柱状固体复合结构对斜入射超声波的散射

较详细阐述了三层柱状固体复合结构对斜入射超声波的散射理论.厚度远小于声波波长和内层半径的中间圆环可模拟为内外层媒质之间的界面薄层.将声波斜入射时中间国环层力学量的传递矩阵作线性近似展开,我们首次建立了描述界面薄层的三维弹簧物理模型,由此进一步分析了固体界面处的声学边界条件.利用弹簧模型,我们最后从数值上研究了玻璃纤维/铝基复合结构中界面薄层力学参量的变化对斜入射超声散射截面积的影响.     

Scattering of plane guided waves obliquely incident on a straight feature with uniform cross-section

A frequency-domain finite element (FE) method is presented for modeling the scattering of plane guided waves incident on an infinitely-long, straight feature with uniform cross-section in a planar host waveguide. The method utilizes a mesh of 2-dimensional finite elements with harmonic shape functions in the perpendicular direction. The model domain comprises a cross-section through the feature and short lengths of the adjoining host waveguide. A spatial frequency equal to the wavenumber of the desired incident mode multiplied by the sine of the desired incidence angle is prescribed for the element shape functions. An integral representation of the incident mode is used to determine a suitable system of harmonic forces to uniquely excite that mode. These are applied at nodes through the thickness of the host waveguide on one side of the feature. The displacement field is measured at nodes through the thickness of the host waveguide on either side of the feature and decomposed into reflected and transmitted modes. The cases of guided wave transmission in a featureless waveguide and the reflection of guided waves from a free-edge are examined as validation cases. Finally, the results for transmission at an adhesively-bonded stiffener are presented and compared with experimental measurements.     

Multiple scattering of an obliquely incident plane acoustic wave from a grating of immersed cylindrical shells

The study of the interaction of acoustic waves with cylindrical structures has numerous applications including the ultrasonic nondestructive testing of materials. In this paper, using a new mathematical model presented for the scattering of obliquely incident plane acoustic waves from a grating of immersed cylindrical shells, a detailed study of the resonant interaction of A-wave resonances originating from the shells is conducted. The nature of A-wave resonances and the effect of center-to-center distance of the shells on these resonances are examined. It is observed that this resonant interaction not only results in the splitting of A-wave resonances, but also causes an increase in resonance amplitudes. This interaction phenomenon is not seen in Rayleigh, whispering gallery and guided wave resonances. It is also shown that increasing the angle of wave incidence to the grating weakens the A-wave resonant interactions. The numerical results obtained from the mathematical model are compared to experimental results available in the literature for gratings composed of two and three aluminum shells. The numerical results are in very good agreement with their experimental counterparts.     

Reflection of Lamb waves obliquely incident on the free edge of a plate

The reflection of obliquely incident symmetric and anti-symmetric Lamb wave modes at the edge of a plate is studied. Both in-plane and Shear-Horizontal (SH) reflected wave modes are spawned by an obliquely incident in-plane Lamb wave mode. Energy reflection coefficients are calculated for the reflected wave modes as a function of frequency and angle of incidence. This is done by using the method of orthogonal mode decomposition and by enforcing traction free conditions at the plate edge using the method of collocation. A PZT sensor network, affixed to an Aluminum plate, is used to experimentally verify the predictions of the analysis. Experimental results provide support for the analytically determined results.     

Scattering of E and H polarized waves from covered cylindrical structures

A modification of the method of discrete sources (MMDS) is applied for solving 2D scattering problems by metal (or dielectric) cylindrical structure covered with a dielectric layer. The scattering of E (or H) polarized incident plane and cylindrical wave was considered. The problems of accuracy, choosing auxiliary contours and impedance approximation in scattering problem are discussed.     

圆柱空腔上裂纹的爬波检测方法

通过牛顿迭代法求解了固体内部圆柱空腔上爬波的频散方程,分析了爬波的频散和衰减特性。利用动态光弹法显示了爬波的直观图像和圆柱空腔附近各散射波的空间关系。根据爬波具有的频散、衰减以及辐射横波特征,设计了斜入射脉冲回波实验装置,测量了特定位置处裂纹反射爬波辐射出的横波信号,其与柱面反射波的时差和理论预测一致。进一步实验研究发现,爬波回波幅度与特定位置的裂纹长度具有近似单调的对应关系,在裂纹长度较大时,回波幅度趋于稳定。以上工作为圆柱空腔上裂纹的爬波定量检测提供了物理基础和实现方法。     

Spectral responses of gyrotropic chiral sculptured thin films to obliquely incident plane waves

Gyrotropic chiral sculptured thin films (STFs) exhibit optical activity due to their structural chirality, local anisotropy, and magneto-optic gyrotropy. We adapted two algorithms for nongyrotopic chiral STFs to investigate the circular-polarization-sensitivity of gyrotropic chiral STFs to incident plane waves. The impacts of gyrotropy and oblique angles of incidence on the reflectances and the transmittances were examined, and several conclusions drawn. In particular, we found that the incorporation of gyrotropy results in a blueshift of the Bragg regime.     

Circumferential resonance modes of solid elastic cylinders excited by obliquely incident acoustic waves

When an immersed solid elastic cylinder is insonified by an obliquely incident plane acoustic wave, some of the resonance modes of the cylinder are excited. These modes are directly related to the incidence angle of the insonifying wave. In this paper, the circumferential resonance modes of such immersed elastic cylinders are studied over a large range of incidence angles and frequencies and physical explanations are presented for singular features of the frequency-incidence angle plots. These features include the pairing of one axially guided mode with each transverse whispering gallery mode, the appearance of an anomalous pseudo-Rayleigh in the cylinder at incidence angles greater than the Rayleigh angle, and distortional effects of the longitudinal whispering gallery modes on the entire resonance spectrum of the cylinder. The physical explanations are derived from Resonance Scattering Theory (RST), which is employed to determine the interior displacement field of the cylinder and its dependence on insonification angle.     

平面声波斜入射到水中无限长圆柱壳体的纯弹性共振散射

斜入射情况下水中弹性圆柱壳体的共振声散射问题至今还很少被研究。本文导出了平面声波斜入射时水中无限长圆柱壳体纯弹性共振散射函数的简单而明显的表达式。针对中空铝圆柱壳体(b/a=0.8)详细计算了不同入射角时纯弹性共振散射的分波共振谱,同时还给出了远场反向散射形态函数及其刚硬背景隔离,发现形态函数受吻合频率的影响很大。文中详细计算了斜入射时无固次复频率平面上的共振复极点分布,并由此计算了不同入射角时各阶共振模式,特别是附加共振模式所对应螺旋环绕波的相速度频散曲线。这些结果十分有助于认识声波斜入射下圆柱壳体的共振和再辐射的物理本质。     

Helical normal waves near a cylindrical cavity in an elastic medium

The properties of helical waves arising near a cylindrical cavity in an elastic medium are described. These waves are a manifestation of aperiodic (in angle) solutions to the dynamic elasticity equations. The dispersion characteristics of the waves are determined, and the spatial structure of the waves is described.     

Maxwell stress distributions in chiral sculptured thin films due to obliquely incident plane waves

When a circularly polarized plane wave is obliquely incident on a chiral sculptured thin film (STF), the Maxwell stress dyadic exhibits a decreasing periodic variation across the thickness of the film. Normal and tangential surface tractions exist on the two faces of the chiral STF, as well as a net normal pressure across the film. These stresses are affected by the incidence angle of light, and are maximized when (i) the incident plane wave and the chiral STF are co-handed, (ii) the wavelength falls within a regime called the Bragg regime, (iii) the ratio of film thickness to the structural period of the chiral STF reaches a saturation value, and (iv) the deviation from normal incidence is small.     

Propagation of p-polarized electromagnetic waves obliquely incident on stratified random media: Random phase approximation

We consider the propagation of p-polarized electromagnetic waves obliquely incident on stratified random dielectric media. Using the invariant imbedding method generalized to random media and applying the random phase approximation, we derive a simple analytical expression of the localization length and calculate the disorder-averaged reflectance and transmittance and the fluctuations of the localization length and the reflectance as functions of the incident angle. We also calculate the disorder-averaged intensity profile of the magnetic field inside the random medium. We find that within the random phase approximation, the p wave can be delocalized and transmitted completely at a certain critical incident angle, which is bigger than the Brewster angle in the uniform case.     

Transverse magnetic scattering of two incident plane waves by a dielectric coated cylindrical reflector

Scattering characteristics of two plane waves are investigated for a circular cylinder covered by a dielectric substance. Fields are assumed to be transverse magnetic (TM) and represented in an exponential series form. The diffracted radiations are found by applying the boundary conditions to the wave functions. The wave transformation method and the orthogonality of the exponential functions are respectively employed to obtain an infinite series in the solution. Numerical results are evaluated by reducing the infinite series to a finite number of terms and comparing estimates with the single plane wave scattering situation.     

Scattering of antiplane shear waves by layered circular elastic cylinder

An exact analytical solution for the scattering of antiplane elastic waves by a layered elastic circular cylinder is obtained. The solution and its degenerate cases are compared with other simpler models of circular cylindrical scatterers. The effects of the geometrical and physical properties of the interphase are studied. Numerical results confirm the existence of a resonance mode in which the scatterer's core undergoes a rigid-body motion when the outer layer of the scatterer is very compliant. This resonance mode has been attributed [Liu et al., Science 289, 1734 (2000)] to a new mechanism for the band gap formed in the extremely low frequency range for phononic crystals made of layered spherical scatterers. Numerical results also show the existence of a similar resonance mode when the outer layer of the scatterer has very high mass density.     

Diffraction of an obliquely incident wave beam by a rectangular aperture

The diffraction problem of an obliquely incident wave beam on a rectangular aperture can be reduced to that of normal incidence by expressing the incident wave beam in a form convenient for the discussion of the problem. In this paper the diffraction field is obtained by using this expression. The field is then expanded into a series of beam mode functions. The expansion coefficient of the series can be expressed in a simple form. A numerical example of the coefficient is shown for the diffraction by a half plane.