利用声辐射模态对声场进行重构

声辐射模态是定义在振动表面上的一组互相独立的基函数,描绘了振动表面的多极子辐射模式。本文利用声辐射模态对平板辐射的声场进行重构，并同时就频率和模态数对误差的影响进行了分析。针对复杂振动表面幅射的声场，重构时需正则化处理。数值计算结果和对应的理论值达到很好的吻合。     

结构声辐射的振动模态分析和声辐射模态分析研究

基于辐射声功率的二次型表达式,采用有限元法、Rayleigh积分和边界元法对结构声辐射进行了振动模态分析和声辐射模态分析研究。振动模态间的耦合对辐射声功率影响的研究表明:结构各阶振动模态自身对结构辐射声功率的贡献是增大结构的辐射声功率,而振动模态间的耦合可能会增大结构辐射声功率,也可能会减小结构辐射声功率,或对辐射声功率没有影响。而且,当振动模态间的耦合作用对辐射声功率的影响不大时,采用振动模态控制可取得较好的减振降噪双重控制效果。将混合的Helmholtz积分方程方法用广义逆引入到三维复杂结构声辐射分析的声辐射模态公式中,解决了特征频率下解不唯一问题。还研究了正方形封闭空间结构声辐射模态的辐射效率和形状,并对结构声辐射的振动模态控制和声辐射模态控制进行了讨论。     

复杂结构声辐射模态的计算

结构辐射阻矩阵的特征向量就是其声辐射模态,复杂结构的辐射阻矩阵获取困难阻碍了声辐射模态理论的进一步应用。为此提出一种基于等效源方法的复杂结构辐射阻矩阵计算方法,由此形成了一套完整的计算复杂结构声辐射模态方法。最后通过仿真算例对影响结构辐射阻矩阵计算精度的因素进行了分析,给出了复杂结构辐射阻矩阵构造的一般原则。理论推导和数值仿真算例表明所提出的复杂结构声辐射模态计算方法是有效的。该方法简化了复杂结构声辐射模态的计算,计算效率较高。     

基于声辐射模态讨论声能量辐射与传递

声辐射模态表示了振动声源表面的辐射模式。基于声辐射模态讨论了振动声源表面声能量辐射和声场中声能量传递的性质,给出声能量辐射和传递的模式。采用表面声强描述振动声源表面的声能量辐射,采用声强描述声能量在声场中的传递。表面声强和声强可分解成两部分,一部分将辐射的声能量传递到远场;另一部分表现为振动声源与声场之间的能量交换。针对矩形板分析了声能量辐射和传递,数值计算结果与理论结果一致。结果表明基于声辐射模态讨论声能量辐射与传递是可行的和有效的。     

On the contribution of circumferential resonance modes in acoustic radiation force experienced by cylindrical shells

A body insonified by a constant (time-varying) intensity sound field is known to experience a steady (oscillatory) force that is called the steady-state (dynamic) acoustic radiation force. Using the classical resonance scattering theorem (RST) which suggests the scattered field as a superposition of a resonance field and a background (non-resonance) component, we show that the radiation force acting on a cylindrical shell may be synthesized as a composition of three components: background part, resonance part and their interaction. The background component reveals the pure geometrical reflection effects and illustrates a regular behavior with respect to frequency, while the others demonstrate a singular behavior near the resonance frequencies. The results illustrate that the resonance effects associated to partial waves can be isolated by the subtraction of the background component from the total (steady-state or dynamic) radiation force function (i.e., residue component). In the case of steady-state radiation force, the components are exerted on the body as static forces. For the case of oscillatory amplitude excitation, the components are exerted at the modulation frequency with frequency-dependant phase shifts. The results demonstrate the dominant contribution of the non-resonance component of dynamic radiation force at high frequencies with respect to the residue component, which offers the potential application of ultrasound stimulated vibro-acoustic spectroscopy technique in low frequency resonance spectroscopy purposes. Furthermore, the proposed formulation may be useful essentially due to its intrinsic value in physical acoustics. In addition, it may unveil the contribution of resonance modes in the dynamic radiation force experienced by the cylindrical objects and its underlying physics.     

通过声辐射模态研究结构声辐射的有源控制

以简支平板为例,通过声辐射模态建立了弹性结构声辐射的有源主动控制策略。并分析了声辐射模态的数学和物理意义。研究发现在中、低频时,声辐射模态对应的辐射效率随着模态阶数的增加而迅速降低。在此基础上,本文提出了一种新的控制策略,即抵消前k阶声辐射模态的伴随系数,使得前k阶声辐射模态的声功率为零。本文以点力作动器作为控制力源进行了数值计算研究。     

The relationship between acoustic radiation modes and structural modes and its applications

Both acoustic radiation modes and structural modes play an important role in the field of structure-borne sound, however, little work has been done for inherent relations between these two kinds of modes. This paper is focused on the relationship between the radiation modes and structural modes and its physical mechanisms. First, a governing equation for relating the radiation mode and structural mode is given based on the characteristics of the modes. Then, using the symmetric or anti-symmetric properties of two kinds of modes, the corresponding relations are presented. And then, numerical examples are given to verify the theoretical investigations, and it has been shown that, for a simply supported rectangular panel vibrating at low frequencies, the first radiation mode is dominant corresponding to (odd, odd) structural modes; the following radiation modes are respectively dominant corresponding to (even, odd), (odd, even), and (even, even) structural modes. Finally, such relations are applied to active acoustic structural control and provide a direct help for the design of active control strategy and arrangement of the secondary forces.     

结构振动模态和声辐射模态之间的对应关系及其应用

声辐射模态和结构振动模态之间的内在关系一直缺乏有效的证明。该文证明并揭示了结构振动模态和声辐射模态之间的对应关系,而且对该关系的有效性和实用性进行了验证。首先从声辐射模态和振动模态的概念出发,利用结构振速的模态叠加特性,建立了两种模态之间的联系方程式;在此基础上根据各种模态形状的对称或反对称性推导出两种模态之间的对应关系;然后对其进行了数值仿真验证。研究表明:对于简支矩形平板而言,在低频范围内,奇-奇振动模态对应的主导声辐射模态是第1阶;偶-奇模态对应第2阶;奇-偶模态对应第3阶;偶-偶模态对应第4阶。最后将这种对应关系应用于结构声辐射有源控制中,通过对主导声辐射模态进行抵消,取得了很好的控制效果。     

一种辐射零点可控的紧凑型滤波贴片天线

提出了一种辐射零点可控的紧凑型滤波贴片天线。该滤波天线以基本的微带贴片天线为原型,主要由一个简单的金属辐射贴片和两个对称的分割形槽组成。两个分割形槽蚀刻在金属贴片上,使得高/低频段分别产生两个宽边辐射零点,从而引入滤波选频功能。该结构未引入额外滤波电路和其他寄生单元,节省了空间尺寸,结构更加紧凑;两个辐射零点独立可控,提高了设计的灵活度。且在实现滤波选频功能的同时,对天线增益的影响很小。利用HFSS仿真软件优化滤波天线结构,制作了一个实物模型并进行了测试。测试结果与仿真结果基本一致。测试结果表明,提出的滤波天线工作在2.40 GHz,两个独立可控的辐射零点分别位于1.96 GHz和2.66 GHz,平均实际增益约为7.0 dBi,带外抑制水平超过39 dB。     

声场重构的声辐射模态阶数分析

利用声辐射模态法对椭球状声源辐射声场进行重构,分析了模态阶数对相对误差的影响,以及模态阶数与频率的关系;同时深入探讨了声源形状变化对模态阶数选取的影响。研究发现利用较少的模态阶数即可得到很好的重构效果,且声源形状的变化对重构所需模态阶数的影响较小,因此可将该方法用于任意形状声源的重构,体现了此方法在声场重构中的优越性。     

利用源强密度声辐射模态重建声场

为了利用声场中少量测点声压数据精确重建复杂结构的辐射声场,提出了源强密度声辐射模态分析理论和声场重建公式.在结构表面定义的空间上,利用以源强密度分布函数为参量的结构辐射声功率泛函表达式定义了一个线性自伴正辐射算子,该算子的特征函数为结构的源强密度声辐射模态.然后通过对矩形平板和带有半球帽的圆柱体的源强密度声辐射模态的分析,证明了源强密度声辐射模态具有空间滤波特性,并利用该性质建立了声场重建公式.球体仿真和平板实验验证了所提出的声场重建方法的可行性和稳健性.基于源强密度声辐射模态的声场重建方法简单,利用较少测点数据就可以获得较高的声场重建精度,特别适合于复杂结构的低频声场重建.     

声辐射模态和球谐波函数在球源声场重建中的比较

声辐射模态和球谐波函数在球源声场重建中均有应用,两者具有很多相似性,都具有相同的多极子辐射模式和\     

Study of acoustic field modulation in the regenerator by double loudspeakers method

A model to modulate acoustic field in a regenerator of a thermoacoustic system by the double loudspeakers method is presented in this paper. The equations are derived for acoustic field modulation. They represent the relations among acoustic field (complex pressure p(0), complex velocity u(0), and acoustic impedance Z(0)), driving parameters of loudspeakers (voltage amplitude and its phase difference), and operating parameters involved in a matrix H (frequency, temperature of regenerator). The range of acoustic field is adjustable and limited by the maximal driving voltages of loudspeakers according to driving parameters. The range is simulated and analyzed in the amplitude-phase and complex coordinate planes for a given or variable H. The simulated results indicate that the range has its intrinsic characteristics. The expected acoustic field in a regenerator can be obtained feasibly by the modulation.     

基于声辐射模态的有源结构声传入及其辐射控制

从辐射模态的概念和角度研究利用结构误差传感方法对弹性封闭空间结构声辐射进行传感和有源控制。首先分析了辐射模态的数学和物理意义并揭示了辐射模态与声腔模态之间的内在耦合关系。通过声辐射模态建立了弹性封闭空间结构声辐射传感和有源控制模型,并提出了通过传感器阵列测量结构表面有限点的振速分布和设计特定的辐射模态空间滤波器来获得控制所需的误差信号。在此基础上对封闭空间结构声辐射有源控制和误差传感策略进行了深入的理论和数值仿真分析,重点讨论了传感器的数量和布放对辐射模态传感及其有源控制效果的影响。结果表明:辐射模态与声腔模态的耦合具有严格的选择性,各阶辐射模态的形状和与相耦合的主导声模态在耦合面上的形状非常相似;利用结构传感技术传感封闭空间的辐射模态时测点不足或空间采样不足将可能产生较严重的模态泄漏问题,使得不希望的结构模态泄露进所测的辐射模态当中来。在低频范围内,一般只需传感并最小化前三阶有效辐射模态声势能,在更低频和空间声模态频率附近,只需最小化前一阶最有效辐射模态声势能,便能和总声势能最小化策略控制效果基本一样。     

利用声辐射模态重构任意目标的散射声场

水下目标散射声场的重构可以作为水下目标散射特性的研究基础。本文主要利用声辐射模态对水下目标进行散射声场重构研究。首先,在借助声传递矩阵给出的任意结构声辐射模态的流体域求解方法基础上,通过理论证明了目标的散射声压与声辐射模态具有函数关系。其次,借助声场分布模态的概念,同时考虑到声场分布模态病态及声压测量易受噪声污染,提出基于声辐射模态的正则化散射声场重构算法。仿真结果表明,波数越低,重构所需声辐射模态阶数越少,在较高波数时仅需总模态数的大约20%即可对声场进行重构。与基于边界元的声场重构算法相比,计算量减小了至少80%,且克服了赫姆霍兹积分方程最小二乘法仅对球壳结构的重构效果较好而不适用于长条形结构重构的缺陷。     

A comprehensive discrete-time computer modeling of acoustic Transmission Line loudspeakers

The Transmission Line loudspeaker is an audio loudspeaker enclosure topology devoted to extending the low frequency range near the loudspeaker frequency resonance. A few models based on physical properties of damped pipes have been proposed to characterize the Transmission Line loudspeaker systems. Unfortunately, Thiele/Small parameters, which are usually employed in enclosure designs, are not useful as parameters of design for these loudspeakers. In this paper, a comprehensive numerical formulation of a Transmission Line loudspeaker is presented, which is based in a finite difference approach of the governing equations, including the effects of the absorbing material allocated inside the pipe. The influence of the main empirical parameters is tested on the proposed model, which is also compared to a real prototype for validation purposes.     

The decoupling of the active structural acoustic control based on the theory of radiation modes

With the theory of radiation modes,piezoceramics are used as control actuators in the active control of sound radiation.According to the characteristics of the first four radiation mode shapes,the arrangement of four group of actuators is presented.Theoretical analysis and numerical calculation demonstrate that the four group of actuators can not only reduce the sound power effectively,but also decouple the control equations.While controlling of the sound powers of the first four radiation modes,these actuators can convert the complicated control system with multiple input/output into several simple and independent systems with single input/output.     

基于声辐射模态的有源控制解耦

在声辐射模态有源噪声控制策略框架下,选择压电陶瓷片作为控制作动器。根据前四阶声辐射模态形状特点提出了四种压电作动器位置布置方法。理论分析及数值计算表明,以这种方式布放的压电作动器不仅能有效地降低结构辐射的声功率,而且控制过程中这四组作动器分工明确,从而将控制方程解耦。在控制前几阶声辐射模态声功率时可以将复杂的多输入/多输出控制系统转变为几个简单的、互相独立的单输入/单输出控制系统。     

Transient modal radiation of axisymmetric sources: Application to loudspeakers

The present study proposes a transient model of the acoustic radiation of axisymmetric structures. The pressure field is approximated by the Rayleigh integral corresponding to a monopole source distribution over the non-planar vibrating surface. The displacement field is expanded on the linear modes of the structure and a change of variables in the Rayleigh integral is then proposed in the case of a monotonic profile function to compute the Spatial Impulse Response associated to each mode of vibration efficiently. The results are compared to the formulation obtained in the case of planar and spherical sources. The method of calculation is then derived in the case of a typical loudspeaker profile (association of a truncated cone with a spherical cap). Finally, the present approach is used to estimate the nonlinear radiation pattern of a prototype loudspeaker and predictions are compared to measurements in anechoic room.     

On the analytical solutions of the Hamiltonian of a Frenkel exciton for the lattice of a regular polyhedral Cluster

The Coulomb Hamiltonian of a small-radius exciton on a cluster whose atoms occupy the sites of a group lattice is studied. The spectrum of Frenkel excitons can be obtained analytically for definite modes by the methods of harmonic analysis of the lattice Hamiltonian. The carbon cluster C₆₀ with icosahedral symmetry is given as an example. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 7, 578–582 (10 October 1998)