提高阿基米德螺旋相控阵换能器焦点声压的仿真研究

针对阿基米德螺旋相控阵换能器焦点声压不足的问题,通过有限元仿真,分别讨论了换能器阵元形状和频率改变与声场的变化关系,从焦点声压、偏转范围、栅瓣水平、焦域大小等方面进行了研究。结果表明,相同频率下,扇形阵元阿基米德螺旋相控阵换能器的焦点声压比圆形阵元时的焦点声压提高了32.28%,偏转范围为20 mm×20 mm×40 mm;在扇形阵元形状的情况下,频率选择0.9~1.0 MHz,不仅能获得较高的焦点声压,同时还能保证改善聚焦性能。文章的仿真结果为阿基米德螺旋相控阵换能器提高焦点声压,满足深部组织消融治疗需要的高功率要求提供了有用的设计参考。     

Modeling and underwater characterization of cymbal transducers and arrays

The cymbal is a miniaturized class V flextensional transducer that was developed for potential use as a shallow water sound projector and receiver. Single elements are characterized by high Q, low efficiency, and medium power output capability. Its low cost and thin profile allow the transducer to be assembled into large flexible arrays. Efforts were made to model both single element and transducer arrays by coupling finite element analysis (ATILA) and the integral equation formulation (EQI). The pressure and velocity distributions on the surface elements were calculated by ATILA and later used with EQI to calculate the far held properties of the transducer element and arrays. It eliminates the mesh of the fluid domain and makes the 3-D model of a transducer possible. Three-dimensional models of a cymbal transducer and a 3×3 cymbal array were developed in the modeling. Very good agreement was obtained between modeling and measurement for single element transducers. By coupling finite element analysis with the integral equation method using boundary elements, acoustic interaction effects were taken into account. Reasonable agreement was obtained between calculation and measurement for a 3×3 array     

Ultrasonic field modeling: a comparison of analytical, semi-analytical, and numerical techniques

Modeling ultrasonic fields in front of a transducer in the presence and absence of a scatterer is a fundamental problem that has been attempted by different techniques: analytical, semi-analytical, and numerical. However, a comprehensive comparison study among these techniques is currently missing in the literature. The objective of this paper is to make this comparison for different ultrasonic field modeling problems with various degrees of difficulty. Four fundamental problems are considered: a flat circular transducer, a flat square transducer, a circular concave transducer, and a point focused transducer (concave lens) in the presence of a cavity. The ultrasonic field in front of a finite-sized transducer can be obtained by Huygens-Fresnel superposition principle that integrates the contributions of several point sources distributed on the transducer face. This integral which is also known as the Rayleigh integral or Rayleigh-Sommerfeld integral (RSI) can be evaluated analytically for obtaining the pressure field variation along the central axis of the transducer for simple geometries, such as a flat circular transducer. The semi-analytical solution is a newly developed mesh-free technique called the distributed point source method (DPSM). The numerical solution is obtained from finite element analysis. Note that the first three problems study the effect of the transducer size and shape, whereas the fourth problem computes the field in presence of a scatterer.     

Design and optimization of an OPFC ultrasonic linear phased array transducer

In contrast to piezoceramics, orthotropic piezoelectric fibre composites (OPFC) which can be used as actuator/sensor elements in damage detection show clear advantages because of their high sensitivity along the fibre direction and directivity. The focusing acoustic field distribution of the OPFC phased array transducer is analyzed by the finite element method together with directivity analysis in metallic materials. The optimal array parameters such as spacing, width and number of elements are obtained by studying the total displacement changes as various parameters change at the focus point. The feasibility of an OPFC ultrasonic phased array transducer for damage detection is validated.     

Modeling of piezoelectric multilayer ceramics using finite elementanalysis

For medical ultrasound imaging, 2-D array transducers have greater versatility than linear arrays. Unfortunately, the tiny array elements in a 2-D array have poor signal-to-noise ratio (SNR). We have previously shown that SNR is increased in 2-D array transducers made from piezoelectric multilayer ceramics. Conventional one-dimensional models provide accurate results when comparing multilayer ceramic performance relative to single layer transducers. However, these models are not accurate when comparing simulations directly to measurements. Because multilayer ceramics have a complex structure, a 3-D model, such as finite element analysis, is needed for accurate simulations. We modeled four arrays that were previously fabricated: a single layer and multilayer 1 MHz, 2-D array element, and a single layer and multilayer 2.25 MHz, 1.5-D array element that can focus and steer in azimuth but only steer in the elevation dimension. We compared the simulated and measured impedance plots for each transducer. The finite element analysis plots accurately predicted the impedance for each vibration mode. On the other hand, the one dimensional KLM transmission line model could simulate only the thickness mode vibrations and the results were inaccurate compared to measurements. We also simulated the transmit output pressure for the 2.25 MHz arrays and compared the results to measurements. The simulated pressure vs. time plots and their spectra were accurate when compared to measurements. Finally, we obtained a series of images that show the impulse response vibrations for the 2.25 MHz, arrays. These animations show the vibration modes in the complex multilayer ceramic structure. Measurements were not available to confirm the animations. Our results show that finite element analysis in three dimensions is a valuable tool to predict the performance of multi-layer transducers     

Modeling of transient ultrasonic wave propagation using the distributed point

Transient ultrasonic waves in a fluid medium generated by a flat circular and a point-focused transducer of finite size are modeled by the distributed point source method (DPSM). DPSM is a Green's-function-based semi-analytical mesh-free technique which is modified here to incorporate the transient loading from a finite-sized acoustic transducer. Conventional DPSM solves acoustic problems in steady-state frequency domain. Here, DPSM is extended to the time domain without the fast Fourier transform (FFT) but using the Green's function in the time domain. This modified method is denoted t-DPSM. Harmonic point sources of DPSM are replaced by time-dependent point sources in t-DPSM. Generated t-DPSM results are compared with the finite element (FE) results for both focused and flat circular transducers. The developed method is used to solve the transient problem of wave scattering by an air bubble in a fluid as the bubble is moved horizontally or vertically from the focal point of the focused transducer. The received energy signal is compared for different eccentricities.     

一款宽带圆柱阵研究

圆柱阵换能器具有水平全向的优势,已广泛应用在水声探测领域。文章研究了一款宽带圆柱阵,利用匹配层技术拓宽圆柱阵阵元的带宽,通过有限元仿真优化单个换能器阵元带宽、发送电压响应和阻抗等参数。同时通过仿真以阵元错位密集方式形成圆柱阵,对阵元的个数及排列方式进行仿真优化,制作了一款宽带圆柱阵并进行了测量,圆柱阵直径为400 mm,高度为435 mm,圆柱阵的工作频段为20~30 kHz,频带内起伏3 dB,最大发送电压响应为160.5 dB,圆柱阵-3 dB水平波束宽度为360°。     

基于遗传算法的单矢量水听器多目标方位估计

矢量水听器能同时获得声场中某一点的声压标量和质点振速矢量,获得了比常规声压水听器更多的信息。矢量水听器自身是一个空间共点阵,具有一定的空间指向性,这些特点使矢量信号处理技术与声压信号处理技术具有重大差异。根据单个矢量水听器多目标分辨的数学模型,即声压和振速的偶次阶矩组成的非线性联立方程组,研究了该方程的解算方法,给出了可以使用遗传算法求解该非线性方程组的结论和计算精度。     

换能器组阵对声场指向性的影响

根据点声源的声场指向性函数,推导出了考虑换能器振动面积时单个超声波换能器的指向性函数和由其组成的矩形阵列的指向性函数,研究了单个超声波换能器和其组成阵列的指向性。计算分析了阵元面积、阵元间距及阵元数目对超声波换能器阵列指向性的影响,为高指向性噪声的控制和声武器对抗提供帮助。     

A closed-form field analysis of a broad-band annular array

A closed-form transient field response under the paraxial approximation for an impulse wave excited by a circularly symmetric ultrasonic transducer is derived. The analysis is based on linear transform techniques to obtain the impulse response of a planar or a lensed transducer such as a disk or an annulus in the whole field of view. A closed-form solution is obtained for the focal plane response of a nonuniform aperture with an apodizing function represented by a polynomial of the radial distance on the transducer surface. Moreover, a closed-form impulse response for a planar annular is derived without the paraxial approximation and taking into account the obliquity factor. For a phased annular array, the impulse responses of array elements are convolved with the delayed excitation pulse and then summed to get the resultant field disturbance of the array. These results provide an effective means of studying the focusing characteristics of a phased annular array, including its focusing delay and apodizing quantization error effects.     

敷设覆盖层圆板水下爆炸响应理论计算方法研究

为研究敷设覆盖层圆板水下爆炸响应,提出一种理论计算方法。敷设覆盖层对圆板水下爆炸响应影响包括两方面:一为对冲击载荷的影响,二为在冲击载荷作用下对响应的影响。该理论计算方法运用波在多层介质传播理论得到湿表面压力,并积分得到冲量,运用等效均一化理论得到覆盖层与钢板整体结构的等效参数,根据圆板振动理论得到圆板真空振动方程,通过考虑水附加质量的影响修正圆板振动频率,最后根据初始条件得到圆板的响应。将理论方法的结果与有限元结果通过实例进行对比,证明该理论计算方法可以很好地预测圆板振动的位移响应。     

The diffraction response interpolation method

Computer modeling of the output voltage in a pulse-echo system is computationally very demanding, particularly when considering reflector surfaces of arbitrary geometry. A new, efficient computational tool, the diffraction response interpolation method (DRIM), for modeling of reflectors in a fluid medium, is presented. The DRIM is based on the velocity potential impulse response method, adapted to pulse-echo applications by the use of acoustical reciprocity. Specifically, the DRIM operates by dividing the reflector surface into planar elements, finding the diffraction response at the corners of the elements, calculating the response integrated over the surface element by time-domain convolutions with analytically determined filters, and summing the responses from the individual surface elements. As the method is based on linearity, effects such as shadowing, higher-order diffraction, nonlinear propagation, cannot be directly incorporated in the modeling. The DRIM has been compared to other modeling tools when possible. Excellent agreement between the results obtained with the DRIM and the alternative techniques have been found, and the DRIM offers reductions in computation time in the range from 30 to 400 times. Experimental results obtained using a planar circular transducer together with cylindrical reflectors were compared to DRIM results and fairly good agreement was observed.     

A new algorithm to calculate the transient near-field of ultrasonic phased arrays

An algorithm valid for an accurate calculation of the near-field in the scanning plane of ultrasonic phased arrays is presented. Using the classical time-domain impulse response approach, a simple analytical expression for the impulse response at points lying in the central plane of a narrow rectangular aperture is decided. An expression for the array impulse response is then obtained by superposition. The proposed solution is useful for an efficient computation of transient and continuous wave (CW) pressure fields without requiring any far-field or paraxial approximations. Moreover, the convolution-impulse response approach applied to phased arrays constitutes an important tool for the analysis of array fields. Some numerical examples are presented, in which the advantages of using the array impulse response in the field analysis are shown. Several aspects of array fields not currently described in literature are included in the examples.     

Frequency-invariant pattern synthesis of conformal array antenna with low cross-polarisation

Despite their potential and promising advantages over classical planar arrays, conformal arrays also present many challenges to the antenna designer, including varying element normal due to curvature, serious cross-polarisation effect, limited operational bandwidth and so on. A uniform method for the element polarised pattern transformation of arbitrary 3D conformal arrays is presented based on Euler rotation. A space-time-polarisation filter structure is proposed for the pattern synthesis of conformal array, in which the finite impulse response (FIR) filters assigned to every element are used to acquire the frequency-invariant array pattern and the element polarisation diversity in array global coordinates is used to depress the cross-polarisation level. The optimal weight vector is obtained by alternating projection method. The alternating projection method is a powerful and attractive method for the pattern synthesis in that it requires relatively smaller amount of computation burden and a wide variety of desirable constraints can be freely implemented in a -visible- way, which is usually impossible for other optimisation method. The pattern synthesis method proposed has established a unified frame for the frequency-invariant and low cross-polarisation pattern synthesis of conformal array. Simulation results are provided to demonstrate the effectiveness and behaviour of the proposed method.     

Radiation impedance of collapsed capacitive micromachined ultrasonic transducers

The radiation impedance of a capacitive micromachined ultrasonic transducer (CMUT) array is a critical parameter to achieve high performance. In this paper, we present a calculation of the radiation impedance of collapsed, clamped, circular CMUTs both analytically and using finite element method (FEM) simulations. First, we model the radiation impedance of a single collapsed CMUT cell analytically by expressing its velocity profile as a linear combination of special functions for which the generated pressures are known. For an array of collapsed CMUT cells, the mutual impedance between the cells is also taken into account. The radiation impedances for arrays of 7, 19, 37, and 61 circular collapsed CMUT cells for different contact radii are calculated both analytically and by FEM simulations. The radiation resistance of an array reaches a plateau and maintains this level for a wide frequency range. The variation of radiation reactance with respect to frequency indicates an inductance-like behavior in the same frequency range. We find that the peak radiation resistance value is reached at higher kd values in the collapsed case as compared with the uncollapsed case, where k is the wavenumber and d is the center-to-center distance between two neighboring CMUT cells.     

Assessing and improving acoustic radiation force image quality using a 1.5-D transducer design

A 1.5-D transducer array was proposed to improve acoustic radiation force impulse (ARFI) imaging signal-to-noise ratio (SNRARFI) and image contrast relative to a conventional 1-D array. To predict performance gains from the proposed 1.5-D transducer array, an analytical model for SNRARFI upper bound was derived. The analytical model and 1.5-D ARFI array were validated using a finite element modelbased numerical simulation framework. The analytical model demonstrated good agreement with numerical results (correlation coefficient = 0.995), and simulated lesion images yielded a significant (2.92 dB; p < 0.001) improvement in contrast-tonoise ratio when rendered using the 1.5-D ARFI array.     

First-order design sensitivities for transient conduction problems by an adjoint method

An adjoint approach is presented for the design sensitivity analysis of transient conduction problems. Variations of a general design functional are expressed in explicit form with respect to all design quantities, i.e. material properties, shape, applied thermal loads including convection, and initial conditions. The methodology incorporates the mutual energy between the real and adjoint thermal problems and a geometric mapping to describe shape variations. Finite element implementation of the method is discussed and an example is provided. Some potential difficulties that might be encountered when using the adjoint method with the finite element method are addressed. These involve the application of impulse loadings and Dirac temperature fields in the adjoint loadings.     

A new approach to calculate the field radiated from arbitrarily structured transducer arrays

A efficient time-domain algorithm, based on the spatial pulse response approach, is proposed for the determination of the acoustic fields radiated by means of acoustical sources. The computations are performed by the discrete representation array modelling (DREAM) procedure, specially adapted to study the planar and arbitrarily structured multielement transducer arrays. DREAM, based on the discrete representation computational concept, acts as the generator of the array velocity potential impulse response, and thus, does not require any analytical solutions prior to the computations. The computations are valid for all field regions and may be performed for any excitation form. Apart from the classic case of rigid baffle conditions, the free and soft planar baffle also can be considered. The use of the time-domain solution for causal Green's function for lossy media enables the wideband absorption effects to be modeled. The accuracy of computations depends on temporal and spatial discretization and can be obtained as required. The quantitative rules, which determine the required discretizations to be predicted, are proposed. The computational examples show that DREAM allows the different and various transducers to be modeled. Its possibilities are illustrated by computations for the multielement transducers, including the beam-steered, amplitude-weighted sonar array, the focusing annular transducer, and the diverging and converging cylindrical array.     

水平激励下任意截面柱形储液罐内液体的晃动响应

采用半解析法研究水平激励下任意截面柱形储液罐内液体的晃动响应。基于叠加原理,将液体运动速度势分为两部分:刚体速度势和摄动速度势。满足非齐次边界条件的刚体速度势可解析得到;以自由晃动模态为广义坐标、时间为变量的摄动速度势可由模态叠加法设出。将整个速度势函数代入自由表面波方程,利用模态的正交性得到动力响应方程。结果与有限元非常吻合。     

Computationally efficient sound field calculations for a circular array transducer

A computationally efficient method is presented for calculating field pressure distributions from a circular phased array transducer. This method employs a form of the rectangular radiator approach modified for use with the geometry of a circular array. The curved surface of the elements, radiating either continuous wave or pulsed excitation signals, is divided into incremental rectangular areas small enough so that the Fraunhofer approximation can be applied. Once the directivity of a single element is found, the array beam pattern can be calculated using superposition and suitable coordinate transformations. The validity of this approach is verified through comparisons with experimental data from a circular phased array. The results show that the location and amplitude of the grating lobes and main lobe width can be predicted with reasonable accuracy by using this method.