P1波在非饱和土地基表面的反射特性

非饱和土是地表天然土体中最常见的一种形式。与饱和土不同,非饱和土内可传播四种体波:一种剪切波(S波)和三种压缩波(P1波、P2波、P3波)。其中P1传播特性与饱和土中的快压缩波相似:传播速度最快,且衰减系数最低。因此,该文运用非饱和孔隙介质理论阐述了弹性波在非饱和土中的传播特性,分析了平面P1波在非饱和土介质自由边界上的反射问题。根据边界条件,分别导出了在非饱和土自由边界上的四种反射波:反射P1波、反射P2波、反射P3波及反射S波的振幅反射系数及能量反射系数的理论表达式,并且在此基础上进行了数值计算。算例中讨论了四种反射波的振幅反射系数及能量反射系数受P1波入射角及地基土体饱和度变化的影响情况。结果表明:各反射波的振幅反射系数及能量反射系数不仅与入射角有关,也受到饱和度变化的影响。这些结论对土动力学的理论研究以及工程地震勘探具有一定指导意义。     

非饱和地基中Love波的传播特性

基于非饱和多孔介质的波动方程,考虑了土中水,气体与土骨架之间的粘性耦合作用,建立了弹性半空间上非饱和土层中Love波的弥散方程。首先分析了饱和度与频率对非饱和孔隙介质中剪切波速的影响。然后运用数值方法得到了不同饱和度下土层中多种Love模态波的弥散特性和位移分布情况,并用图表的形式给出。数值计算结果表明,上覆非饱和土层中Love波的传播速度和衰减系数不仅具有频散性,而且与土层的饱和度有关。在不同饱和度时的高模态(n≥2)的Love波的截止频率值不同。此外,讨论了饱和度对Love波水平位移幅值的影响。     

S波由饱和土入射于弹性土时在界面上的反射与透射

从地震工程实际出发，借助Biot多孔介质中的波动方程，根据各种界面条件导出了S波从饱和土入射于弹性土时在交界面上反射与透射的一般计算公式。作为算例，数值计算分析了S波从饱和土入射于饱和土与弹性土交界面时，饱和土中P1、P2和S波的反射系数以及弹性土中P波、SV射系数与界面排水条件、入射角以及频率之间的关系。结果表明：各种波的反射、透射系数与入射角、入射频率以及界面排水条件有关系。     

简谐荷载作用下非饱和土地基中波阻板隔振效果研究

鉴于非饱和土地基振动问题的普遍性和复杂性,环境振动下非饱和土地基振动控制已成为土动力学的研究热点。基于单相弹性介质和非饱和多孔介质理论,对简谐荷载作用下非饱和土地基中设置单相固体波阻板的隔振效果进行了研究。考虑地表排水排气的边界条件,利用Fourier积分变换和Helmholtz矢量分解原理,建立了动荷载作用下地基动力响应的计算列式。分析了非饱和土地基中土体饱和度、荷载频率、波阻板的埋深、厚度以及弹性模量对其隔振性能的影响规律。结果表明：非饱和土地基中设置波阻板能够取得很好的隔振效果。地表位移幅值随饱和度和波阻板埋深的减小而显著降低,随荷载频率、波阻板的厚度和弹性模量的增大而明显减小。     

高饱和度饱和土中结构对爆炸波反射规律的实验研究

介绍了高饱和度饱和土介质中结构和刚性边界反射爆炸波试验的背景，目的和方法。给出了爆炸载荷作用下饱和土中模型结构表面和刚性边界压力和动量的实测波形，并对实验结果进行了分析，得到了爆炸波在结构和刚性边界上的反射规律和反射系数。结构上的压力反射系数在0.4-1.4之间，刚性边界上的压力反射系数在1.0-2.0之间。     

和土体中线弹性连续屏障的隔振分析

基于Biot波动理论,推导了饱和土中S波入射线弹性固体连续屏障时反射P1波、P2波、S波的反射系数与透射S波、P波的透射系数的解析解。进行算例分析,得出各反射透射系数与线弹性固体连续屏障密度、泊松比及弹性模量的关系。结果表明：线弹性固体隔振结构密度对P1波和P2波反射系数基本无影响;而随着线弹性固体隔振结构密度的增大,S波的反射和透射系数及P波的透射系数均逐渐减小,且渐趋稳定;线弹性固体连续屏障泊松比和弹性模量的变化对P1波P2波反射系数及P波透射系数基本无影响,而对S波的反射系数和透射系数影响较大,S波的反射系数随着线弹性固体连续屏障的泊松比和弹性模量的增大而增高,S波的透射系数随着泊松比的增大而减小,随着弹性模量的增大而增大。     

非饱和土地基中P1波通过复合多层波阻板的传播特性研究

基于弹性波在非饱和多孔介质与单相弹性介质中的传播理论,考虑在非饱和土地基中设置一定厚度的复合多层波阻板(复合多层波阻板以3层为例),利用Helmholtz矢量分解定理,推导了非饱和土地基中P₁波通过复合多层波阻板的透射、反射振幅比的解析解。通过数值算例分析了层间波阻板剪切模量和密度等物理、力学参数对非饱和土地基中P₁波通过复合多层波阻板时传播特性的影响规律。结果表明：复合多层波阻板中层间波阻板材料的剪切模量对透、反射系数影响显著,层间波阻板材料的密度对透、反射系数影响较小。故严格控制层间波阻板的剪切模量可以获得很好的隔振效果,这为复合多层波阻板在地基振动控制领域中的应用提供理论指导。     

直角平面边界固定半圆形夹杂对稳态入射平面SH波的散射

利用复变函数法、多极坐标及傅里叶级数展开技术求解了二维直角平面介质边界固定半圆形夹杂对稳态入射平面SH波的散射问题。首先构造出介质边界处不存在固定半圆形夹杂时的入射波场和反射波场；其次建立介质边界处存在固定半圆形夹杂时夹杂边界产生的能够自动满足直角边应力自由条件的散射波解，从而利用叠加原理可写出介质内的总波场。利用夹杂边界处位移条件和傅里叶级数展开方法列出求解散射波中未知系数的无穷代数方程组，在满足计算精度的前提下通过有限项截断，得到相应有限代数方程组的解，最后通过算例具体讨论了二维直角平面水平边界点的位移幅度比和相位随无量纲波数、入射波入射角、及夹杂位置的不同而变化的情况，结果表明了该算法的有效实用性。     

Rayleigh波作用下地下结构地震反应影响分析

采用基于时域粘弹性人工边界的Rayleigh波输入方法,进行了土-地下结构相互作用体系在Rayleigh波作用下的动力时程反应分析,对Rayleigh波作用下地下结构的地震反应特性进行研究。重点讨论了地下结构材料强度、结构厚度以及土层刚度等因素对Rayleigh波作用下地下结构地震反应的影响。结果表明Rayleigh波对浅埋地下结构的地震动力反应影响显著,将使结构产生较大的内力与变形,在地下结构抗震设计尤其是浅埋地下结构的抗震设计时应予以足够的重视。     

爆轰波碰撞聚能效应及其数值分析

为了掌握爆轰波碰撞时的爆压和能量汇聚的规律,对爆轰波各种碰撞的爆压变化进行研究。首先基于爆轰波碰撞理论分析.得出爆轰波在正碰撞、斜碰撞和马赫反射三种条件下的爆压变化,确定马赫反射发生的条件,然后绘制入射角、偏离角和反射角间的关系曲线。应用Ls-dyna数值软件对爆轰波碰撞产生马赫反射的过程进行模拟。对比模拟和理论计算结果得知.对于多方指数为2.4的铵油炸药,马赫反射发生在斜爆轰波入射角为46.4°时,此时马赫波后压强达到最大值13.2 GPa,并在马赫波后形成高压区域。     

Reflection of Plane Waves in a Semiconducting Medium under Photothermal Theory

In this paper photothermal theory was used to study the reflection of waves at the surface of a semi-infinite semiconconducting medium. Using the harmonic wave method, the reflection coefficient ratios were obtained analytically under coupled thermoelastic theory and plasma theory for an incident CI wave, which is one coupled thermoelastic plasma wave and an incident rotational wave. The variations of the amplitude of reflection coefficient ratios with the angle of incidence are shown graphically for silicon. Effects of the thermal frequency, the thermoelastic coupling parameter, and the thermoelectric coupling parameter were given by numerical results. Also, the energy ratios for reflected waves were computed to check the numerical results.     

Reflection of plane waves in thermo-diffusion elasticity without dissipation under the effect of rotation

The governing equations of rotating thermoelastic solids with diffusion are solved in context of the Green–Naghdi theory (Type II) to show the numerical existence of four coupled plane waves. The required boundary conditions at the stress free and thermally insulated surface of the model are satisfied to obtain the reflection coefficients of various reflected waves for an incident plane wave. These coefficients are found to depend on rotation parameter, the angle of incidence of striking waves, thermo-diffusion parameters, and other material constants. Complex absolute values of speeds and reflection coefficients are computed for a particular material representing the model. Graphical representation of numerical results show the effects of rotation and diffusion on speed and reflection coefficients of plane waves.     

Reflection and transmission of waves from a plane interface between two microstretch solid half-spaces

In this paper, we have investigated the wave propagation and their reflection and transmission from a plane interface between two different microstretch elastic solid half-spaces in perfect contact. It is shown that there exist five waves in a linear homogeneous isotropic microstretch elastic solid, one of them travel independently, while other waves are two sets of two coupled waves. It is also shown that these waves travel with different velocities, three of which disappear below a critical frequency. Amplitude ratios and energy ratios of various reflected and transmitted waves are presented when a set of coupled longitudinal waves and a set of coupled transverse waves is made incident. It is found that the amplitude ratios of reflected and transmitted waves are functions of angle of incidence, frequency and are affected by the elastic properties of the media. Some special cases have been reduced from the present formulation.     

Reflection of piezothermoelastic waves from the charge and stress free boundary of a transversely isotropic half space

The present paper concentrates on the study of propagation and reflection characteristics of waves from the stress free, thermally insulated/isothermal boundary of a piezothermoelastic half space. The non-classical (generalized) theories of linear piezo-thermoelasticity have been employed to investigate the problem. In the two-dimensional model of the transversely isotropic piezothermoelastic medium, there are three types of plane waves quasi-longitudinal (QL), quasi-transverse (QT) and thermal wave (T-mode), whose velocities depend on the angle of incidence and frequency. These waves are dispersive in character and are also affected by piezoelectric as well as pyroelectric properties of the materials. The low and high frequency approximations for the speeds of propagation and the attenuation coefficients of these waves have been obtained. The quasi-longitudinal (QL), quasi-transverse (QT) and thermal wave (T-mode) incident cases at the stress free, thermally insulated or isothermal open circuit boundary of a transversely isotropic piezothermoelastic half space are considered to discuss the reflection characteristics of various waves. The amplitude ratios of reflected waves to that of incident one in each case have been obtained. The special cases of normal and grazing incidence are also derived and discussed. Finally, the numerical computations of reflection coefficients are carried out for cadmium Selenide (CdSe) material by using Gauss elimination procedure. In addition the phase velocities and attenuation coefficients are also computed along various directions of wave propagation. The obtained results in each case are presented graphically.     

Acoustic reflection from the boundary of anisotropic thermoviscoelastic solid with fluid

Vertical slownesses of waves at a boundary of an anisotropic thermoviscoelastic medium are calculated as roots of a polynomial equation of degree eight. Out of the corresponding eight waves, the four, which travel towards the boundary are identified as upgoing waves. Remaining four waves travel away from the boundary and are termed as downgoing waves. Reflection and refraction of plane harmonic acoustic waves are studied at a plane boundary between anisotropic thermoviscoelastic solid and a non-viscous fluid. At this fluid-solid interface, an incident acoustic wave through the fluid reflects back as an attenuated acoustic wave and refracts as four attenuating waves into the anisotropic base. Slowness vectors of all the waves in two media differ only in vertical components. Complex values of vertical slowness define inhomogeneous refracted waves with a fixed direction of attenuation, i.e. perpendicular to the interface. Energy partition is calculated at the interface to find energy shares of reflected and refracted waves. A part of incident energy dissipates due to interaction among the attenuated refracted waves. Numerical examples are considered to study the variations in energy shares with the direction of incident wave. For each incidence, the conservation of incident energy is verified in the presence of interaction energy. Energy partition at the interface seems to be changing very slightly with the azimuthal variations of the incident direction. Effects of anisotropy, elastic relaxation and thermal parameters on the variations in energy partition are discussed. The acoustic wave reflected from isothermal interface is much significant for incidence around some critical directions, which are analogous to the critical angles in a non-dissipative medium. The changes in thermal relaxation times and uniform temperature of the thermoviscoelastic medium do not show any significant effect on the reflected energy.     

考虑地震波幅值衰减的斜入射二维自由场

本文将传统基于地震波垂直入射的自由场构建方案推广到地震波斜入射情况。在假设平面半空间自由场由以特定角度组合入射的平面P波、SV波及其反射波构成的前提下,通过引入介质品质因子、临界幅值比和子波影响距离等参数完成了均匀线弹性介质中基于地表地震记录、考虑地震波衰减影响的自由场构建。通过地基特征点处入射P波、SV波的时、频域特性,特征点位移时程研究了临界幅值比和地震波幅值衰减因素对自由场的影响。结果显示,对于水工结构等低频激励起主要影响的结构来说,构建自由场时临界幅值比的选择具有较大自由性;在岩体较完整、涉及范围较小时,地震波幅值衰减因素对自由场的影响较小,可忽略不计;但在一些极端情况下,地震波幅值衰减因素对自由场的影响可能达到20%左右。     

Reflection and refraction of plane waves at interface between two piezoelectric media

This paper analyses reflection and refraction of plane waves at a perfect interface between two anisotropic piezoelectric media. The equations of elastic waves, quasi-static electric field, and constitutive relationships for the piezoelectric media are derived. A solution based on the inhomogeneous wave theory is developed to address the inconsistency between the numbers of independent wave modes in the media and the numbers of interfacial boundary conditions to obtain accurate reflection and refraction coefficients in case of strong piezoelectric media, where all the elastic and electric continuity conditions across the interface are satisfied simultaneously. The study shows that there exist independent and zero energy wave modes satisfying the general Snell’s law and propagating along the interface for any incident wave angle. These waves can be treated as pseudo surface waves. It is further found that all the reflection/refraction waves including the pseudo surface waves obey the energy conservation law at the interface boundary. In addition, the analysis also reveals that the reflection and refraction elastic waves can turn into pseudo surface waves at some critical incident angles.