ATILA Code Research Articles

Design, development and characterization of a mid-frequency (35 khz) tonpilz transducer array from 0.675PMN-0.325PT piezoceramics

A mid-frequency tonpilz transducer array was designed and analyzed by finite element method using commercial ATILA code and constructed using piezoceramic rings with lead magnesium niobate (PMN)-lead titanate (PT) composition. The morphotropic phase boundary (MPB) 0.675Pb(Mg1/3Nb2/3)O3-0.325PbTiO3 composition was chosen to obtain higher performance from the transducer due to the superior dielectric and electromechanical properties of the MPB compositions. A pure perovskite phase was obtained from the ceramics. Piezoelectric charge coefficient (d33) was measured as 435 pC×N-1. Single tonpilz element and an array consisting of 7-unit array were constructed and later potted in polyurethane for underwater measurements. A second array was also constructed for comparison from commercial hard Pb(Zr,Ti)O3-PZT ceramics. The longitudinal piston mode vibration frequency of the tonpilz transducer was measured around 33 kHz in air and around 35 kHz in water. The PMN-PT based array was found to have a comparable transmit performance and a superior receive performance compared to PZT.

Low Frequency Acoustic Projectors for Underwater Applications

The effect of end cap and PZT materials on the acoustic performance of Cymbal transducer was attempted. Generally there are three frequency bands of interest for identification of the objects in shallow and deep water environments. These are from 1 kHz to 10 kHz; 10 kHz to 100 kHz and 100 kHz to 1 MHz. Currently there is an interest in the lower frequency band and that can be addressed by using cymbal transducers. Cymbal is class V flextensional transducer, it consists of cylindrical ceramic disk sandwiched between two cymbal shaped metal caps with hollow cavities. Cymbals are used as both sound projectors and receivers. Finite Element Analysis (FEA) ATILA code was used to analyze the performance of sound projector and receiver. Three typical ceramic disks and materials used as driving elements and end caps respectively were included in this study.

Attenuation of lamb waves in the vicinity of a forbidden band in a phononic crystal

When a Lamb wave propagates on a plate engraved by a periodic grating, it may exhibit attenuation. This attenuation is related to a coupling of this incident mode with other propagating modes. As the propagation takes place in a periodic medium, the dispersion curves of the modes are of interest because they exhibit passbands and stopbands related to the geometry of the waveguide. The goal of this work is to quantitatively establish the relation between the value of the attenuation of the propagating waves and the width of the forbidden bands appearing inside the Brillouin zone. This study is performed by using a finite element method (ATILA code).

Finite Element Modeling of 2-D Transducer Arrays

Active sonar detects objects underwater by sending out sound waves in pulses, scientists could measure the time it takes these pulses to travel through the water, reflect off of an object, and return to the ship. There are a number of factors limiting the performance of low frequency transducer arrays for active sonar systems including the crosstalk and housing interactions which affects the directivity pattern and the sensitivity. Many important issues in transducer arrays design, such as crosstalk, cannot be accurately studied using analytic method due to the complexity of the partial differential equations involved. Finite element method is the only appropriate way to gain more detailed information. In this paper, a 2-D finite element model is constructed to analyze the crosstalk and structure interactions, using ATILA code and GiD graphical interface, of transducer arrays, consists of six active piezoceramic bars, and developed for shallow water use. The directivity pattern strongly depends on the transducer size versus wavelength, each transducer elements interacts directly with its neighbour and indirectly with the other elements, and the radiated acoustic power may considerably vary from one element to another. It is shown that crosstalk and housing interactions can be reduced through the use of different inter-element materials and housing characteristics.

Finite Element Modeling of a Donut Flextensional Transducer

A new flextensional transducer based on the cymbal device was designed and fabricated. The endcap shape of this device, called the donut, was developed through finite element modeling using the commercially available software code ATILA®. Endcap dimensions that were studied in this research include cap thickness, flange width, and cavity depth. Other parameters considered included piezoelectric material type, thickness of the piezoelectric disk, epoxy thickness, and endcap metal. Fundamental flextensional resonance frequency and effective coupling coefficient, which are two important characteristics that determine the performance and the application opportunities of the transducer, were predicted. Finite element analysis coupled with experimental results suggest that these devices have higher flextensional resonance frequencies compared with cymbals of similar dimensions. Impedance spectroscopy of the donut devices also suggests that the effective electromechanical coupling coefficient is higher than cymbal devices of similar dimensions.

Development of a flextensional transducer for high resolution seismic imaging

Piezoelectric transducers are considered as potential sources for geophysical applications such as 4D monitoring or shallow subsurface survey, which require high repeatability and precise control of the emitted signal. However, the use of piezoelectric sources is limited by their low power and narrow bandwidth. Flextensional transducers are compact, high power, low frequency, wide‐band projectors used in underwater acoustics. The design, fabrication and test of a flextensional transducer for high resolution seismic imaging are presented in this paper. Circuit modeling is used to discuss the general properties of piezoelectric sources radiating in the ground. Finite element simulations (ATILA code) are conducted to design a wide band 500–1500 Hz flextensional transducer. On‐site tests are performed for a typical configuration of shallow subsurface survey. The prototype transducer is compared to a weight drop which constitutes a well‐known seismic source. By taking advantage of the source repeatability and using specific signal processing, it is found that the flextensional transducer is equivalent to weight drop ranging from 300 to 1300 J. Bandwidth is increased by 200 to 300%, leading to a significant improvement of image resolution.

Experimental and finite element modelling studies on single-layer and multi-layer 1–3 piezocomposite transducers

Finite element modelling (FEM) using ATILA code and experimental studies have been carried out on 1–3 piezocomposite transducers. FEM study was initially carried out on a piezocomposite infinite plate and then extended to transducers of finite size. The infinite-plate model results agree well with that of a simple analytical model and experiments. The acoustic performance of multi-layer finite-size piezocomposite transducers was also studied. Transducer stacks were fabricated with different number of layers. The transducer characteristics such as the electrical impedance, the transmitting voltage response (TVR) and the receiving sensitivity (RS) of the 1–3 piezocomposite transducers were evaluated as functions of frequency, ceramic volume fractions and the number of layers. TVR increases and RS decreases with increase in ceramic volume fractions. The model results are found to agree with the experimental data, especially when the number of layers is less.

전기-기계 연성해석 코드 ATILA를 이용한 수중 음향 트랜스듀서 설계

Underwater acoustic transducers are widely used for SONAR application, whose important design parameters are shapes. materials, dimensions and supporting structures. Practical design method of transducers consists of manufacturing, experiments and modifications so that it requires much time and expenses. In this study, an analytical method was developed for the Tonpilz type transducers using the commercial finite element analysis code ATILA which can solve the electro-mechanical coupling problems. A finite element model was established including the transducer elements such as ceramic stack, head mass, tail mass, tensile bolt, and molding layers. The proposed model was verified and modified by comparing the in-air and in-water test results of prototypes. The developed analysis method will be effectively used for the sensitivity analysis of design parameters in transducer design process.

Lamb waves in bulk acoustic wave resonators: Analysis of spurious resonances and design of resonators in the UHF-VHF frequency range

Bulk acoustic wave (BAW) resonators exhibit attractive properties in terms of power handling capacity and on-chip integration to realize filters in the GHz range [K. M. Lakin, IEEE Ultrason. Symp. pp. 895–905 (1999)]. In a BAW resonator, a thin piezoelectric layer (a few mm) deposited between two electrodes is driven in its thickness extensional mode of vibration. To get a high quality factor, this structure is decoupled from the substrate by a multilayer Bragg reflector or a back-etched membrane. A current problem in the design of BAW resonators is the existence of spurious resonances close to the thickness extensional mode which generate ripple in the filter passband. In this paper, these spurious modes are analyzed in terms of Lamb waves resonances. Physical modeling of BAW resonators using finite element ATILA code is presented. The influence of lateral dimensions and electrode geometry on spurious resonances is emphasized. With specific electrode design and electrical excitation, it is demonstrated that lateral modes of Lamb waves can be used to realize resonators in the 50–250-MHz range. Experiments on an AlN piezoelectric layer between Pt electrodes on a SiN membrane are presented. [Work supported by a ST Microelectronics grant (CIFRE).]

Coupling finite element and iterative methods on a solid–solid boundary—Computation of the radiation of buried directional piezoelectric transducers for seismic applications

Based on a theoretical directional source concept for four dimensional seismic monitoring (described in another communication), this work is dedicated to the design of the directional piezoelectric transducer. To describe the interaction of a piezoelectric source with its environment, a model coupling the finite element method with the impedance matrix of the soil is developed. The piezoelectric source and a surrounding spherical soil volume are described using finite element; on the surface of the spherical volume, a condition taking into account the external medium is applied by using an iterative method [Thiruvenkatachar et al., Proc. R. Soc. London, Ser A 309, 331–344 (1969)]. This numerical process is then implemented in the finite element code ATILA which is devoted to the modeling of piezoelectric structures. A transducer acting as the directional concept is designed and its far field radiation patterns are computed. [Work supported by an I.F.P. grant.]

Cymbal and BB underwater transducers and arrays

The cymbal is a miniaturized class V flextensional transducer that was developed for 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 elements and arrays using the ATILA code and the integral equation formulation (EQI).Millimeter size microprobe hydrophones (BBs) have been designed and fabricated from miniature piezoelectric hollow ceramic spheres for underwater applications such as mapping acoustic fields of projectors, and flow noise sensors for complex underwater structures. Green spheres are prepared from soft lead zirconate titanate powders using a coaxial nozzle slurry process. A compact hydrophone with a radially-poled sphere is investigated using inside and outside electrodes. Characterization of these hydrophones is done through measurement of hydrostatic piezoelectric charge coefficients, free field voltage sensitivities and directivity beam patterns.

Design, production and testing of PMN–PT electrostrictive transducers

Lead magnesium niobate ceramics (PMN) are promising materials for application in the field of high power transducers. The advantage of PMN materials are the large strains generated under moderate electric field and the low hysteresis. The electrostrictive effect is non-linear, the corresponding physical constants depend on temperature and frequency and a DC electrical bias is required. These difficulties must be considered at the design stage. A finite element model has been developed and validated in the ATILA code for non-linear static and time-domain analyses. These numerical modelings are used to design and test two Langevin-type electrostrictive transducers. The first transducer is made of PMN–PT–La (90–10–1%) ceramics (TRS Ceramics), the second one of ESC1 ceramics (Morgan Matroc). For given static mechanical prestresses, resonance frequencies and effective coupling coefficients are measured at different DC electric fields and temperatures.

Design of and Fabrication Improvements to the Cymbal Transducer Aided by Finite Element Analysis

A miniature flextensional transducer, the “cymbal,” is an emerging underwater transducer technology for large area and restricted volume transmit and receive arrays. The performance of the device is being evaluated for a number of applications requiring a large number of elements. Simple design, low cost and the ability to tailor performance to the desired application are attractive features of the cymbal. Analysis of the fabrication and performance of the cymbal has revealed that the benefits of the cymbal's flexible design also present production concerns. Asymmetry in the cavity depth or epoxy layer can result in unwanted resonances that can detract from the in-water performance. To avoid these spurious resonances, tolerances in cavity depth could be as low as 5 μm, resulting in low production yields. These and other fabrication concerns have been analyzed through experiment and finite element modeling software using the ATILA code. We were able to identify ways of improving manufacturing yields and minimizing variances to accommodate large array production. The origins of the spurious resonances are discussed along with the performance of a prototype array.

Conical radiating waves from immersed wedges

The finite-element approach has previously been used, with the help of the ATILA code, to model the subsonic and supersonic waves in immersed waveguides [A. C. Hladky-Hennion et al., J. Sound Vib. 212, 265–274 (1998)]. This method has given a precise account of the experimental results and has shown the major effects. In this paper, a new representation of radiating waves is presented, leading to a simple understanding of the physical phenomenon: radiating waves are propagating with the same phase velocity on the surface of a cone, the axis of which is the wedge direction.

A time-domain numerical model for the acoustic scattering from rigid or elastic targets

In order to predict the backscattered echoes from immersed targets, a numerical model based on the space–time Helmholtz–Kirchhoff integral formulation (HKIF) is developed in the EQI code. Two different schemes are implemented for the space–time discretization: a classical finite-element discretization in space and finite difference discretization in time (FEM/FDM) and a space–time finite-element discretization (FEM/FEM). The computed results are provided for the test case of a rigid sphere. Two well-known spurious effects of the discretized HKIF are described: (i) the existence of an instability which grows exponentially as time progresses and (ii) the inaccuracy of the results in the shadow zone. The origin of these effects and the relative performance of the FEM/FDM and FEM/FEM methods are discussed. Finally, the coupling with a finite-element structural model (ATILA code) and its effect on the instability are also presented.

Time analysis of immersed waveguides using the finite element method

The propagation of acoustic waves in immersed waveguides has been previously studied with the help of the finite element method, using the ATILA code [A. C. Hladky-Hennion et al., J. Sound Vib. 200, 519–530 (1997)]. But this method, which is a modal analysis, essentially concerns the case of rectilinear, infinite, and uniform waveguides. Thus this paper deals with another way of solving the problem of wave propagation along waveguides, with the help of a time analysis using finite elements. First, the theoretical formulation is presented for immersed structures. Then, Plexiglas and brass wedge guides, of different apex angles, are considered. When immersed in water, these wedges generate either propagating or radiating wedge waves. The finite element results, using a time analysis, are compared to the previous finite element results, using a modal analysis and to the experiments, leading to a good agreement. Thus the approach can be easily extended to other waveguides whatever their cross sections.

FINITE ELEMENT MODELLING OF RADIATING WAVES IN IMMERSED WEDGES

The propagation of acoustic waves in immersed waveguides has been previously studied with the help of the finite element method, by using the ATILA code (A. C. Hladky-Hennonet al., 1997 JSV200, 519–530). In that paper, the study of the propagating modes along immersed rectilinear wedges was presented, and the theoretical results obtained for Plexiglas wedges agreed well with the experiments. Nevertheless, due to the theoretical formulation, the method was not able to study radiating modes. Thus, the present paper presents a modification of the previous method, with a view to finding either propagating modes or radiating modes. First the formalism is presented, where an original procedure is used to solve the finite element system. Then, wedges, the top angle of which varies, are studied and the finite element results for the wedge wave velocity are compared to experiments, for brass and duralumin samples.

Nonlinear time-domain analysis of electrostrictive materials by the finite element method

Lead magnesium niobate ceramics (PMN) are promising materials for applications in the field of underwater acoustic projectors. A finite element procedure has been developed in the ATILA code to model the static deformation of these materialss [J. C. Debus et al., J. Acoust. Soc. Am. 100, 2584(A) (1996)]. Two different elements are available according to whether or not the saturation of polarization is included. An extension of this model to nonlinear transient analysis is presented in this paper. The procedure is derived for time stepping by finite difference, using a central difference scheme. This new capability is demonstrated by analyzing the transient response of an electrostrictive bar submitted to different electrical excitations (voltage step, charge step, continuous sine). The validation of the model is carried out by comparing the results obtained with the analytical results for a lumped constants model. The validity of commonly used transducer characteristics is discussed to describe electrostrictive transducers. [Work supported by ONR contract and DRET/DCN grant.]

FINITE ELEMENT ANALYSIS OF THE PROPAGATION OF ACOUSTIC WAVES ALONG WAVEGUIDES IMMERSED IN WATER

The finite element approach has previously been used, with the help of the ATILA code, to model the propagation of acoustic waves in waveguides [A.-C. Hladky-Hennion,Journal of Sound and Vibration,194,119–136 (1996)]. In this paper an extension of the technique to the analysis of the propagation of acoustic waves in immersed waveguides is presented. In the proposed approach, the problem is reduced to a bidimensional problem, in which only the cross-section of the guide and the surrounding fluid domain are meshed by using finite elements. Then, wedges the top angles of which vary, are studied and the finite element results of the wedge wave speed are compared with experimental results. Finally, the conclusion indicates a way to extend this approach to waveguides of any cross-section.

Two-dimensional modeling and characterization of PMN electrostrictive materials using the finite-element code ATILA

New electrostrictive lead magnesium niobate ceramics (PMN) are promising materials for applications in the field of actuators, transducers, and motors. These materials have strains roughly an order of magnitude larger than those of the lead zirconate–titanate (PZT) ceramics. However, the use of these electrostrictive materials for practical applications presents some difficulties: highly nonlinear properties, temperature dependence of dielectric permittivity near the dielectric maximum, dc bias field needed. To improve the use of these electrostrictive materials, a better knowledge of the physical tensors of PMN and the development of a numerical tool are necessary. In this study, the development of a two-dimensional electrostrictive element in the ATILA code for nonlinear static analysis and time-domain analysis is presented. Two different models are tested including or not the effect of polarization saturation. The validity of both models is demonstrated by comparing computed strain and charge density with analytical solutions and measured results for a PMN bar at various electric dc fields and mechanical prestresses. Measurements are realized to obtain the complete physical tensor of PMN. Finally, the model is applied to a Janus transducer to describe the application of prestress and the electrical dc polarization.