Transfer function method for investigating the complex modulus of acoustic materials: Rod-like specimen

The complex Young's modulus of acoustic materials as a function of frequency is generally investigated by using a cylindrical or prismatic specimen of the material excited into longitudinal harmonic vibration at one end, the other end being loaded by a mass. The transfer function method is the most advantageous to use for the investigation, which involves the measurement of the vibration amplitudes of the specimen ends and the phase angle between them. In this paper, the transfer function method is analyzed theoretically and experimentally in that frequency range where the specimen can essentially be modelled by a longitudinally vibrating rod (rod-like specimen). The analysis includes the measurability of the transfer function, the role of the measurement errors, the frequency range of the method and the maximum dynamic strain of the specimen. A special application of the method is developed for investigating the complex modulus of low loss materials at the extremes of the absolute value of the transfer function, without measuring the phase angle. Experimental results obtained by both methods are presented.     

Choice of thickness ratio of a coated beam used for investigating the complex modulus of viscoelastic materials

The coated beam method has been widely used for investigating the complex modulus of elasticity of relatively soft viscoelastic materials; e.g., materials for vibration damping. With this method a rectangular section metal beam is coated with the viscoelastic material on one side, or symmetrically on both sides, and the resonances of the bending vibration of the beam are investigated. In this paper a procedure is described for finding the ratio of coating thickness to metal thickness required to obtain accurate results for the complex modulus in such investigations. The contradiction experienced earlier—that a relatively large thickness ratio is required for precision while the nature of the resonance method is such as to demand a small one—is analyzed mathematically. The relationships derived serve as a basis for optimizing the choice of the ratio. Diagrams and a procedure for this are worked out and presented. Finally, a few experimental results obtained with suitable and unsuitable thickness ratios are discussed.     

A Green's function method for surface acoustic waves in functionally graded materials

Acoustic wave propagation in anisotropic media with one-dimensional inhomogeneity is discussed. Using a Green's function approach, the wave equation with inhomogeneous variation of elastic property and mass density is transformed into an integral equation, which is then solved numerically. The method is applied to find the dispersion relation of surface acoustic waves for a medium with continuously or discontinuously varying elastic property and mass density profiles.     

黏弹性吸声材料复弹性模量优化研究

针对黏弹性材料吸声效率问题,利用分层介质声传播理论和数值算法优化了不同物理条件下材料的复弹性模量。采用参数等效的方法分析了含气泡黏弹性材料的声学特性,并给出了此种材料优化后的弹性模量曲线。根据物理模型计算了一定边界条件下材料复弹性模量等吸声系数曲线,得到了几种背衬条件下黏弹性材料吸声系数大于0.8的弹性模量和损耗因子范围。研究表明调节黏弹性材料的复弹性模量可以有效提高材料的吸声性能,吸声系数大于0.8时其弹性模量和损耗因子范围在不同背衬条件下差异较大,发现一定厚度的钢背衬会降低调控复弹性模量的难度,对含气泡黏弹性材料的计算也可得到类似结果。     

A direct numerical simulation method for complex modulus of particle dispersions

We report an extension of the smoothed profile method (SPM) (Y. Nakayama, K. Kim, and R. Yamamoto, Eur. Phys. J. E 26, 361 (2008)), a direct numerical simulation method for calculating the complex modulus of the dispersion of particles, in which we introduce a temporally oscillatory external force into the system. The validity of the method was examined by evaluating the storage G’(w \omega) and loss G”(w \omega) moduli of a system composed of identical spherical particles dispersed in an incompressible Newtonian host fluid at volume fractions of F \Phi = 0 , 0.41, 0.46, and 0.51. The moduli were evaluated at several frequencies of shear flow; the shear flow used here has a zigzag profile, as is consistent with the usual periodic boundary conditions. The simulation results were compared with several experiments for colloidal dispersions of spherical particles.     

金属材料疲劳损伤检测的非线性声学方法*

金属材料的疲劳损伤有前期、后期两个阶段,前期疲劳损伤主要来源于位错,而随着疲劳程度的不断加深,位错密度也不断的增加,这将导致疲劳后期微裂纹的产生。这两个阶段产生声学非线性效应的机理不同,分别用位错模型、微裂纹模型对其产生非线性效应的机理进行了阐述,并对不同阶段的疲劳试样进行了相关实验研究。实验结果表明:对于材料早期疲劳损伤,随着疲劳程度的增加,其接收声波信号中的非线性谐波成分越来越显著,并且随着激励电压的增加,非线性效应更加明显,因此可用接收信号中的谐波激发情况来评估材料的早期疲劳损伤程度。而对于材料疲劳后期出现微裂纹后,其产生的非线性与早期疲劳损伤相比,谐波成分更加丰富,并且随激励电压的增加谐波幅度增加明显,可据此来判断材料中的疲劳损伤阶段。     

“舌簧片振动法”测杨氏模量

对材料的杨氏模量的测定历来是研究材料的力学性质以及结构的重要手段,因此,实验科学工作者在不断地探索用各种不同的实验方法来测量材料的杨氏模量,本文介绍国外（日本）常用的一种测量的方法－舌簧片振动法。     

水声构件材料动态切变模量测量方法研究

阐述了一种新的水声构件材料动态切变模量测量方法,该方法利用宽带参量声源、精密坐标装置和信号处理技术,在小型消声水槽中可以准确测量频率范围20~100kHz、典型尺寸500×500mm²材料样品的动态切变模量。文中先后介绍了测量基本原理、实验装置,给出并分析了测量结果。     

A mixed method for measuring low-frequency acoustic properties of macromolecular materials

A mixed method for measuring low-frequency acoustic properties of macromolecular materials is presented. The dynamic mechanical parameters of materials are first measured by using Dynamic Mechanical Thermal Apparatus(DMTA) at low frequencies, usually less than 100 Hz; then based on the Principles of Time-Temperature Superposition (TTS), these parameters are extended to the frequency range that acousticians are concerned about, usually from hundreds to thousands of hertz; finally the extended dynamic mechanical parameters are transformed into acoustic parameters with the help of acoustic measurement and inverse analysis. To test the feasibility and accuracy, we measure a kind of rubber sample in DMTA and acquire the basic acoustic parameters of the sample by using this method. While applying the basic parameters to calculating characteristics of the sample in acoustic pipe, a reasonable agreement of sound absorption coefficients is obtained between the calculations and measurements in the acoustic pipe.     

水声无源材料插入损失虚拟聚焦测量方法

提出了一种适合在有限尺寸水池中测量水声材料插入损失的方法,称为\     

水声材料性能的自由场宽带压缩脉冲叠加法测量

水声材料的许多声学特性一般可以通过对复反射系数和透射系数计算得到。本文提出一种新的自由场测量方法,即应用宽带脉冲压缩技术在消声水池中测量有限尺寸的大面积材料样品的性能参数,从而使这种标准测量的低频限被明显降低。除传统的回声降低和插入损失参数等外,两个新的参数——消声系数和去耦系数也在评价之列。文中对两块平板样品进行了实验测量,其尺寸约为1m×1m,测量频率范围为 2~20kHz。     

Bacterial luminescence: a new tool for investigating the effects of acoustic energy and cavitation

An assay utilizing luminescent bacteria, Photobacterium phosphoreum, was adapted to assess the antibacterial effects of acoustic energy. Acoustic pressures up to 67 kPa in the 100- to 800-Hz frequency range were applied to bacteria freely suspended in a liquid medium. Bacterial luminescence decreased after sonication, thus showing sensitivity to the effects of acoustic energy. This decreased luminescence was linearly related to exposure duration, appeared independent of acoustic frequency in this range, and was significantly heightened by the presence of cavitation. High-frequency components of the acoustic emission were recorded from the sonicated fluid, and it was found that the decrease in luminescence due to sonication was directly related to the logarithm of the acoustic emission. Viability studies on exposed bacteria indicated a diminution of luminescence without bacterial death. The potential use of luminescent bacteria in assessing the biological effects of acoustic energy-generating systems is discussed.     

复杂地层声波测井时差处理方法研究

在复杂地层(如砂-泥岩薄互层)的声波测井中,由于地层声速变化及界面反射波叠加干扰,导致不同接收器的地层纵波波形幅度差异明显,且相关性很差,使得提取的时差误差较大。这一声场特征可从薄互层声波测井的有限差分数值模拟中看到。针对这一现象,本文利用频率-波数域相关滤波处理技术来消除薄互层声波测井的界面反射干扰,以改善地层纵波波形的相关性。本文给出了砂-泥岩薄互层数字声波测井的现场资料处理实例,处理结果证明了该方法有效地消除了界面反射波的干扰,明显改善了地层纵波的相关性,提高了地层纵波时差曲线的分辨率,清晰地刻画出了薄互层特征。     

水声材料插入损失测量中的声波多途效应抑制方法

提出了一种在非自由声场中测量水声材料插入损失时抑制多途效应的方法,称为\     

A restraining multipath effect method for the measurement of insertion loss of underwater acoustic materials

A method suppressing multipath effect when measuring the underwater acoustic materials in a reverberant field is proposed, which is called "virtual end-fire array method".To weaken the coherence of the same-frequency reflection interference of each path, signal of different phases at different positions was transmitted by a single transducer in the simulation design, and a sharp directionality in the direction of the array length was formed. All signals at the above positions were superimposed t...     

An efficient method for evaluation of the complex probability function: The Voigt function and its derivatives

An efficient method is developed to evaluate the function w(z)=e^-z2(1+(2i/√π)∫^z₀e^t2dt) for the complex argument z = x + iy. The real part of w(z) is the Voigt function describing spectral line profiles; the imaginary part can be used to compute derivatives of the spectral line shapes, which are useful, e.g. in least-squares fitting procedures. As an example of the method a simple and fast FORTRAN subroutine is listed in the Appendix from which w(z) in the entire y ? 0 half-plane can be calculated, the maximum relative error being less than 2 × 10^-6 and 5 × 10^-6 for the real and imaginary parts, respectively.     

Determination of solid materials rigidity modulus by a new nondestructive optical method

We propose a new optical method for the determination of the rigidity modulus G of solid materials. The rigidity modulus is determined by measuring the twisted angle θ as a response of the material sample, depending on the applied force. The measuring of this twisted angle can be carried out by using an adapted polarimetric sensor. The effective measurement of rigidity modulus G for aluminum, Plexiglas and steel was experimentally obtained 1.4464×10¹⁰,0.99417×10⁹ and 1.0395×10¹¹ N m, respectively. The study has demonstrated the effective usefulness of our method for evaluating the rigidity modulus. A good agreement between the theoretical and experimental results was achieved.