Formulation and validation of a Ritz-based analytical model of high-frequency periodically layered isolators in compression

Periodically layered isolators exhibit transmissibility “stop bands” or frequency ranges in which there is very low transmissibility. A two-dimensional axisymmetric model was developed to accurately predict the location of these stop bands for isolators in compression. A Ritz approximation method was used to model the axisymmetric elastic behavior of layered cylindrical isolators. A modal analysis was performed for a single elastomer and metal layer combination or cell. A modal synthesis approach was then used to obtain a model of an n-celled isolator, from which overall isolator modal properties are determined. This model of the dynamic behavior of layered isolators was validated with experiments. Analytical and experimental transmissibilities are compared for test specimens having identical elastomer components, but different geometries and different numbers of cells. In all cases, experimental and analytical transmissibilities are in close agreement at frequencies ranging from zero to those associated with the initial roll-off of the stop bands. For three and four cell cases, minimum stop band analytical transmissibilities lie below the minimum experimental measurements, although an experimental noise floor imposed a minimum transmissibility measurement of approximately 1.4×10⁻⁴. Experiment suggests a practical isolator design could limit the minimum number of cells to three or four to ensure a pronounced stop band attenuation effect. In addition, analytical and experimental transmissibilities are compared for geometrically similar test specimens with differing elastomeric damping properties. The analytical and experimental results show that stop band effectiveness is not appreciably affected by the addition of modest damping.     

Frequency average loss factors of plates and shells

This paper describes a thorough investigation of the measurement of frequency band average loss factors of structural components for use in the statistical energy analysis (SEA) method of computation of vibration levels. The “traditional” method of measurement is to excite the structure by a random force having a flat spectral density in the frequency band of interest. The force is then cut off and the decay of the modes excited in the band is noted. The average loss factor is deduced from the decay curve. The alternative energy method is the subject of this study. In this test the power input from the band limited random force is measured and the spatial average vibration level of the structure is estimated from several surface accelerometers. It is shown that when the modes in the band have similar loss factors (as is usually the case) the energy method gives a result which is very close to that obtained from the decay method. These in turn are close to the arithmetic average of the loss factors of the individual modes in the band. It is shown that only when the band contains one or two very lightly damped modes amongst several more heavily damped modes is there a difference between the two methods. In this case it is better to use the energy result in the SEA calculations.     

一个解决声纳系统同频干扰的新思路

多平台联合作战将是未来海上作战的重要形式之一,多部主动声纳的同时存在使声兼容问题十分突出。由于友舰直达波经历的是单程传播,其强度往往比经历了双程传播的目标回波大的多。通过波形设计可以获得相关系数小的声纳波形,虽然可以从一定程度上缓解声兼容问题,但由于获得的增益有限,并不能从根本上解决这一问题。本文通过对常规检测器的修正,引入能量归一化的概念,有效地消除了能量对检测器的影响,从而解决了这一问题。同时本文还提出了与现有声纳信号处理体系相兼容的频域实现方法,使该算法在工程上的实现成为可能。计算机仿真证明,这一方法是正确有效的。     

EVALUATING THE VIBRATION ISOLATION OF SOFT SEAT CUSHIONS USING AN ACTIVE ANTHROPODYNAMIC DUMMY

Seat test standards require human subjects to be used for measuring the vibration isolation of vehicle seats. Anthropodynamic dummies, based on passive mass-spring- damper systems, have been developed for testing seats but their performance has been limited at low excitation magnitudes by non-linear phenomena, such as friction in the mechanical components that provide damping. The use of an electrodynamic actuator to generate damping forces, controlled by feedback from acceleration and force transducers, may help to overcome these limitations and provide additional benefits. The transmissibilities of five foam cushions have been measured using an actively controlled anthropodynamic dummy, in which damping and spring forces were supplied by an electrodynamic actuator. The dummy could be set up to approximate alternative single-degree-of-freedom and two-degree-of-freedom apparent mass models of the seated human body by varying motion feedback parameters. Cushion transmissibilities were also measured with nine human subjects, having an average seated weight similar to the dummy. At frequencies greater than 4 Hz, mean cushion transmissibilities measured with subjects were in closer agreement with the transmissibilities obtained with a two degree-of-freedom dummy than with a single degree-of-freedom dummy. However, at frequencies between 2 and 4 Hz, cushion transmissibilities obtained with the two-degree-of-freedom dummy showed consistently larger differences from mean transmissibilities with subjects than single-degree-of-freedom dummies, indicating a need for further development of human apparent mass models to account for the effects of magnitude and spectral content of the input motion. Vertical vibration isolation efficiencies (SEAT values) of the five foams were measured with four input motions, including three motions measured in a car. The SEAT values obtained using the active dummy were highly correlated with the median SEAT values obtained with the nine human subjects, with the two-degree-of-freedom apparent mass dummy giving the highest agreement.     

Prediction of sound flanking transmission through two adjacent rooms within a residence building

Flanking transmission has significant effects on the overall sound insulation of two adjacent rooms within a residence building. This study investigates the mechanism of the sound flanking transmission by dividing it into several subsystems with the statistical energy analysis method. The sound energy equations of these subsystems are obtained first, and then,the sound transmissions on each flanking path are predicted and the dominant sound transmission path is determined by solving these equations and calculating the total loss factors of the subsystems and coupling loss factors between subsystems. With respect to a masonry building with heavy-weight homogeneous structure, the results show that:(1) the flanking transmission paths instead of the separating wall may become the dominant ones at low frequencies;(2) all sound transmissions on the flanking paths tend to be consistent at medium and high frequencies, so the sound insulation between two adjacent rooms depends on the direct path of the separating wall;(3) heavy-weight separating walls can be used to reduce the frequency range of the flanking transmission.     

直流老化对CaCu3Ti4O12陶瓷介电性能的影响

在电场为3.5 kV/cm的条件下, 对CaCu₃Ti₄O₁₂陶瓷进行了60 h的直流老化, 研究了老化过程对CaCu₃Ti₄O₁₂陶瓷介电性能和电气特性的影响. J-E特性测试结果表明, 直流老化导致CaCu₃Ti₄O₁₂陶瓷击穿场强、非线性系数和势垒高度明显降低. 介电性能测试结果表明, 低频介电常数和介电损耗明显增大, 并且介电损耗随频率的变化遵从Debye弛豫理论, 可分解为直流电导损耗和弛豫损耗, 直流老化主要导致了电导损耗的增加. 在低温233 K, 介电损耗谱中出现两个弛豫峰, 其活化能分别为0.10, 0.50 eV, 认为对应着晶粒和畴界的弛豫过程, 且不随直流老化而变化. 通过电模量谱对CaCu₃Ti₄O₁₂陶瓷的弛豫过程进行了表征, 发现直流老化导致的界面空间电荷在外施交变电场的作用下符合Maxwell-Wagner极化效应, 并在低频区形成新的弛豫峰. 在高温323-473 K的阻抗谱中, 晶界弛豫峰在直流老化后明显向高频移动, 其对应的活化能从1.23 eV 下降到0.72 eV, 晶界阻抗值下降了约两个数量级. 最后, 建立了CaCu₃Ti₄O₁₂陶瓷的阻容电路模型, 分析了介电弛豫过程与电性能之间的关联.     

双原子分子电子能量损失谱的解谱方法

介绍一种双原子分子电子能量损失谱的解谱方法,在利用已知的双原子分子光谱信息及理论计算的Franck-Condon(FC)因子的基础上,通过二次函数调整整个电子态振动强度的轮廓,减少拟合过程中的待定参数个数,降低对FC因子精确性的要求,提高拟合的精度和可信度.用Mathematica语言编写基于以上方法的数据处理程序,改进算法,提高了软件的运行效率.利用该软件处理氢分子的电子能量损失谱,得到氢分子不同电子态的振动跃迁的截面信息,所得结果与以前的实验结果符合很好.     

Corrected Statistical Energy Analysis Model in a Non-Reverberant Acoustic Space

Statistical Energy Analysis (SEA) is a well-known method to analyze the flow of acoustic and vibration energy in a complex structure. This study investigates the application of the corrected SEA model in a non-reverberant acoustic space where the direct field component from the sound source dominates the total sound field rather than a diffuse field in a reverberant space which the classical SEA model assumption is based on. A corrected SEA model is proposed where the direct field component in the energy is removed and the power injected in the subsystem considers only the remaining power after the loss at first reflection. Measurement was conducted in a box divided into two rooms separated by a partition with an opening where the condition of reverberant and non-reverberant can conveniently be controlled. In the case of a non-reverberant space where acoustic material was installed inside the wall of the experimental box, the signals are corrected by eliminating the direct field component in the measured impulse response. Using the corrected SEA model, comparison of the coupling loss factor (CLF) and damping loss factor (DLF) with the theory shows good agreement.     

A method for analyzing vibration power absorption density in human fingertip

In the current study, we hypothesize that the vibration power absorption density (VPAD) is a good measure for the vibration exposure intensity of the soft tissues of the fingers. In order to calculate the VPAD at a fingertip, we proposed a hybrid modeling approach, which combines a 2D finite element (FE) model with a lumped parameter model. Whereas the lumped components are used to represent the global biodynamic characteristics of the hand-arm system, the FE component is used to predict the detailed stresses, strains, and VPAD in the fingertip. The lumped parameters are determined by using the vibration transmissibilities measured at the fingertip, while the material parameters of the soft and hard tissues of the FE model are adopted from the published experimental data. The proposed model was applied to predict the distributions of dynamic displacement, velocity, and VPAD in the soft tissues of the fingertip. Furthermore, we have derived the frequency weighting based on the VPAD of the soft tissue. The preliminary analysis indicated that the VPAD-based frequency weighting is substantially different from the ISO weighting in that the ISO frequency weighting emphasizes the effect of the vibration at frequencies lower than 25 Hz whereas the VPAD-based weighting generally emphasizes the resonant responses of the finger. Our analysis indicated that the VPAD-based weighting was fairly consistent with the finger surface vibration transmissibility at frequencies greater than the first resonance, suggesting that the finger surface transmissibility may be used as an alternative frequency weighting for assessing the finger vibration exposure. The proposed method provides a practical and efficient tool to simulate the detailed biodynamic responses of a complex biological system to vibration.     

The thermal effects on high-frequency vibration of beams using energy flow analysis

In this paper, the energy flow analysis (EFA) method is developed to predict the high-frequency response of beams in a thermal environment, which is a topic of concern in aerospace and automotive industries. The temperature load applied on the structures can generate thermal stresses and change material properties. The wavenumber and group velocity associated with the in-plane axial force arising from thermal stresses are included in the derivation of the governing energy equation, and the input power is obtained from the derived effective bending stiffness. In addition, effect of temperature-dependent material properties is considered in the EFA model. To verify the proposed formulation, numerical simulations are performed for a pinned–pinned beam in a uniform thermal environment. The EFA results are compared with the modal solutions for various frequencies and damping loss factors, and good correlations are observed. The results show that the spatial distributions and levels of energy density can be affected by the thermal effects, and the vibration response of beams increases with temperature.     

Binding energy of metals in pseudo-ion approximation

On the basis of pseudopotential theory we obtain a simple expression for the interaction energy between ions in a metallic system replacing the ion form factor in the direct (Coulomb) interaction by the pseudo-ion form factor of the indirect (conduction mediated) interaction. This substitution can be justified for non-overlapping radially symmetric rigid ions. For the pseudo-ion form factor (which includes ionic and orthogonalization effects) a model function is proposed and the model parameters are determined for lithium, sodium, potassium, rubidium and aluminium by fitting to experimental phonon dispersion curves. Using these form factors and an appropriate dielectric function we proceed to calculate binding energies. One finds that the values obtained show a remarkable agreement with experimental results. This suggests that the proposed reduced expression for the interaction energy and its numerical determination from experimental phonon curves is a good approximation method in evaluating and understanding the binding energy of a metal.     

A new method for accurately determining the modal equivalent stiffness ratio of bonded piezoelectric structures

This paper describes new methods for measuring the modal equivalent stiffness ratios and modal electromechanical coupling coefficients of piezoelectric elements attached to a host structure such as a beam. Modal equivalent stiffness ratios and modal electromechanical coupling coefficients are essential for estimating the performance and determining an optimum design of active vibration control and passive vibration suppression systems that use piezoelectric elements. Accurate determination of these modal parameters is also useful for other systems including piezoelectric sensors and energy generators. This paper not only describes the measurement methods but also presents the theoretical formulations derived by taking into account the effect of adhesive bonds. The formulations in this paper demonstrate the necessity of experimental measurements and the accuracy enhancements that the theoretical estimations can provide. Conventional methods for obtaining the modal equivalent stiffness ratios are sensitive to measurement errors, which result in the loss of accuracy, rendering these methods unreliable for many practical applications. The proposed methods use an inductor instead of an open circuit to address the abovementioned issue and, thereby, provide significant improvement in the accuracy. Because the loss factors of the experimental apparatus tend to compromise the accuracy of the proposed methods, a method using a negative resistor is proposed, theoretically analyzed, and confirmed to eliminate some of the errors introduced by loss factors. The advantages of the proposed methods and the effectiveness of theoretical analysis, considering the effect of adhesive bonds, are verified experimentally.     

线耦合平板瞬态高频振动响应预报

提出了一种用于线耦合平板瞬态高频振动分析的预报方法.基于瞬态统计能量分析,从子系统能量平衡方程的动力学相似性,推导出了时域尺度变换法则:在时间尺度上进行缩尺变换,而损耗因子相应地成反比变换。在此基础上,针对线耦合平板的能量传递特点,导出了两种不同变换方式:一种对结构的材料参数进行变换,另一种对结构的几何参数进行变换。采用两种连接方式的线耦合平板模型对时域尺度变换方法进行数值验证,结果表明该方法能以较高的计算效率准确获得结构的瞬态高频振动响应。      

混合表面等离子体激元的纳米激光器设计

为了实现纳米激光器的性能优化,设计了一种基于纳米线、半圆形氟化镁、三角形空气槽和金属脊结构的纳米激光器模型。模型中耦合在低折射率电介质层中的SPP模式和纳米线波导可以在低折射率间隙下像电容器那样存储光能,从而使低折射率的空气槽场强明显增大。应用有限元法在COMSOL Multiphysics软件下,分析了该纳米激光器模型的电场分布、模式特性、品质因数和增益阈值随着设计结构几何参数变化的规律,通过各部分折线图的综合分析来得出模型性能的数据。分析表明：该模型的光场约束能力较强且传播损耗较低,其中归一化面积最小可达到0.004 8,有效传输损耗最小可达到0.002。波导模场区域和限制因素表明,该激光器模型可以实现输出光场的亚波长约束。该模型基本实现了低增益阈值、低传输损耗和高品质因数的要求。     

The effects of design modifications on the apparent coupling loss factors in SEA-like analysis

At high frequencies it is often desirable to describe the behaviour of a structure in terms of subsystem energies. The most important method used for high frequency analysis is statistical energy analysis (SEA). Recently, the frequency range in which finite element analysis is applied is being extended to higher frequencies resulting in SEA-like analysis. Methods such as energy distribution modelling can be used to obtain the matrix of energy influence coefficients (EICs); the EIC matrix can be inverted to estimate SEA-like “apparent” coupling loss factors (ACLFs). The ACLFs so estimated depend on details of global modal properties, especially at low and moderate modal overlap. This has implications for design modifications, for example by adding damping treatment to one subsystem, since generally all the EICs change and hence so do all the ACLFs. In principle a full re-analysis is required; this is in contrast to classical SEA. This paper describes these problems and their causes and approximations to the SEA-like parameters of the modified system are proposed. Estimates of the response of the structure after modifications can be found without full re-analysis, leading to a computationally efficient method. The case studies show good agreement between the estimates based on the proposed approaches and the ones based on full re-analysis. The net outcome is that the ACLFs can be estimated after the modification has been made in a manner similar to conventional SEA.     

The conduction electron hole coupling in beryllium metal

The 1s spectrum in beryllium metal and the plasmons accompanying it have been measured by the XPS method. The analysis shows that the plasmons are created with about equal probability by direct energy loss and by the conduction electron hole coupling.     

A novel approach to calculate inductance and analyze magnetic flux density of helical toroidal coil applicable to Superconducting Magnetic Energy Storage systems (SMES)

In this paper, formulas are proposed for the self and mutual inductance calculations of the helical toroidal coil (HTC) by the direct and indirect methods at superconductivity conditions. The direct method is based on the Neumann’s equation and the indirect approach is based on the toroidal and the poloidal components of the magnetic flux density. Numerical calculations show that the direct method is more accurate than the indirect approach at the expense of its longer computational time. Implementation of some engineering assumptions in the indirect method is shown to reduce the computational time without loss of accuracy. Comparison between the experimental measurements and simulated results for inductance, using the direct and the indirect methods indicates that the proposed formulas have high reliability. It is also shown that the self inductance and the mutual inductance could be calculated in the same way, provided that the radius of curvature is >0.4 of the minor radius, and that the definition of the geometric mean radius in the superconductivity conditions is used. Plotting contours for the magnetic flux density and the inductance show that the inductance formulas of helical toroidal coil could be used as the basis for coil optimal design. Optimization target functions such as maximization of the ratio of stored magnetic energy with respect to the volume of the toroid or the conductor’s mass, the elimination or the balance of stress in some coordinate directions, and the attenuation of leakage flux could be considered. The finite element (FE) approach is employed to present an algorithm to study the three-dimensional leakage flux distribution pattern of the coil and to draw the magnetic flux density lines of the HTC. The presented algorithm, due to its simplicity in analysis and ease of implementation of the non-symmetrical and three-dimensional objects, is advantageous to the commercial software such as ANSYS, MAXWELL, and FLUX. Finally, using the presented algorithm, magnetic flux density lines in several examples are drawn.     

Transmission loss of honeycomb sandwich structures with attached gas layers

Layering gasses of differing acoustic impedances on a panel substantially reduced the amount of sound energy transmitted through the panel with respect to the panel alone or an equivalent-thickness single species gas layer. The additional transmission loss derives from successive impedance mismatches at the interfaces between gas layers and the resulting inefficient energy transfer. Attachment of additional gas layers increased the transmission loss by as much as 17 dB at certain frequencies. The location and ordering of the gasses with respect to the panel were important factors in determining the magnitude of the total transmission loss. Theoretical analysis using a transfer matrix method was used to calculate the frequency dependence of sound transmission for the different configurations tested. The method accurately predicted the relative increases in transmission loss observed with the addition of different gas layer configurations.     

Dynamic analysis of a unidirectional periodic isolator,consisting of identical masses and intermediate distributed resilient blocks

An analytical procedure for the dynamic analysis of the unidirectional periodic isolator, consisting of n concentrated masses and n intermediate arbitrary blocks is developed. Complex polynomials depending on the four pole parameters of the mounts and on the frequency of excitation are introduced, to express analytical forms for the impedances and transmissibilities of the general system. By means of these polynomials, the frequency equation of the undamped isolator can be derived directly, for free or fixed boundary conditions. Application of the method was made with isolators consisting of masses and distributed elements of rubber with internal damping.