Study on the reflection of photothermal waves in a semiconducting medium under generalized thermoelastic theory

In this article, coupled generalized thermoelastic with thermal relaxation time and plasma theories were used to study the reflection problem at the surface of a semiinfinite semiconconducting medium during a photothermal process. Using the harmonic wave method, the reflection coefficient ratios were obtained analytically for the incident CI wave and incident rotational wave. The variations of the amplitude of reflection coefficient ratios with the angle of incidence are shown graphically for silicon. Effects of several parameters (thermal relaxation time, thermoelastic coupling parameter, and thermoelectric coupling parameter) on reflection coefficient ratios were given by 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.     

平面S波在非饱和土自由边界上的反射问题研究

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S波在非饱和土层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波的振幅反射率及能量反射率的理论表达式,并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率及能量反射率受平面S波入射角度及土层饱和度变化的影响情况。计算结果表明：各反射波的振幅反射率及能量反射率不仅与入射角有关,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相关工程地震勘探具有一定指导意义。     

The effect of rotation on the reflection of magneto-thermoelastic waves under thermoelasticity without energy dissipation

Summary In this paper reflection of magneto-thermoelastic waves is employed to study the effect of rotation and the magnetic field on the plane harmonic waves of a rotating semi-infinite elastic solid nearby a vacuum under Green and Naghdi theory. The expressions for the reflection coefficients, which are the ratios of the amplitudes of the reflected waves to the amplitude of the incident wave, are obtained. The effect of rotation, the magnetic field, coupling parameter and frequency on the reflection ratios are illustrated graphically. Comparisons are made with the results predicted by GN theory of type II in the presence and absence of rotation and magnetic field. A comparison is also made with the results predicted by GN theory of types II and III in the presence of the magnetic field and rotation.     

利用波动法研究曲梁结构中的波形转换和能量传递

基于Flugge理论,建立了薄壁均质常曲率曲梁面内运动的6阶微分控制方程,得到了曲梁的频散特性曲线和6种波的轴向位移和径向位移的比值,推导了位移和内力响应的表达式以及物理域和波数域的变换矩阵。利用波的传递和反射矩阵对曲梁和半无限长直梁耦合时的能量传递系数和反射系数进行了求解分析。对于半无限长直梁中给定的拉伸波或弯曲波入射,得到了和频率,曲率半径和伸展角度相关的各种波传递和反射的能量系数表达式。数值结果表明,纵波和弯曲波在经过曲梁结构之后发生了波形转换,并研究了能量传递和反射系数随频率,伸展角度,曲梁曲率半径和截面尺寸比的变化。结果表明,无限长直梁和曲梁耦合系统中,低频时,经过曲梁反射和传递后的弯曲波和纵波会相互转化;高频时弯曲波和纵波都能够没有散射地通过曲梁而进行传播。为改善高频时曲梁中的能量衰减效果,研究了在曲梁结构中插入单个、多个中间支撑或阻振质量块时的能量传递和反射系数。结果表明,阻振质量块能够很好地阻止高频时曲梁中能量的传递,对于周期分布的多个阻振质量块,能量传递系数随频率的变化存在周期结构的阻带特征。这些研究结果为曲梁结构的设计提供定性的理论基础。     

Reflection and Refraction of Micropolar Magneto-thermoviscoelastic Waves at the Interface between Two Micropolar Viscoelastic Media

Using micropolar generalized thermoviscoelastic theories, problems of reflection and refraction of magneto-thermoeviscoelastic waves at the interface between two viscoelastic media are studied when a uniform magnetic field permeates the media. Coefficient ratios of reflection and refraction are obtained using continuous boundary conditions. Some special cases are considered, i.e., the absence of micropolar and viscous effects. By numerical calculations, variations of the amplitude ratios of reflection and refraction coefficients with the angle of incidence are shown graphically for incident rotational and dilatational waves at the interface between two media (one medium is aluminium-epoxy micropolar iscoelastic material, and the other is magnesium crystal micropolar viscoelastic material). Comparing the generalized thermoelastic theories developed by Lord and Shulman (LS) and by Green and Lindsay (GL) in this paper to conventional dynamics (CD) theory the effects of a magnetic field and viscosity are shown numerically in this paper.     

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。     

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。     

Scattering of oblique water waves by two thin unequal barriers with non-uniform permeability

The scattering of obliquely incident water waves by two unequal permeable barriers with variable permeability is investigated for two types of barriers, namely partially immersed barriers and bottom-standing barriers, under the consideration of the theory of linear water waves. The barriers are present in water of uniform finite depth. The velocity potential is expanded by using Havelock’s expansion of water wave potential and employing Havelock’s inversion formula together with the conditions on the permeable barriers; the boundary value problem is reduced to a coupled Fredholm-type vector integral equations. The integral equations are solved using the multi-term Galerkin approximation where the unknown functions are approximated in terms of Chebyshev polynomials. The numerical results for the reflection coefficient, the transmission coefficient and the energy dissipation are depicted graphically. Known results for two identical as well as two non-identical impermeable barriers and for a single and twin permeable barriers are recovered in the limiting cases.     

Ultrasonic guided wave scattering in a plate overlap

Guided wave scattering in a plate overlap is investigated by numerical calculations and experimental measurements of transmission and reflection factors from the overlap region. In the numerical study, a hybrid boundary element-finite element method is used to calculate the guided wave scattered field from the overlap region. Transmission and reflection factors are calculated for incident A0 and S0 Lamb and n0 shear horizontal waves, including higher modes generated through mode conversion phenomena. In addition, parametric studies of transmission and reflection factors in this problem are performed numerically over various incident modes, frequencies, and overlap lengths. For verification and comparison with numerical results, experiments were conducted to measure the transmission and reflection factors for incident Lamb and shear horizontal waves in steel plates with two different overlap areas. The experimental results agree well with the numerical calculations. The numerical and experimental results show that it is highly feasible to carry out efficient Lamb wave nondestructive evaluation (NDE) in overlapped plates and in multilayer structures with various lap joints by selecting various modes and tuning frequency.     

Water wave scattering by a pair of thin vertical barriers with submerged gaps

The scattering of obliquely incident water waves by two thin vertical barriers with gaps at different depths has been studied assuming linear theory. Using Havelock’s expansion of water wave potential, the problem is reduced to two pairs of integral equations of the first kind, one pair involving a horizontal component of velocity across the gaps and the other pair involving the difference of potentials across each wall. These two pairs of integral equations can be solved approximately by employing a Galerkin single-term approximation technique to obtain numerical estimates for the reflection and transmission coefficients. These estimates for the reflection and transmission coefficients thus obtained are seen to satisfy the energy identity. The reflection coefficient is plotted against wave number in a number of figures for different values of various parameters involved in the problem. It is observed that the reflection coefficient vanishes at discrete frequencies when the vertical barriers are identical. For nonidentical vertical barriers the reflection coefficient never vanishes, though at some wave number it becomes close to zero. The results for a single barrier and fully submerged two barriers, and for a single barrier with a narrow gap, are also recovered as special cases.     

A study on photothermal waves in an unbounded semiconductor medium with cylindrical cavity

The theory of coupled plasma, thermal, and elastic waves was used to investigate the wave propagation on semiconductor material with cylindrical cavity during photo-thermoelastic process. An unbounded material, elastic semiconductor containing a cylindrical cavity with isotropic and homogeneous thermal and elastic properties has been considered. The inner surface of cavity is constrained, and the carrier density is photogenerated by an exponentially decaying pulse boundary heat flux. The eigenvalue approach, together with Laplace transform techniques, was used to obtain the analytical solutions. Numerical computations have been done for a silicon-like semiconductor material, and the results are presented graphically to estimate the effect of the coupling between the plasma, thermal, and elastic waves. The graphical results indicate that the thermal activation coupling parameter is an important phenomenon and has a great effect on the distribution of field quantities.     

粘接结构中垂直入射纵波的准静态模型解

研究了板状粘接结构中垂直入射纵波的准静态模型解。在将粘接界面简化为准静态模型（QSM）的情况下,推导了界面为完好连接且上下基体为同种材料的板状粘接结构中垂直入射纵波的声反射和透射系数表达式。首先将纵波的准静态模型解和精确解进行了比较以阐释准静态模型的适用条件;接着分析了法向刚度系数和界面相对质量的变化对纵波反射和透射特性的影响。结果表明,在特定频率下,随着刚度系数或界面相对质量的增加,纵波的反射和透射系数的幅值分别减小和增大至某一稳定值。研究成果可为实验时采用纵波垂直入射检测粘接结构提供一定的理论指导。     

声波由粘弹性介质向流体介质入射情况下的声反射分析

在研究含腔体的结构的声学特性时,会遇到声波从粘弹性介质向流体介质入射的情况。主要研究了声波从粘弹性介质向流体介质斜入射情况下的声反射特性,分析表明：反射声波中有横波和纵波同时存在,纵波声压反射系数随入射角度的增大逐渐增大,横波的声压反射系数随入射角度的增加先增大后减小,在垂直入射时只有纵波,而没有横波存在。这些结论为进一步研究带空腔结构的声学特性打下了基础。     

Thermoelastic wave propagation in a random medium and some related problems

The mean waves in a medium with random inhomogeneities are studied within the theory of linear thermoelasticity. Under the assumption of small random fluctuations approximate integro-differential equations governing the mean displacement and temperature fields are derived. For the elastic case the material behaves effectively as a viscoelastic body with memory. The dispersion equation is obtained for the thermoelastic case. This equation is analyzed for some special cases. The random effects introduce attenuation and change of phase speeds for the compressional and shear waves. For weak thermoelastic coupling, the shear wave is not affected by the random thermal properties. Explicit results are obtained for general and special cases. In general the mean fields are coupled in a complicated way. Therefore an uncoupled theory is presented. Then the problems with random boundary conditions or a randomly varying boundary are discussed. Different perturbation methods are given. Two examples are provided respectively by the heat conduction across a rough surface and the hydrodynamic theory of lubrication under a random loading.     

Thermoelastic Lamb waves in a transversely isotropic plate bordered with layers of inviscid liquid

Analysis for the propagation of thermoelastic waves in a homogeneous, transversely isotropic, thermally conducting plate bordered with layers of inviscid liquid or half space of inviscid liquid on both sides, is investigated in the context of coupled theory of thermoelasticity. Secular equations for homogeneous transversely isotropic plate in closed form and isolated mathematical conditions for symmetric and anti-symmetric wave modes in completely separate terms are derived. The results for isotropic materials and uncoupled theories of thermoelasticity have been obtained as particular cases. It is shown that the purely transverse motion (SH mode), which is not affected by thermal variations, gets decoupled from rest of the motion of wave propagation and occurs along an in-plane axis of symmetry. The special cases, such as short wavelength waves and thin plate waves of the secular equations are also discussed. The secular equations for leaky Lamb waves are also obtained and deduced. The amplitudes of displacement components and temperature change have also been computed and studied. Finally, the numerical solution is carried out for transversely isotropic plate of zinc material bordered with water. The dispersion curves for symmetric and anti-symmetric wave modes, attenuation coefficient and amplitudes of displacement and temperature change in case of fundamental symmetric (S₀) and skew symmetric (A₀) modes are presented in order to illustrate and compare the theoretical results. The theory and numerical computations are found to be in close agreement.     

Generalized thermoelastic waves in spherical curved plates without energy dissipation

In this article, the propagation of thermoelastic waves in orthotropic spherical curved plates subjected to stress-free, isothermal boundary conditions is investigated in the context of the Green–Naghdi (GN) generalized thermoelastic theory (without energy dissipation). The theoretical formulation is based on the linear GN thermoelastic theory. The coupled wave equation and heat conduction equation expressed by the displacement and temperature are obtained. By the Legendre orthogonal polynomial series expansion approach, the coupled controlling equations are solved. The convergence of the method is demonstrated through a numerical example. The dispersion curves of thermal modes and elastic modes are illustrated simultaneously. Dispersion curves of the corresponding purely elastic spherical plate are also shown to analyze the influence of thermoelasticity on elastic modes. The displacement, temperature and stress distributions of both elastic modes and thermal modes are calculated to show their differences. A thermoelastic spherical plate with a different ratio of radius to thickness is considered to show the influence of the ratio on the characteristics of thermoelastic 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.     

Wave propagation in micropolar mixture of porous media

This paper is concerned with the possible propagation of waves in an infinite porous continuum consisting of a micropolar elastic solid and a micropolar viscous fluid. Micropolar mixture theory of porous media developed by Eringen [A.C. Eringen, Micropolar mixture theory of porous media, J. Appl. Phys. 94 (2003) 4184–4190] is employed. It is found that there exist four coupled longitudinal waves (two coupled longitudinal displacement waves and two coupled longitudinal microrotational waves) and six coupled transverse waves in a continuum of this micropolar mixture. All the waves are found to attenuate and dispersive in nature. A problem of reflection of coupled longitudinal waves from a free boundary surface of a half-space consisting the mixture of a micropolar elastic solid and Newtonian liquid, is investigated. The expressions of various amplitude ratios and surface responses are derived. Numerical computations are performed to find out the phase velocity and attenuation of the waves. The variation of amplitude ratios, energy ratios and surface responses are also computed for a specific model. All the numerical results are depicted graphically. Some limiting cases have also been discussed.     

Coupling plane wave received by an annular aperture into a single-mode fiber in the presence of atmospheric turbulence

The efficiency of coupling a plane wave into a single-mode fiber can be reduced by both the aperture obstruction of receivers and the turbulence-induced degradation of optical coherence. Using the Gaussian approximation to the mutual coherence function of the incident optical field, we derived an analytical solution for the fiber-coupling efficiency when a plane wave, propagating through atmospheric turbulence, is received by an annular-aperture receiver and coupled into a single-mode fiber. It is a function of the coupling geometry, the aperture-radius-to-coherence-radius ratio (ARCRR), and the aperture-obstruction parameter. It is found by the numerical optimization method that the optimal coupling geometry depends on both the ARCRR and the aperture-obstruction parameter. The results obtained are useful for analyzing and designing a fiber-coupling system influenced by atmospheric turbulence.