersion relation for Case I and Case II are obtained. The influence of corrugation, porosity, and heterogeneity on the phase velocity of Rayleigh-type wave, for both cases, is highlighted and demonstrated through numerical computation and graphical discussion. Neglecting corrugation at the common interface, expressions of phase velocity of the Rayleigh-type wave for both cases are derived in a closed form as a special case of the problem. Comparison between the presence and the absence of both heterogeneity and poroelasticity in the substrate of the composite structure is a key in the present study.     

Poroelastic Response of Orthotropic Fractured Porous Media

An algorithm is presented for inverting either laboratory or field poroelastic data for all the drained constants of an anisotropic (specifically orthotropic) fractured poroelastic system. While fractures normally weaken the system by increasing the mechanical compliance, any liquids present in these fractures are expected to increase the stiffness somewhat, thus negating to some extent the mechanical weakening influence of the fractures themselves. The analysis presented in this article quantifies these effects and shows that the key physical variable needed to account for the pore-fluid effects is a factor of (1 − B), where B is Skempton’s second coefficient and satisfies 0 ≤ B < 1. This scalar factor uniformly reduces the increase in compliance due to the presence of communicating fractures, thereby stiffening the fractured composite medium by a predictable amount. One further aim of the discussion is to determine the number of the poroelastic constants that needs to be known by other means to determine the rest from remote measurements, such as seismic wave propagation data in the field. Quantitative examples arising in the analysis show that, if the fracture aspect ratio a_f @ 0.1{a_f \simeq 0.1} and the pore fluid is liquid water, then for several cases considered, Skempton’s B @ 0.9{B \simeq 0.9}, and so the stiffening effect of the pore-liquid reduces the change in compliance due to the fractures by a factor 1 - B @ 0.1{1 - B \simeq 0.1}, in these examples. The results do, however, depend on the actual moduli of the unfractured elastic material, as well as on the pore-liquid bulk modulus, so these quantitative predictions are just examples, and should not be treated as universal results. Attention is also given to two previously unremarked poroelastic identities, both being useful variants of Gassmann’s equations for homogeneous—but anisotropic—poroelasticity. Relationships to Skempton’s analysis of saturated soils are also noted. The article concludes with a discussion of alternative methods of analyzing and quantifying fluid-substitution behavior in poroelastic systems, especially for those systems having heterogeneous constitution.     

Interaction of rarefaction waves with wet foam

The interaction of rarefaction waves of different shapes with wet water foams is studied experimentally. It is found that the observed values of the pressure are greater, while the surface velocity is lower than the corresponding values predicted by the pseudogas model. The foam breakdown starts as the pressure decreases by 0.3 atm relative to the initial pressure. During downstream propagation of the rarefaction-wave leading edge the propagation velocity decreases.Using of water-based foams as effective screens for damping blast waves in different technological processes has caused considerable interest in studying wave propagation in such systems. The pressure wave dynamics in a foam have been investigated in much detail, both experimentally and theoretically [1–3]. However, the interaction of rarefaction waves with foam has practically never been studied, although it was mentioned in [4] that the unloading phase following the compression wave phase is one of the factors defining the damaging action of blast waves. Besides blast-wave damping, rarefaction wave propagation takes place if such waves are used to breakup foam in oil-producing wells [5].Below, the interaction of rarefaction waves of different shapes with wet water foams is studied. The vertical shock tube described in detail in [3] was used in these experiments.Brest. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 76–82, March–April, 1995.     

青鱼鳍骨、肋骨和鳃盖骨微观结构与力学性能的比较研究

本文从材料学角度定量分析了青鱼鳍骨、肋骨、鳃盖骨的微观结构、成分及力学特性。利用电子显微镜观察了鳍骨、肋骨、鳃盖骨的微观结构;通过X射线衍射、电镜能谱以及煅烧的骨灰综合分析,探讨了青鱼鳍骨、肋骨、鳃盖骨的有机、无机成分之间的密切联系;进行了青鱼鳍骨、肋骨、鳃盖骨的拉伸实验;利用显微硬度计对干、湿状态下的鳍骨、肋骨、鳃盖骨进行了硬度测试。结果显示,鳍骨无机物含量较多,鳃盖骨有机物较多,肋骨介于两者之间;矿化胶原蛋白束在鳍骨中的排列非常规则,在鳃盖骨中排列不是很规则,在肋骨中排列较规则;鳍骨中矿化胶原纤维束间孔洞非常少,骨质密实,而在腮盖骨中孔洞很多,骨质稀疏;干的鱼骨显微硬度均大于湿的鱼骨。结论是,鳍骨、肋骨、鳃盖骨的微观结构、成分及力学特性存在差异,其中鳍骨的力学性能明显强于鳃盖骨,肋骨介于二者之间,水份对青鱼鳍骨、肋骨、鳃盖骨的硬度有明显的影响。     

Novel evolutionary behaviors of localized wave solutions and bilinear auto-Bäcklund transformations for the generalized (3+1)-dimensional Kadomtsev–Petviashvili equation

Water waves are common phenomena in nature, which have attracted extensive attention of researchers. In the present paper, we first deduce five kinds of bilinear auto-Bäcklund transformations of the generalized (3+1)-dimensional Kadomtsev–Petviashvili equation starting from the specially exchange identities of the Hirota bilinear operators; then, we construct the N-soliton solutions and several new structures of the localized wave solutions which are studied by using the long wave limit method and the complex conjugate condition technique. In addition, the propagation orbit, velocity and extremum of the first-order lump solution on (x, y)-plane are studied in detail, and seven mixed solutions are summarized. Finally, the dynamical behaviors and physical properties of different localized wave solutions are illustrated and analyzed. It is hoped that the obtained results can provide a feasibility analysis for water wave dynamics.

     

Propagation of torsional surface wave in anisotropic poroelastic medium under initial stress

The present work deals with the possibility of propagation of torsional surface wave in fluid saturated poroelastic layer lying over nonhomogeneous elastic half space. Both the media are assumed to be under compressive initial stress. The half space has two types of inhomogeneity, viz; hyperbolic and quadratic. The dispersion equation for torsional wave in porous layer has been derived and observed that the presence of fluid in pores increases the velocity of the torsional surface wave but the phase velocity diminishes due to the presence of compressive initial stress in the porous layer. It is also observed that the velocity of the torsional surface wave increases due to the increase of initial stress in inhomogeneous half space. The inhomogeneity factor due to quadratic and hyperbolic variations in rigidity, density and initial stress of the medium decreases the phase velocity as it increases.     

Wave propagation in transversely isotropic cylinders

Various approaches have been used for model1ing problems dealing with interaction of acoustic/elastic waves with transversely isotropic cylinders. The authors developed the first mathematical model for the scattering of acoustic waves from transversely isotropic cylinders [Honarvar, F., Sinclair, A.N., 1996. Acoustic wave scattering from transversely isotropic cylinders. Journal of the Acoustical Society of America 100, 57–63.]. In the current paper, this model is used for derivation of the frequency equations of longitudinal and flexural wave propagation in free transversely isotropic cylinders. Consistency of this model with the physics of the problem is demonstrated and a systematic solution to the corresponding equations is developed. Numerical results obtained for a number of transversely isotopic cylinders are used for verification of the mathematical model.     

Measurements of dynamic properties of concrete structures using flexural wave propagation characteristics

Flexural wave propagation characteristics influence the impact noise generation of concrete structures that are found in building floors, railroads, bridges, and many other engineering structures. The flexural vibration of the structure is affected by concrete dynamic properties. The purpose of this study is to measure the concrete dynamic characteristics using a wave propagation approach. The flexural wave speeds, bending stiffness and their loss factors were measured. The measured characteristics are essential for understanding sound radiation and vibration dissipation capabilities of the concrete structures. Various concrete beam structures were made and tested. The dynamic stiffness and loss factor were influenced by its components and showed frequency-dependent variation, especially for the measured loss factor.