混合压电分流电路作用下声子晶体杆振动带隙结构分析

对于电阻电感(RL)及负阻抗变换器(NIC)混合压电分流电路分别采用紧密及间隔排列方式进行带隙结构计算,并且针对分流电路中电阻、电感及电容对于局域共振带隙的影响进行研究。采用传递矩阵法建立了压电分流电路作用下声子晶体杆带隙分析的理论模型,并运用MATLAB语言对带隙结构进行编程仿真计算。通过电阻、电感、电容参数的匹配及电路不同排列方式的对比,最终得到了在混合间隔压电分流电路作用下宽度为13 kHz的带隙,并对振动控制系统稳定性进行了分析。研究结果表明:采用混合压电分流电路会对杆件带隙结果产生影响,且采用压电片间隔排列的方式会使带隙宽度明显扩大。      

LCR分流电路下压电声子晶体智能材料的带隙

将带有LCR分流电路的压电陶瓷片对贴在铝和环氧树脂组成的声子晶体结构中.使智能材料的机械振动与压电陶瓷的压电效应耦合起来,推导出机械振动在压电陶瓷片上的等效附加应力;使LCR分流电路中的电磁振荡效应和声子晶体的能带特性有机结合,计算了在分流电路作用下智能材料扭转和弯曲振动的带隙特性,研究了电阻、电感、电容元件的改变对压电声子晶体智能材料带隙的影响.研究结果表明:在合理尺寸下,随着分流电路中电阻值的增大,带隙的频率范围变宽,但衰减幅值有所降低;电感和电容值的增大都可以使带隙向低频移动,带隙的衰减幅值随着电感值的增大而升高,但随着电容值的增大而降低.从而给压电声子晶体智能材料减震降噪的控制提供了一种新思路.     

Band gap structure analysis of phononic crystal rods with hybrid shunted piezoelectric patches

The band gap structures by arranging hybrid shunted piezoelectric materialswith resistance inductive(RL) circuit and negative impedance converter(NIC) closely and at intervals are presented.The theoretical model is built using transfer matrix method.Then the MATLAB computing language is utilized to simulate the band gap structures.Meanwhile,the effects of the resistance,inductance and capacitance on the local resonant gap are studied.By comparing different combinations of resistance,inductance and capacitance as well as different arrangement of circuits,a 13 kHz band gap is reached under the effect of arranging hybrid periodic shunted piezoelectric patches at intervals and the stability of the system is also analyzed.It is proved that utilizing hybrid shunted piezoelectric patches would have a clear impact on the band gap structure of phononic crystal rods.Moreover,the band gap would be clearly enlarged by arranging hybrid piezoelectric patches at intervals.     

Singular variation property of elastic constants of piezoelectric ceramics shunted to negative capacitance

Piezoelectric shunt damping has been widely used in vibration suppression, sound absorption, noise elimination, etc.In such applications, the variant elastic constants of piezoelectric materials are the essential parameters that determine the performances of the systems, when piezoelectric materials are shunted to normal electrical elements, i.e., resistance,inductance and capacitance, as well as their combinations. In recent years, many researches have demonstrated that the wideband sound absorption or vibration suppression can be realized with piezoelectric materials shunted to negative capacitance. However, most systems using the negative-capacitance shunt circuits show their instabilities in the optimal condition, which are essentially caused by the singular variation properties of elastic constants of piezoelectric materials when shunted to negative capacitance. This paper aims at investigating the effects of negative-capacitance shunt circuits on elastic constants of a piezoelectric ceramic plate through theoretical analyses and experiments, which gives an rational explanation for why negative capacitance shunt circuit is prone to make structure instable. First, the relationships between the elastic constants c_(11), c_(33), c_(55) of the piezoelectric ceramic and the shunt negative capacitance are derived with the piezoelectric constitutive law theoretically. Then, an experimental setup is established to verify the theoretical results through observing the change of elastic constant c_(55) of the shunted piezoelectric plate with the variation of negative capacitance.The experimental results are in good agreement with the theoretical analyses, which reveals that the instability of the shunt damping system is essentially caused by the singular variation property of the elastic constants of piezoelectric material shunted to negative capacitance.     

Peculiar transmission property of acoustic waves in a one-dimensional layered phononic crystal

In this article, we report both theoretical calculation and experimental observation of acoustic waves abnormally through a one-dimensional layered transmitted phononic crystal at frequencies within the band gap into a material of large acoustic impedance mismatch, with an efficiency as high as unity. The transmission peaks can be interpreted as a result of the interference of acoustic waves reflected from all periodically aligned interfaces. The condition for the appearance of peaks is analyzed in detail and the optimized layer number is given for different configurations.     

声波在二维固/流声子晶体中的禁带特性研究

采用时域有限差分法(FDTD),分析了声波在二维四方点阵铝/空气组合声子晶体中的禁带特性,并利用实验测试验证了理论分析的正确性.在此基础上研究了两种不同声阻抗率比固(实心圆柱和空心圆管)/流系统声子晶体的禁带特性.对于实心圆柱体,分析了有限尺寸结构声子晶体在传播方向上的层数对声波传播特性的影响,得到了这两种系统在不同填充率下取得最大声波禁带宽度所需的最少层数.同时指出,在低声阻抗率比条件下,对于空心圆管填充物,通过选取适当的半径比,可以获得比实心柱体更宽的方向带隙.     

内插扩张室声子晶体管路带隙特性研究

声子晶体管路的带隙特性,可以实现管路系统在特定频率下的噪声控制.利用二维模态匹配法推导出单个内插扩张室元胞的传递矩阵,结合Bloch定理,得到声子晶体管路的能带结构计算方法;验证了二维方法在计算能带结构时的准确性.研究发现,内插扩张室声子晶体管路存在布拉格带隙和局域共振带隙.进一步研究了晶格常数以及内插管长度对能带结构的影响,结果表明,晶格常数主要控制布拉格带隙,而内插管长度对局域共振带隙有较大的影响,并研究了两种参数变化下的带隙耦合.研究结果可以为管路降噪设计提供新的思路.     

Band structures of two dimensional solid/air hierarchical phononic crystals

The hierarchical phononic crystals to be considered show a two-order “hierarchical” feature, which consists of square array arranged macroscopic periodic unit cells with each unit cell itself including four sub-units. Propagation of acoustic wave in such two dimensional solid/air phononic crystals is investigated by the finite element method (FEM) with the Bloch theory. Their band structure, wave filtering property, and the physical mechanism responsible for the broadened band gap are explored. The corresponding ordinary phononic crystal without hierarchical feature is used for comparison. Obtained results show that the solid/air hierarchical phononic crystals possess tunable outstanding band gap features, which are favorable for applications such as sound insulation and vibration attenuation.     

基于Timoshenko梁模型的周期充液管路弯曲振动带隙特性和传输特性

充液管路的固液耦合振动广泛存在于各种工程领域中,对其弯曲振动控制进行研究具有重要意义.将声子晶体的周期性思想引入到管路结构设计中,将管壁设计成沿轴向交替排列的周期性复合结构.基于Timoshenko梁模型,采用传递矩阵法计算了固液耦合条件下周期管路结构的弯曲振动能带结构及其传输特性,同时分析了材料阻尼系数、周期和非周期支撑对带隙特性的影响.充液周期管路结构的弯曲振动带隙特性为管路的振动控制提供了一条新的技术途径. 关键词： 声子晶体 充液管路 振动带隙     

径向声子晶体隔声特性*

该文构造了由两种匀质材料交替分布的径向声子晶体柱壳模型。首先,针对声波在其中的轴对称传播情况进行了理论分析,建立了声波由内向外传播的传递矩阵,进而导出了声压透射系数和隔声量表达式。采用数值分析的方法系统地讨论了径向声子晶体柱壳的隔声特性,并与单一材质柱壳的传播规律进行对比分析,其次,借助有限元仿真分析的手段对数值结果进行了验证。最后,详细分析了内外流体的特性阻抗对径向声子晶体柱壳隔声特性的影响,得到了相应的参数影响规律。研究表明,径向声子晶体柱壳存在声波带隙,导致其在带隙范围内的隔声效果远远优于单材质柱壳,并且该结构的固有特性突破了质量定律的限制;声波带隙内表面局域态现象出现与否由内外声场和结构场共同决定。     

Ultra-Wideband Wave Reactances of Capacitive Grids

The accuracy of transmission line models of two-dimensional freestanding capacitive grids is studied on a very wide frequency band. The grids are of infinite extent in the transverse directions and are illuminated by a linearly polarized normally incident plane wave. Comparison with reference results deduced from Finite-Difference Time-Domain (FDTD) simulations allows determining the range of validity of commonly used equivalent circuits It is shown that their accuracy strongly depends on the dimensions of the grids and the operating wavelength. Although very convenient, their implementation for calculating the frequency response of multi-layer systems could lead to unreliable results. Two closed-form new models are thus proposed. The first one results from an optimized expression of the well-known Marcuvitz's impedance, and the second one involves a series resonant LC circuit shunted by an additional capacitance. Both formulations are very accurate for a wide range of grid geometries and over the whole visible region (wavelength > grid constant).     

Simplified Estimation of Critical Quantities for Short-Line Fault Interruption

From analyses of equations derived in a previous paper for critical interrupting conditions for an arc shunted by both resistance and capacitance in parallel, or for short-line fault interruption with capacitance shunting, further analytical expressions useful for prediction of limiting conditions are derived. Examples, based on observed relations of Cassie-Mayr arc model parameters to current rate of change for a particular SF6 blast circuit breaker, show realistic plots of limiting short-line fault currents versus line length with capacitance shunting. Also shown are required capacitance shunt values as functions of busfault current, fault fraction, line length, and number of series breaks. Included in the equations are circuit voltage and frequency and line surge impedance. Finally, it is shown that similar relations can be derived by using an approach suggested by A. M. Cassie in 1939.     

Enhancement of phononic band gaps in ternary/binary structure

Based on the transfer matrix method (TMM) and Bloch theory, the interaction of elastic waves (normal incidence) with 1D phononic crystal had been studied. The transfer matrix method was obtained for both longitudinal and transverse waves by applying the continuity conditions between the consecutive unit cells. Dispersion relations are calculated and plotted for both binary and ternary structures. Also we have investigated the corresponding effects on the band gaps values for the two types of phononic crystals. Furthermore, it can be observed that the complete band gaps are located in the common frequency stop-band regions. Numerical simulations are performed to investigate the effect of different thickness ratios inside each unit cell on the band gap values, as well as unit cells thickness on the central band gap frequency. These phononic band gap materials can be used as a filter for elastic waves at different frequencies values.     

平板二维声子晶体声波能带结构研究

利用超元胞法,研究由钢板上生长有限长度的钢柱体形成的散射体嵌入环氧树脂基体中所构成的平板二维声子晶体的声波能带结构,分析散射体的几何参数如柱体的高、半径和板的厚度对声波带隙的影响。研究结果表明:(1)这种新型的声子晶体具有很宽的带隙,且带隙出现在低频范围内;(2)散射体的几何参数对带隙的宽度有很大的影响,它们是控制带隙宽度的主要因素。     

Focusing of sound in a 3D phononic crystal

We present a combined experimental and theoretical study of phonon focusing phenomena in a pass band above the complete band gap in a 3D phononic crystal. Wave propagation was found to depend dramatically on both frequency and incident direction. This propagation anisotropy leads to very large negative refraction, which can be used to focus a diverging ultrasonic beam into a narrow focal spot with a large focal depth. The experimental field patterns are well explained using a Fourier imaging technique, based on the 3D equifrequency surfaces calculated from multiple scattering theory.     

A novel multimode negative inductance negative resistance shunted electromagnetic damping and its application on a cantilever plate

Based on the characteristic of the electromagnetic damping, a novel multimode vibration control treatment, negative inductance negative resistance electromagnetic shunt damping (NINR-EMSD), is proposed and employed to control multimode vibration of a cantilever plate. The negative inductance of the shunt impedance can cancel the inherent inductance of the electromagnet, and the impedance of circuit consisted of the coils and shunt will be a pure resistance and the shunt current will be frequency independent when the inductance of the shunt and the electromagnet are equal with each other. The negative resistance cancels the resistance of electromagnet, and as a result the resistance and the current of the closed circuit will change, which make it feasible to control the multimode vibration of the system. Electromechanical coupling coefficient is obtained based on the equivalent current method. The governing equation of the plate with the electromagnetic shunt damping (EMSD) is established according to Hamilton's principle. Multimode vibration control of the system is simulated and experiments are carried out to verify the performance of the NINR-EMSD. The numerical predictions and experimental results agree well with each other and show that: the negative inductance negative resistance (NINR) of the shunt impedance can increase the damping of the structure notably; the decrease of the resistance of shunt impedance have a significant contribution to the improvement of vibration control performance; the first four modes vibration of the plate can be suppressed simultaneously with the NINR-EMSD.     

负载不匹配对大功率速调管输出特性的影响

 采用微波等效电路和3维电磁场计算软件研究了负载不匹配对大功率速调管输出腔的谐振频率、间隙阻抗和外观品质因数的影响。并采用1维大信号计算软件研究了负载不匹配对速调管效率的影响。对C波段速调管的研究表明：对于单间隙输出腔,负载不匹配对谐振频率影响较小,对间隙阻抗和等效外观品质因子影响较大,当负载驻波比为1.5时,谐振腔的谐振频率变化约35 MHz,间隙阻抗实部最大值变化为3 660~7 998 Ω,等效外观品质因子变化为36.9~93.5,中心频率处的效率下降4.6%。对于滤波器加载输出电路,负载不匹配对阻抗-频率特性和效率-频率特性有较大影响,当负载驻波比为1.5时,中心频率处的效率下降11.2%。当负载驻波比小于1.2时,负载失配对速调管性能的影响较小。     

A multiple degree of freedom electromechanical Helmholtz resonator

The development of a tunable, multiple degree of freedom (MDOF) electromechanical Helmholtz resonator (EMHR) is presented. An EMHR consists of an orifice, backing cavity, and a compliant piezoelectric composite diaphragm. Electromechanical tuning of the acoustic impedance is achieved via passive electrical networks shunted across the piezoceramic. For resistive and capacitive loads, the EMHR is a 2DOF system possessing one acoustic and one mechanical DOF. When inductive ladder networks are employed, multiple electrical DOF are added. The dynamics of the multi-energy domain system are modeled using lumped elements and are represented in an equivalent electrical circuit, which is used to analyze the tunable acoustic input impedance of the EMHR. The two-microphone method is used to measure the acoustic impedance of two EMHR designs with a variety of resistive, capacitive, and inductive shunts. For the first design, the data demonstrate that the tuning range of the second resonant frequency for an EMHR with non-inductive shunts is limited by short- and open-circuit conditions, while an inductive shunt results in a 3DOF system possessing an enhanced tuning range. The second design achieves stronger coupling between the Helmholtz resonator and the piezoelectric backplate, and both resonant frequencies can be tuned with different non-inductive loads.     

测量强流电子加速器输出电压的电容分压器

研制了一种结构简单、拆装方便的自积分电容分压器,用于测量强流电子加速器二极管输出电压。介绍了电容分压器的结构,计算了其电容量,并通过仿真的方法分析了前端电阻及其杂散参数对测量波形的影响,结果表明:当前端电阻杂散电容较大时,测量波形出现过冲现象;而前端电阻对地电容较大时,会影响测量波形的前沿。将电容分压器用于测量强流电子加速器二极管输出电压,并运用水电阻分压器对其进行了标定,所测得波形与电阻分压器基本一致,分压比为563 007,可以用于测量半高宽为100 ns的高压脉冲。     

Enhanced plane wave expansion analysis for the band structure of bulk modes in two-dimensional high-contrast solid–solid phononic crystals

Plane wave expansion analyses that use the inverse rule to obtain the Fourier coefficients of the elastic tensor instead of the more conventional Laurent's rule, exhibit faster convergence rates for solid–solid phononic crystals. In this work, the band structure convergence of calculations using the inverse rule is investigated and applied to the case of high acoustic impedance contrast solid–solid phononic crystals, previously known for convergence difficulties. Results are contrasted to those obtained with the conventional plane wave expansion method. The inverse rule is found to converge at a much rate for all ranges of impedance contrast, and the ratio between the computational times needed to obtain a convergent band structure for a high-contrast solid–solid phononic crystal with the conventional plane wave expansion method using 1369 reciprocal lattice vectors is as large as 6800:1. This ratio decreases for material sets with lower impedance contrast; however, the inverse rule is still faster for a given error threshold for even the lowest impedance contrast phononic crystals reported in the literature. This convergence enhancement is a major factor in reconsidering the plane wave expansion method as an important tool in obtaining propagating elastic modes in phononic crystals.