Rickard C. Loftman

Analytical/numerical matching for efficient calculation of scattering from cylindrical shells with lengthwise constraints

Structural discontinuities in highly coupled fluid–structure systems are modeled by an approach called analytical/numerical matching (ANM). This method separates the low-resolution global influence of a discontinuity from the relatively high-resolution local effects. A continuous, smoothed replacement for a fundamental structural discontinuity is constructed so that the system is identically unchanged beyond a small smoothing region. Simultaneously, the precise local effect of smoothing the discontinuity is retained in analytical form. The smoothed problem is solved by numerical techniques, with rapid convergence and reduced computational cost. The original discontinuous character is restored using the analytical expression for the local difference between the smoothed and the original problems. ANM has been successfully applied to two-dimensional cases of acoustic scattering from a thin, infinitely long cylindrical shell, with multiple structural discontinuities. Local solutions for longitudinal line dis...

The application of analytical/numerical matching to structural discontinuities in structural/acoustic problems

Analytical/numerical matching (ANM) is introduced to more efficiently model structural discontinuities in structural/acoustic problems. The general method is explained in detail for the simple example problem of normal incidence acoustic scattering from a periodically line-supported elastic membrane. A modal series solution exists for this problem. The most slowly convergent part of this solution, the dominant high-resolution (large wave number) content, is removed from the series representation and summed in closed form in what is called the ANM local solution. This local solution is represented by a piecewise polynomial that is zero outside of a small region. The remaining part of the solution, containing the overall low resolution content, is called the ANM global solution and converges very rapidly. In the present example, the series representing the global solution falls by three powers of the index faster than the classical modal solution. The result is an ANM composite (local plus global) solution that requires far less computational effort to resolve. In addition to providing a clear abstraction of the method, the example problem allows the equivalence of the ANM solution to be verified, and indicates the importance of resolving the fine scale effects of discontinuities in constrained scattering problems.

Methods for adaptively varying gain during ultrasound agent quantification

Methods are provided for automatic setting of parameters for contrast agent quantification. Various processes may improve quantification. For example, for consistency in contrast agent quantification, a gain or other setting of an ultrasound system is automatically determined in response to destruction of the contrast agent or at the initiation of the contrast agent quantification procedure. Automatic setting of an adaptive gain provides equalized image intensity for each repetition of a contrast agent quantification procedure based on a same triggering event, the destruction of contrast agent. By synchronizing the adaptive setting algorithms with contrast agent destruction, similar base line information is provided for each iteration of a contrast agent quantification procedure. As another example, the contrast agent gain setting treats acoustic signals representing tissue or other non-contrast agent structure as noise, mapping the tissue values to a substantially constant low value within the dynamic range. As yet another example, by segmenting out blood pools or other areas of contrast agent likely to have contrast agents even after destruction, the resulting gain is more likely sensitive to the detection of perfused contrast agents.

Computationally efficient modeling of structural inhomogeneities by analytical/numerical matching

Solving structural acoustic problems in the mid‐frequency range is a challenging task. Computation is expensive due to both the large well‐coupled nature of the domain and resolution constraints such as small flexural wavelength. In addition, discrete structural elements such as ribs and stiffeners cause localized high‐resolution content that requires much greater resolution than would be otherwise warranted. A method called analytical/numerical matching (ANM) alleviates this additional computational burden. The ANM method captures the particular influence of the inhomogeneity on the structure in an analytically expressed local solution. The governing equation is then used to show that the extraction of this local solution by superposition amounts to replacing the original discrete influence of the inhomogeneity by a smoothed forcing derived from the local solution. The result is a smoother problem that can be computed more efficiently and without the loss of any information. The method has been demonstra...

Improving convergence in scattering problems by smoothing discrete constraints using an approximate convolution with a smoothed composite Green’s function

A method for efficiently treating discrete structural constraints using an approximate Green’s function approach to smooth the constraint influence is presented. A method called analytical/numerical matching is used to formulate a composite Green’s function that captures the local high‐resolution content associated with the discrete force in a separate analytic local solution. This local solution in turn implies a smooth replacement for the original discrete force. This replacement is approximately integrated following the Green’s function formalism modified by a Taylor expansion of the forcing strength function. A smooth replacement for the discrete constraint results. This new smoothed problem converges more rapidly than the original discrete one. However, the difference between the smooth solution and the original is retained in the analytic local solution. The result is a composite solution of the original system that is more accurate for a given computational resolution compared with treating the dis...

Generalization of analytical numerical matching for structural acoustic scattering with discontinuities using a composite Green’s function approach

Analytical numerical matching (ANM), when applied to structural acoustics, efficiently models structural discontinuities by superposing high‐resolution local analytical solutions at discontinuities upon a low‐resolution global numerical solution. This composite solution is very accurate and computationally efficient. Previously, ANM composite solutions have been developed for several specific problem geometries. A method for treating general constraint configurations using ANM is presented using the Green’s function concept, which models general structural constraints as an integration of point force solutions of the unconstrained structure. The general local solution is found by integration of the ANM local solution derived in the case of a point force. The point force local solution is analytic, known explicitly, and independent of overall geometry. The complementary global solution is far smoother than the original problem and, therefore, can be more efficiently calculated. In short, a general discrete...

Application of finite element analysis and analytical numerical matching to scattering from fluid‐loaded structures with discontinuities

Analytical numerical matching (ANM) is an analysis method that separates problems into high‐resolution local and low‐resolution global solutions. A method is presented to treat discontinuities, such as structural attachments, within the ANM local solution by high‐resolution solid modeling using finite element analysis. The global problem, which is subjected only to smooth distributed forces, can then be solved by lower order methods, such as shell theory. Both the local and global solutions are more easily solved than the original problem, and the resulting composite solution is very computationally efficient. The approach is a novel way to embed local highly refined solutions within a broader problem. The method is illustrated by several sample problems including a vibrating beam with constraints, and acoustic scattering from a fluid loaded shell.

Acoustic scattering from flexible bodies with discontinuities using analytic/numerical matching

Analytical/numerical matching (ANM) is a hybrid scheme combining a low‐resolution global numerical solution with a high‐resolution local analytical solution to form a composite solution. ANM is applied to scattering from a fluid‐loaded cylindrical membrane with a discontinuity, e.g., a point impedance. This coupled fluid/structural problem utilizes the addition and subtraction of canceling distributed forces at the discontinuity. The problem divides into one with the point force and distributed force in opposition, and another with only a distributed force. Conditions are imposed on the problem with the distributed force opposing the point force, leading to a structural response with only local motion and minimal radiation. This local problem can be solved analytically in simplified form. The remaining problem with only a distributed force is a low‐resolution global numerical problem and can be solved efficiently. The local and global problems are dynamically coupled in the composite solution. The scatter...