Sonar - Listens to material properties
By Paul G. Schreier
SONAR has been in use for decades to detect submerged objects, but researchers are finding how to extract new information from its echoes.
Figure 1: SONAR frequency response of a scuba tank (modeled as an empty cylindrical shell) computed with a model implemented in COMSOL Multiphysics. TS (target strength) is a logarithmic measure of the echo at a large distance from the target.
With the help of multiphysics modeling software, a group of researchers at the NATO Undersea Research Centre in La Spezia, Italy-Dr. Mario Zampolli, Dr. Alessandra Tesei, Dr. Gaetano Canepa, and Dr. Finn Jensen-are studying how to use low-frequency echoes to determine what an object is made of.
SONAR-as its name implies (SOund NAvigation Ranging)-uses sound waves traveling through water to detect and identify objects. The technique is similar to the more widely known radar (RAdio Detection And Ranging), which is based on electromagnetic waves instead of acoustic waves. radar is not used underwater because radio waves cannot reach very far in that medium due to absorption. During WWII, sonar was used primarily to detect submarines; today these techniques are used to look for undersea objects such as shipwrecks and for measuring fish abundances and distributions. Similar acoustic techniques are being applied to wide-ranging applications from ultrasonic NDT (nondestructive testing), acoustictransducer design, and geoacoustics.
SONAR has traditionally used frequencies for which the wavelengths are far smaller than the size of the objects being studied. This makes it possible to discriminate the shape of objects rather well and leads to advanced applications such as underwater acoustic cameras. However, it is difficult to identify the material of an object using high-frequency signals. Thus researchers are turning their attention to low-frequency schemes (Figure 1).
Information in the low frequencies
"Researchers", reports Dr. Zampolli, "have found out that these low-frequency echoes can also contain information that describes other properties of a submerged object such as the physics of its materials. This is because solids, unlike liquids, support not only longitudinal vibrations but also transverse, or shear, vibrations and thus can propagate sound in a number of modes."
Figure 2: Using the inverse Fourier transform, the model converts the frequency domain response into a time-domain echo, which can in turn the transformed into a time-frequency spectrogram. That spectrogram exhibits various "ringing" features that are closely related to the object's material properties and the geometry.
Particularly useful is the Lamb wave, a complex wave that travels through the entire thickness of a material layer. Propagation of these waves depends on the material's density as well as its elastic and material properties; they are also influenced by the selected frequency and material thickness.
A physical model of the waves´ propagation would have to consider that there is more than one relevant wavelength: besides the sound wave that bounces off the structure, there are also the solidborne waves in the structure. It´s also known that the longitudinal wave travels along the interface between the elastic solid and the water more quickly than the shear waves and than the Lamb waves. In fact, the Lamb waves can be up to two orders of magnitude shorter than the wavelength of the sound in water.
And yet, the Lamb wave effects in the bounced sound waves contain a great deal of information. For example, you can understand the physical properties of an elastic shell by examining the Lamb wave´s resonance effects.
An advanced sonar receiver must therefore deal with a complex signal made up of multiple waves that taken together determine the echo's resonant structure. Making matters more complex is the fact that there are no analytical models that describe such activity, so it's necessary to unscramble the signal by knowing the underlying physics. In short, you need to know what to look for in such a signal. Only with a mathematical model can a researcher predict the form and structure of the low-frequency waveform emitting from a submerged object.
Fluid-structure interaction
Figure 3: By using Berenger PML boundary conditions, it is not necessary to model the surrounding water.
Dr. Zampolli's team built such a model using COMSOL Multiphysics. This multiphysics model describes the frequency-domain elastic-displacement wave equation for a submerged object and couples it to an acoustic-wave equation that describes the waves in the fluid domain. Because the Lamb waves are so short, a finite element model of the object must have many more degrees of freedom than you might expect. "These slow, short waves present a real challenge in the modeling process", notes Dr. Zampolli. "This is a very challenging field," he adds, "and getting a mesh and convergence is difficult".
For their initial model, that of a cylinder with two end caps representing a scuba tank, the team treated the 3D geometry as an axisymmetric 2D problem. They then solved a set of independent 2D problems and added these solutions together through an azimuthal Fourier series to reconstruct the 3D field (Figure 2). "COMSOL Multiphysics´ underlying and open structure," comments Dr. Zampolli, "allows us to implement the equations we need to reduce computational memory. "Although the target must be axisymmetric, the incident sonar signal need not be so. Perfectly matched layers (PMLs) absorb outgoing waves, making it possible to simulate efficiently a target immersed in an infinite fluid domain using a finite-sized mesh (Figure 3).
Thanks to smart use of COMSOL Multiphysics´ features, their modeling method significantly reduces problem size, and now they´re even able to model echoes from objects in the midfrequency regime.
Dr. Zampolli believes that COMSOL Multiphysics is very well suited for such work. "Our studies don't fall into conventional areas, so there are no specialized tools for this type of project. With COMSOL Multiphysics, though, you can tailor virtually everything to your particular needs, and I find the package very impressive. For instance, I use weak-form modeling heavily for the azimuthal Fourier decomposition of the structural-acoustics equations." Now that the software is also available in a 64-bit version, Zampolli feels that "I'd take my first stab at any problem with COMSOL Multiphysics."
Read the research paper at:
www.comsol.com/academic/papers/1009