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.     

Experimental measurements of acoustical properties of snow and inverse characterization of its geometrical parameters

Snow is a sound absorbing porous sintered material composed of solid matrix of ice skeleton with air (+water vapour) saturated pores. Investigation of snow acoustic properties is useful to understand the interaction between snow structure and sound waves, which can be further used to devise non-destructive way for exploring physical (non-acoustic) properties of snow. The present paper discusses the experimental measurements of various acoustical properties of snow such as acoustic absorption coefficient, surface impedance and transmission losses across different snow samples, followed by inverse characterization of different geometrical parameters of snow. The snow samples were extracted from a natural snowpack and transported to a nearby controlled environmental facility at Patsio, located in the Great Himalayan range of India. An impedance tube system (ITS), working in the frequency range 63–6300 Hz, was used for acoustic measurements of these snow samples. The acoustic behaviour of snow was observed strongly dependent upon the incident acoustic frequency; for frequencies smaller than 1 kHz, the average acoustic absorption coefficient was found below than 0.4, however, for the frequencies more than 1 kHz it was found to be 0.85. The average acoustic transmission loss was observed from 1.45 dB cm⁻¹ to 3.77 dB cm⁻¹ for the entire frequency range. The real and imaginary components of normalized surface impedance of snow samples varied from 0.02 to 7.77 and −6.05 to 5.69, respectively. Further, the measured acoustic properties of snow were used for inverse characterization of non-acoustic geometrical parameters such as porosity, flow resistivity, tortuosity, viscous and thermal characteristic lengths using the equivalent fluid model proposed by Johnson, Champoux and Allard (JCA). Acoustically derived porosity and flow resistivity were also compared with experimentally measured values and good agreement was observed between them.     

A derivation of the Christoffel equation with damping

This paper provides a derivation of the Christoffel eigenvalue equation for acoustic wave propagation in an acoustically damped piezoelectric medium. The damping tensor is shown to couple into both the stress and displacement constitutive equations. Application of the quasi-static approximation leads to an additional term in the Christoffel equation that generates a complex k-vector, due both to introduction of a complex term and to breaking of symmetry in the left-hand side of the eigenvalue equation, subsequently resulting in damping and a phase shift for a plane wave solution. Shown are the effects of damping on the eigenvalues of the piezoelectrically stiffened Christoffel equation for plane wave propagation in unconstrained quartz over a 1 MHz to 1 GHz frequency range.     

消声管道声学性能计算的二维等几何有限元方法及应用

将等几何有限元方法应用于消声管道的声学性能计算,使用二维等几何有限元方法求解管道截面的声学特征值,考虑了存在穿孔边界和吸声材料边界的情况,进而使用特征值计算消声管道的传递损失。对包覆式消声管道进行传递损失的计算,结果与二维有限元方法吻合较好.对圆形截面的特征值计算结果表明,在计算量相同的情况下,等几何有限元方法取得了比传统有限元方法更好的计算精度.在不同结构参数条件下对消声管道的声学性能进行计算,结果与三维数值方法吻合良好。方法能够在宽频范围内较好地预测消声管道的传递损失。     

半空间球面波函数叠加法重构声源直接辐射声场

提出了基于半空间球面波函数叠加的声场重构方法,以重构含有限声阻抗边界半空间中声源直接辐射的声场。在半空间中多极子声源声压场的解析解的基础上,构造出以边界声阻抗为参量的半空间球面波函数的正交基;通过求逆获得半空间总声压解的基函数系数,同时也获得声源直接辐射声场即自由空间中的基函数系数,进而重构出声源直接辐射的声场。在边界声阻抗已知和边界声阻抗未知两种条件下,对该方法进行了仿真验证和参数分析,并在全消声室内进行了实验验证。结果表明,所提方法能重构出半空间中典型声源即球形声源和平面声源的直接辐射声场;该方法在边界声阻抗已知时的重构精度与稳定性高于在边界声阻抗未知时的情形。     

Ultrasonic characterization of thermally grown oxide in thermal barrier coating by reflection coefficient amplitude spectrum

The thermally grown oxide (TGO) growth at the interface of ceramic coating/bond coating in thermal barrier coatings (TBCs) was evaluated by ultrasonic reflection coefficient amplitude spectrum (URCAS). A theoretical analysis was performed about the influence of acoustic impedance match relationship between the ceramic coating and its adjacent media on URCAS. The immersion ultrasonic narrow pulse echo method was carried out on the TBC specimen before and after oxidation under 1050 °C × 1 h for 15 cycles. The resonant peaks of URCAS obtained before and after oxidation showed that TGO which generated between the ceramic coating and bond coating due to the oxidation, changed the acoustic impedance match between the ceramic coating and its adjacent media. This method is able to nondestructively characterize the generation of TGO in TBCs, and is important to practical engineering application.     

Acoustic impedance microscopy for biological tissue characterization

A new method for two-dimensional acoustic impedance imaging for biological tissue characterization with micro-scale resolution was proposed. A biological tissue was placed on a plastic substrate with a thickness of 0.5 mm. A focused acoustic pulse with a wide frequency band was irradiated from the “rear side” of the substrate. In order to generate the acoustic wave, an electric pulse with two nanoseconds in width was applied to a PVDF-TrFE type transducer. The component of echo intensity at an appropriate frequency was extracted from the signal received at the same transducer, by performing a time–frequency domain analysis. The spectrum intensity was interpreted into local acoustic impedance of the target tissue. The acoustic impedance of the substrate was carefully assessed prior to the measurement, since it strongly affects the echo intensity. In addition, a calibration was performed using a reference material of which acoustic impedance was known. The reference material was attached on the same substrate at different position in the field of view. An acoustic impedance microscopy with 200 × 200 pixels, its typical field of view being 2 × 2 mm, was obtained by scanning the transducer. The development of parallel fiber in cerebella cultures was clearly observed as the contrast in acoustic impedance, without staining the specimen. The technique is believed to be a powerful tool for biological tissue characterization, as no staining nor slicing is required.     

薄膜的光学特性分析

通过CAD,对高反膜、增透膜和干涉滤光片的光学特性进行了研究和分析,指出设计和使用中应注意的问题.     

Comparison of models for predicting the transmission loss of plenum chambers

New experimental data for the transmission loss of plenum chambers are compared to results obtained using several different and well known prediction models. Results for transmission loss as a function of frequency in 1/3 octave bands are presented for a series of plenum chamber configurations of various sizes and interior acoustical treatments. In the experimental work the transmission loss was determined from simultaneous measurements at two upstream and two downstream microphones.     

Analytic bounds on transmission probabilities

We develop some new analytic bounds on transmission probabilities (and the related reflection probabilities and Bogoliubov coefficients) for generic one-dimensional scattering problems. To do so we rewrite the Schrödinger equation for some complicated potential whose properties we are trying to investigate in terms of some simpler potential whose properties are assumed known, plus a (possibly large) “shift” in the potential. Doing so permits us to extract considerable useful information without having to exactly solve the full scattering problem.     

Reflection and transmission of acoustic waves on multilayered porous media

Based on the Boit theory of acoustic wave propagation in fluid-satu-rated porous medium we have studied in this paper the acoustic reflection andtransmission on multilayered porous media,in which the adequate boundaryconditions across the interfaces are taken into account.Numerical calculationsof the reflection and transmission coefficients at different incident angles andfrequencies of the fast compressional wave incident on porous media with threeor four layers are presented.The results indicate that the maximum or mini-mum reflection and transmission coefficients appear at certain ratios of thewavelength to the thickness.The acoustic incident angle and porous mediumproperties are shown to affect significantly these coefficients.As an example,the measured transmission coefficients in a water-saturated fused glass beadsample are in good agreement with theoretical prediction.     

阻抗复合消声器声学性能有限元预测方法及分析

为计算和分析具有复杂结构的阻抗复合式消声器的宽频消声性能,建立了一种高效声学有限元方法,给出了不同边界条件下的边界积分处理细节,得到有限元全局系数矩阵表达式,设计出计算程序框架以实现这些算法,其求解规模和计算速度与商业软件相比有优势。为计算阻抗复合式消声器的传递损失,通过阻抗管测量和数据拟合得到了吸声材料声学特性的经验公式。计算和测量了两通穿孔阻抗复合式消声器的传递损失,二者良好的吻合验证了声学有限元方法和计算程序的正确性。研究表明,插管长度影响消声器在中高频段的消声特性,右侧隔板上穿孔会消除共振峰,中高频消声性能随着出口管穿孔率的增加而提升。     

北极跨冰层水中声源方位估计实验与分析

为了获取北极冰下声源方位信息,在北极冰层上方布放检波器和冰下投放声弹声源开展了冰下声源的分频段方位估计实验。研究结果表明,冰下声源方位估计的误差、准确率与检波器接收信号频段(或冰下声源信号频段)有关。采用低频段的接收信号进行方位估计时准确率较高,误差均值较小,所用接收信号频段≤250 Hz时,方位估计准确率可达72.9%;反之,采用高频段的接收信号进行方位估计时准确率低,误差均值较大。采用不同频段接收信号进行冰下声源方位估计时,误差大小与该站位相同频段内的反射系数的变化有关:反射系数变化较大时,误差较大;否则,误差较小。     

Sound transmission across orthotropic laminates with a 3D model

This investigation examines the propagation of elastic waves in orthotropic materials to explain the sound insulation of FRP (Fiber Reinforced Plastics). The mechanical characteristics of an orthotropic material generally require nine independent parameters: three Young’s moduli, three shear moduli and three Poisson’s ratios. Three-dimensional analysis is performed with the elastic wave equations of an orthotropic material. The transfer matrix method which expresses the relationship between stress and velocity is adopted to calculate the sound transmission loss across an orthotropic material. Further, the transfer matrix method can only be calculated under the continuous boundary condition in the interface of each FRP layer. The boundary conditions which are indicated above are velocity and stress. The numerical results are compared with the experimental results. Additionally, along with varying material properties such as Young’s modulus, the acoustical properties of the orthotropic material are explained and discussed later.     

Sound transmission loss across specially orthotropic laminates

This work studies the sound transmission loss across composite material in order to understand the sound-insulating capacity at various frequencies. A so-called specially orthotropic laminate was examined. The material properties in thickness direction are different from those in in-plane directions but it is isotropic in the laminating plane. Thus the specially orthotropic laminate can be analyzed by two-dimensional acoustic analysis. The sound transfer matrix of specially orthotropic single layer is determined by stress and velocity. The boundary conditions between different interface planes and the transfer matrix related to these conditions yield the mathematical model of the sound wave that propagates in composite materials. The experimental and numerical results of sound transmission loss are compared. Arrangement of various material properties and their sound penetrating characteristic were investigated and discussed.     

用传递矩阵法预测单层或多层微孔板的吸声性能

提出用实验测得含不同孔径孔的微孔板声阻抗率来预测由其形成的单层或多层微孔板的吸声特性，并用传递矩阵法来预测该微孔板的各种组合结构的整体吸声性能。采用该方法获得的微孔板吸声性能曲线与实测结果相当接近，能较好地预测各种组合微孔板的吸声性能。表明传递矩阵法是预测较复杂形式微孔板结构吸声性能的一种有效的方法。     

用路径积分方法研究势垒散射

本文利用量子力学路径积分的基本思想,严格导出单重势垒与双重势垒的反射系数和透射系数的解析表达式,为研究多重势垒量子阱结构的散射提供一种新的理论方法.     

Simple expressions of the reflection and transmission coefficients of fundamental Lamb waves by a rectangular notch

The scattering of Lamb waves by a two-dimensional rectangular notch is investigated for rapid inspection of defects in a structure. To derive the reflection and transmission coefficients of the scattered waves in a simple way, the scattering caused by the notch is analyzed through the composition of individual scattering processes. Linear equations corresponding to the reflection and transmission coefficients are constructed along with scattering graphs. For an illustration of the efficacy of the presented method, the scattering of fundamental symmetric and anti-symmetric modes are inspected according to the depth and width of a notch in a plate. Validity of these expressions is demonstrated by the comparison of the theoretical analysis results with those from the finite element analysis.     

Bounding the Bogoliubov coefficients

While over the last century or more considerable effort has been put into the problem of finding approximate solutions for wave equations in general, and quantum mechanical problems in particular, it appears that as yet relatively little work seems to have been put into the complementary problem of establishing rigourous bounds on the exact solutions. We have in mind either bounds on parametric amplification and the related quantum phenomenon of particle production (as encoded in the Bogoliubov coefficients), or bounds on transmission and reflection coefficients. Modifying and streamlining an approach developed by one of the present authors [M. Visser, Phys. Rev. A 59 (1999) 427-438, arXiv:quant-ph/9901030], we investigate this question by developing a formal but exact solution for the appropriate second-order linear ODE in terms of a time-ordered exponential of 2×2 matrices, then relating the Bogoliubov coefficients to certain invariants of this matrix. By bounding the matrix in an appropriate manner, we can thereby bound the Bogoliubov coefficients.