Mario Zampolli

A computationally efficient finite element model with perfectly matched layers applied to scattering from axially symmetric objects

A frequency-domain finite-element (FE) technique for computing the radiation and scattering from axially symmetric fluid-loaded structures subject to a nonsymmetric forcing field is presented. The Berenger perfectly matched layer (PML), applied directly at the fluid-structure interface, makes it possible to emulate the Sommerfeld radiation condition using FE meshes of minimal size. For those cases where the acoustic field is computed over a band of frequencies, the meshing process is simplified by the use of a wavelength-dependent rescaling of the PML coordinates. Quantitative geometry discretization guidelines are obtained from a priori estimates of small-scale structural wavelengths, which dominate the acoustic field at low to mid frequencies. One particularly useful feature of the PML is that it can be applied across the interface between different fluids. This makes it possible to use the present tool to solve problems where the radiating or scattering objects are located inside a layered fluid medium. The proposed technique is verified by comparison with analytical solutions and with validated numerical models. The solutions presented show close agreement for a set of test problems ranging from scattering to underwater propagation.

Acoustic scattering from a solid aluminum cylinder in contact with a sand sediment: Measurements, modeling, and interpretation

Understanding acoustic scattering from objects placed on the interface between two media requires incorporation of scattering off the interface. Here, this class of problems is studied in the particular context of a 61 cm long, 30.5 cm diameter solid aluminum cylinder placed on a flattened sand interface. Experimental results are presented for the monostatic scattering from this cylinder for azimuthal scattering angles from 0 degrees to 90 degrees and frequencies from 1 to 30 kHz. In addition, synthetic aperture sonar (SAS) processing is carried out. Next, details seen within these experimental results are explained using insight derived from physical acoustics. Subsequently, target strength results are compared to finite-element (FE) calculations. The simplest calculation assumes that the source and receiver are at infinity and uses the FE result for the cylinder in free space along with image cylinders for approximating the target/interface interaction. Then the effect of finite geometries and inclusion of a more complete Greens function for the target/interface interaction is examined. These first two calculations use the axial symmetry of the cylinder in carrying out the analysis. Finally, the results from a three dimensional FE analysis are presented and compared to both the experiment and the axially symmetric calculations.

Validation of finite element computations for the quantitative prediction of underwater noise from impact pile driving

The acoustic radiation from a pile being driven into the sediment by a sequence of hammer strikes is studied with a linear, axisymmetric, structural acoustic frequency domain finite element model. Each hammer strike results in an impulsive sound that is emitted from the pile and then propagated in the shallow water waveguide. Measurements from accelerometers mounted on the head of a test pile and from hydrophones deployed in the water are used to validate the model results. Transfer functions between the force input at the top of the anvil and field quantities, such as acceleration components in the structure or pressure in the fluid, are computed with the model. These transfer functions are validated using accelerometer or hydrophone measurements to infer the structural forcing. A modeled hammer forcing pulse is used in the successive step to produce quantitative predictions of sound exposure at the hydrophones. The comparison between the model and the measurements shows that, although several simplifying assumptions were made, useful predictions of noise levels based on linear structural acoustic models are possible. In the final part of the paper, the model is used to characterize the pile as an acoustic radiator by analyzing the flow of acoustic energy.

Benchmark problems for acoustic scattering from elastic objects in the free field and near the seafloor

Results from a workshop organized in 2006 to assess the state of the art in target scatter modeling are presented. The problem set includes free-field scenarios as well as scattering from targets that are proud, half-buried, or fully buried in the sediment. The targets are spheres and cylinders, of size O(1 m), which are insonified by incident plane waves in the low-frequency band 0.1-10 kHz. In all cases, the quantity of interest is the far-field target strength. The numerical techniques employed fall within three classes: (i) finite-element (FE) methods and (ii) boundary-element (BE) techniques, with different approaches to computing the far field via discretizations of the Helmholtz-Kirchhoff integral in each case, and (iii) semianalytical methods. Reference solutions are identified for all but one of the seven test problems considered. Overall, FE- and BE-based models emerge as those being capable of treating a wider class of problems in terms of target geometry, with the FE method having the additional advantage of being able to deal with complex internal structures without much additional effort. These capabilities are of value for the study of experimental scenarios, which can essentially be envisioned as variations of the problem set presented here.

Computing the far field scattered or radiated by objects inside layered fluid media using approximate Green’s functions

A numerically efficient technique is presented for computing the field radiated or scattered from three-dimensional objects embedded within layered acoustic media. The distance between the receivers and the object of interest is supposed to be large compared to the acoustic wavelength. The method requires the pressure and normal particle displacement on the surface of the object or on an arbitrary circumscribing surface, as an input, together with a knowledge of the layered medium Greens functions. The numerical integration of the full wave number spectral representation of the Greens functions is avoided by employing approximate formulas which are available in terms of elementary functions. The pressure and normal particle displacement on the surface of the object of interest, on the other hand, may be known by analytical or numerical means or from experiments. No restrictions are placed on the location of the object, which may lie above, below, or across the interface between the fluid media. The proposed technique is verified through numerical examples, for which the near field pressure and the particle displacement are computed via a finite-element method. The results are compared to validated reference models, which are based on the full wave number spectral integral Greens function.

Parabolic equation solution of seismo-acoustics problems involving variations in bathymetry and sediment thickness

Recent improvements in the parabolic equation method are combined to extend this approach to a larger class of seismo-acoustics problems. The variable rotated parabolic equation [J. Acoust. Soc. Am. 120, 3534-3538 (2006)] handles a sloping fluid-solid interface at the ocean bottom. The single-scattering solution [J. Acoust. Soc. Am. 121, 808-813 (2007)] handles range dependence within elastic sediment layers. When these methods are implemented together, the parabolic equation method can be applied to problems involving variations in bathymetry and the thickness of sediment layers. The accuracy of the approach is demonstrated by comparing with finite-element solutions. The approach is applied to a complex scenario in a realistic environment.

Radiation impedance matrices for rectangular interfaces within rigid baffles: Calculation methodology and applications

The coupling of sound fields through a finite-sized aperture in a plane rigid baffle where the region (half-space) on one side is unbounded can be described by an integral equation which constitutes a boundary condition for the field on the other side of the aperture. Such a boundary condition, when the pressure and the normal velocity are expanded in basis functions defined over the aperture, can be recast into a matrix form relating the coefficients of the basis functions in the expansions, the principal feature being a matrix of fourfold (double-area) integrals analogous to those encountered in studies of radiation from flexible pistons in rigid baffles. A substantial analytical reduction to sums of single nonsingular integrals is derived for the elements of this radiation impedance matrix when the aperture is rectangular and the basis functions are expressible as a sum of products of exponential functions of the Cartesian coordinates of the aperture plane, with the exponential coefficients being arbitrary complex numbers. The validity of the result is substantiated by its reduction to previously published results for less general cases. Its utility is demonstrated with the example of diffraction by a square hole in a screen.

Tank measurements of scattering from a resin-filled fiberglass spherical shell with internal flaws.

This paper presents results of acoustic inversion and structural health monitoring achieved by means of low to midfrequency elastic scattering analysis of simple, curved objects, insonified in a water tank. Acoustic elastic scattering measurements were conducted between 15 and 100 kHz on a 60-mm-radius fiberglass spherical shell, filled with a low-shear-speed epoxy resin. Preliminary measurements were conducted also on the void shell before filling, and on a solid sphere of the same material as the filler. These data were used to estimate the constituent material parameters via acoustic inversion. The objects were measured in the backscatter direction, suspended at midwater, and insonified by a broadband directional transducer. From the inspection of the response of the solid-filled shell it was possible to detect and characterize significant inhomogeneities of the interior (air pockets), the presence of which were later confirmed by x-ray CT scan and ultrasound measurements. Elastic wave analysis and a model-data comparison study support the physical interpretation of the measurements.

Passive acoustic detection of closed-circuit underwater breathing apparatus in an operational port environment.

Divers constitute a potential threat to waterside infrastructures. Active diver detection sonars are available commercially but present some shortcomings, particularly in highly reverberant environments. This has led to research on passive sonar for diver detection. Passive detection of open-circuit UBA (underwater breathing apparatus) has been demonstrated. This letter reports on the detection of a diver wearing closed-circuit UBA (rebreather) in an operational harbor. Beamforming is applied to a passive array of 10 hydrophones in a pseudo-random linear arrangement. Experimental results are presented demonstrating detection of the rebreather at ranges up to 120 m and are validated by GPS ground truth.

Extension of the Rotated Elastic Parabolic Equation to Beach and Island Propagation

Improvements in the capability of handling sloping interfaces and boundaries with the parabolic equation method have been an active area of research. Recent progress in accurately treating range-dependent seismoacoustic problems has involved coordinate transformation techniques. The variable-rotated parabolic equation is among recent advances in this area. The solution rotates the coordinate axes to achieve greater accuracy in the presence of range-dependent bathymetry. At points of slope change the rotated solution interpolates and extrapolates the field into adjacent regions. This approach is extended to solve problems involving variable topography (above-ocean-surface sediments) by accounting for the transition and boundary conditions at the water/solid/air interfaces. It is applied to range-dependent problems of sound transmission up a beach and through an island. The method is benchmarked for accuracy against a finite-element solution.