Régis Bossut

Finite element modeling of radiating structures using dipolar damping elements

The finite element modeling of a radiating structure can be performed by surrounding this structure with a limited fluid domain, upon the external boundary of which a nonreflexion condition is prescribed for the acoustic field. This condition can be implemented with the help of damping finite elements which are attached to the external boundary and are designed to absorb the successive components of the pressure field multipolar expansion [Bayliss et al., ICASE Rep. No. 80/1, NASA, Langley (1980)]. This paper describes an axisymmetrical finite element which damps the monopolar and dipolar components of the radiated field. Then, it provides an original extrapolation algorithm to compute farfield quantities (sound pressure level or transmitting voltage response, directivity patterns,...) from the previously obtained nearfield. Finally, it demonstrates the accuracy of the method in two test cases and describes its application to the analysis of a free‐flooded ring transducer used in sonar devices.

Application of the finite element method to two‐dimensional radiation problems

Acoustic fields radiated by vibrating elastic bodies immersed in an infinite fluid domain are, in general, quite difficult to compute. This paper demonstrates in the two‐dimensional (2‐D) case that the radiated near field can be easily obtained using the finite element method if dipolar damping elements are attached to the mesh external circular boundary. These elements are specifically designed to absorb completely the first two components of the asymptotic expansion of the radiated field. Then, the paper provides a new extrapolation method to compute far‐field pressures from near‐field pressures, using the 2‐D Helmholtz equation and its solution obeying the Sommerfeld radiation condition. These developments are valid for any radiation problem in 2D. Finally, two test examples are described, the oscillating cylinder of order m and a finite width planar source mounted in a rigid or a soft baffle. This approach is the generalization to 2‐D problems of a previously described approach devoted to axisymmetrical and three‐dimensional (3‐D) problems [R. Bossut et al., J. Acoust. Soc. Am. 86, 1234–1244 (1989)]. It has been implemented in the ATILA code. It is well suited to the modeling of high‐frequency transducers for imaging and nondestructive testing.

Finite-element modeling of lead magnesium niobate electrostrictive materials: Dynamic analysis

A finite-element model is proposed for the time-domain analysis of electrostrictive materials. Homs material model, developed for lead magnesium niobate (PMN) ceramics, is used. It includes the quadratic dependence of strain with polarization, the saturation of polarization, assumes constant temperature, and excludes hysteresis. The theoretical formulation is justified by the principle of virtual works. The numerical model is obtained after discretization in space and time. The validation is performed by comparing numerical results with semianalytical results for an electrostrictive spherical shell subjected to a step in voltage or in charge. From these results, a method to compute the coupling coefficient of electrostrictive materials, based on Ikedas definition, is proposed and applied to a bar with parallel electric field.

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.

Analysis of magnetostrictive transducers by the ATILA finite element code

New magnetostrictive rare‐earth‐iron alloys offer an attractive opportunity for the design of high‐power low‐frequency transducers [F. Claeyssen, J. Acoust. Soc. Am. Suppl. 1 81, S89 (1987)]. In order to optimize the design of this particular class of transducers, a model based on a new variational principle has been derived following a classical finite element method approach. This model describes the three‐dimensional dynamic behavior of heterogeneous electrochemically coupled structures. Due to the reduced‐scalar‐potential formulation of the magnetic field, the model has been relatively easily implemented within the ATILA finite element code. In this paper, a general view of the method is given and first computation results on test structures are presented.

On the localization of the antisymmetric flexural edge waves for obtuse angles

It is well known that the existence of edge waves is directly related to the localization of the acoustic field in the wedge. In this paper, it is shown experimentally and numerically that, for wedge angles smaller than about 100° (this angle may vary from one material to an other), the edge modes are confined in the tip of the wedge and may be considered as localized. For higher wedge angles, the analysis of the results shows a delocalization of the guided waves, which induces a new repartition of the acoustical energy in the wedge and a decrease in the amplitude of the wedge wave. This observation is numerically verified via an analysis in the time domain. Experiments realized on obtuse wedges demonstrate that the first ASF mode may be detected for wedge angles up to about 110°.

Finite‐element methods applied to the propagation of acoustic wave along immersed wedges

Immersed in water, wedges can generate either propagating or radiating acoustic guided waves according to the value of the apex angle. The propagation of such waves is analyzed with the help of two methods based on finite‐element methods: a time analysis [A. C. Hladky‐Hennion et al., J. Acoust. Soc. Am. 104, 64–71 (1998)] and a modal analysis for which an original numerical technique is suggested to describe the radiating (or supersonic) modes. The finite‐element results obtained with the two methods for brass and duraluminum wedges are compared to the experimental measurements. A good agreement is observed for either subsonic or supersonic regions.

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 electrostr...

Application of damping elements to the modeling of underwater radiating structures

In the finite element method, the damping or radiating elements are often used to limit the extension of the modeling of the propagation media surrounding the radiating structure, and thus to reduce the number of fluid elements. The radiation condition is generally related to the spherical wave acoustic impedance. Recently, an improved radiating element has been developed [R. Bossut and J. N. Decarpigny, J. Acoust. Soc. Am. Suppl. 1 74, S23 (1983)], based on Bayliss et al.s results [ICASE Rep. No. 80‐1, USRA (1980)], which takes account of the dipolar contribution of the wave impedance. The work described here demonstrates that with this damping element, the F.E.M. computed pressure map, on the radiating structure and in the nearfield, is given with low error, even if the radiating surface stands deeply inside the farfield limit. Thus, a finite element analysis can provide, even with a reduced mesh, an accurate starting point for the computation of the farfield, with the help of a Helmholtz integral or a...

An improvement of the finite radiating element formulation—Application to the modeling of a radiating free‐flooded transducer

At low frequencies, the limit of a free‐flooded cylinder farfield is very far from the acoustic center. Thus, modeling this submerged structure by the finite element method requires a large number of fluid elements, when the radiation boundary condition is represented by an outgoing spherical (monopolar) wave. A radiating element has been created, that uses a radiating impedance of both monopolar and dipolar waves. With this new element, the radiating surface can be much closer to the transducer, and then the number of fluid elements decreases significantly. Unfortunately, one cannot obtain directly the farfield directivity pattern, because the radiating surface is inside the nearfield zone. However, it is possible to find it by a simple algorithm. This algorithm can also be used in an acoustical tank whenever its size is too small to measure the far acoustic field of a large transducer.