Publications

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Finite element analysis of transient acoustic phenomena on unbounded exterior domains is very common in engineering analysis. In these problems there is a common need to compute the acoustic pressure at points outside of the acoustic mesh, since meshing to points of interest is impractical in many scenarios. In aeroacoustic calculations, for example, the acoustic pressure may be required at tens or hundreds of meters from the structure. In these cases, a method is needed for post-processing the acoustic results to compute the response at far-field points. In this paper, we compare two methods for computing far-field acoustic pressures, one derived directly from the infinite element solution, and the other from the transient version of the Kirchhoff integral. Here, we show that the infinite element approach alleviates the large storage requirements that are typical of Kirchhoff integral and related procedures, and also does not suffer from loss of accuracy that is an inherent part of computing numerical derivatives in the Kirchhoff integral. In order to further speed up and streamline the process of computing the acoustic response at points outside of the mesh, we also address the nonlinear iterative procedure needed for locating parametric coordinates within the host infinite element of far-field points, the parallelization of the overall process, linear solver requirements, and system stability considerations.

In this report we derive both time and frequency-domain methods for inverse identification of sources in elastodynamics and acoustics. The inverse/design problem is cast in a PDE-constrained optimization framework with efficient computation of gradients using the adjoint method. The implementation of source inversion in Sierra/SD is described, and results from both time and frequency domain source inversion are compared to actual experimental data for a weapon store used in captive carry on a military aircraft. The inverse methodology is advantageous in that it provides a method for creating ground based acoustic and vibration tests that can reduce the actual number of flight tests, and thus, saving costs and time for the program.

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Salinas provides a massively parallel implementation of structural dynamics finite element analysis, required for high fidelity, validated models used in modal, vibration, static and shock analysis of structural systems. This manual describes the theory behind many of the constructs in Salinas. For a more detailed description of how to use Salinas, we refer the reader to Salinas, User's Notes. Many of the constructs in Salinas are pulled directly from published material. Where possible, these materials are referenced herein. However, certain functions in Salinas are specific to our implementation. We try to be far more complete in those areas. The theory manual was developed from several sources including general notes, a programmer notes manual, the user's notes and of course the material in the open literature.

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This work presents a methodology based on the concept of error in constitutive equations for the inverse reconstruction of viscoelastic properties using steady-state dynamics. The ECE algorithm presented herein consists of two main steps. In the first step, kinematically admissible strains and dynamically admissible stresses are generated through two auxiliary forward problems. In the second step, a new update of the complex shear and bulk moduli as functions of frequency are obtained by minimizing an ECE functional that measures the discrepancy between the kinematically admissible strains and the dynamically admissible stresses. The feasibility of the methodology is demonstrated through two numerical experiments. It was found that the magnitude and phase of the complex shear modulus can be accurately reconstructed in the presence of noise, while the magnitude of the bulk modulus is more sensitive to noise and can be reconstructed with less accuracy, in general, than the shear modulus. Furthermore, the phase of the bulk modulus, which is related to energy dissipation, can be accurately reconstructed.

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Salinas provides a massively parallel implementation of structural dynamics finite element analysis, required for high fidelity, validated models used in modal, vibration, static and shock analysis of structural systems. This manual describes the theory behind many of the constructs in Salinas. For a more detailed description of how to use Salinas , we refer the reader to Salinas, Users Notes. Many of the constructs in Salinas are pulled directly from published material. Where possible, these materials are referenced herein. However, certain functions in Salinas are specific to our implementation. We try to be far more complete in those areas. The theory manual was developed from several sources including general notes, a programmer notes manual, the user's notes and of course the material in the open literature.

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In this report we will describe some nonlinear eigenvalue problems that arise in the areas of solid mechanics, acoustics, and coupled structural acoustics. We will focus mostly on quadratic eigenvalue problems, which are a special case of nonlinear eigenvalue problems. Algorithms for solving the quadratic eigenvalue problem will be presented, along with some example calculations.

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An a posteriori error estimator is developed for the eigenvalue analysis of three-dimensional heterogeneous elastic structures. It constitutes an extension of a well-known explicit estimator to heterogeneous structures. We prove that our estimates are independent of the variations in material properties and independent of the polynomial degree of finite elements. Finally, we study numerically the effectivity of this estimator on several model problems.

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In this paper, weak formulations and finite element discretizations of the governing partial differential equations of three-dimensional nonlinear acoustics in absorbing fluids are presented. The fluid equations are considered in an Eulerian framework, rather than a displacement framework, since in the latter case the corresponding finite element formulations suffer from spurious modes and numerical instabilities. When taken with the governing partial differential equations of a solid body and the continuity conditions, a coupled formulation is derived. The change in solid/fluid interface conditions when going from a linear acoustic fluid to a nonlinear acoustic fluid is demonstrated. Finite element discretizations of the coupled problem are then derived, and verification examples are presented that demonstrate the correctness of the implementations. We demonstrate that the time step size necessary to resolve the wave decreases as steepening occurs. Finally, simulation results are presented on a resonating acoustic cavity, and a coupled elastic/acoustic system consisting of a fluid-filled spherical tank.

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This manual describes the theory behind many of the constructs in Salinas. For a more detailed description of how to use Salinas , we refer the reader to Salinas, User's Notes. Many of the constructs in Salinas are pulled directly from published material. Where possible, these materials are referenced herein. However, certain functions in Salinas are specific to our implementation. We try to be far more complete in those areas. The theory manual was developed from several sources including general notes, a programer-notes manual, the user's notes and of course the material in the open literature.

Salinas provides a massively parallel implementation of structural dynamics finite element analysis. This capability is required for high fidelity, validated models used in modal, vibration, static and shock analysis of weapons systems. General capabilities for modal, statics and transient dynamics are provided. Salinas is similar to commercial codes like Nastran or Abaqus. It has some nonlinear capability, but excels in linear computation. It is different than the above commercial codes in that it is designed to operate efficiently in a massively parallel environment. Even for an experienced analyst, running a new finite element package can be a challenge. This little primer is intended to make part of this task easier by presenting the basic steps in a simple way. The analyst is referred to the theory manual for details of the mathematics behind the work. The User's Notes should be used for more complex inputs, and will have more details about the process (as well as many more examples). More information can be found on our web pages, 3 or 4. Finite element analysis can be deceptive. Any software can give the wrong answers if used improperly, and occasionally even when used properly. Certainly a solid background in structural mechanics is necessary to build an adequate finite element model and interpret the results. This primer should provide a quick start in answering some of the more common questions that come up in using Salinas.

This report documents the results obtained during a one-year Laboratory Directed Research and Development (LDRD) initiative aimed at investigating coupled structural acoustic interactions by means of algorithm development and experiment. Finite element acoustic formulations have been developed based on fluid velocity potential and fluid displacement. Domain decomposition and diagonal scaling preconditioners were investigated for parallel implementation. A formulation that includes fluid viscosity and that can simulate both pressure and shear waves in fluid was developed. An acoustic wave tube was built, tested, and shown to be an effective means of testing acoustic loading on simple test structures. The tube is capable of creating a semi-infinite acoustic field due to nonreflecting acoustic termination at one end. In addition, a micro-torsional disk was created and tested for the purposes of investigating acoustic shear wave damping in microstructures, and the slip boundary conditions that occur along the wet interface when the Knudsen number becomes sufficiently large.

In this paper, the effect of viscous wave motion on a micro rotational resonator is discussed. This work shows the inadequacy of developing theory to represent energy losses due to shear motion in air. Existing theory predicts Newtonian losses with little slip at the interface. Nevertheless, experiments showed less effect due to Newtonian losses and elevated levels of slip for small gaps. Values of damping were much less than expected. Novel closed form solutions for the response of components are presented. The stiffness of the resonator is derived using Castigliano's theorem, and viscous fluid motion above and below the resonator is derived using a wave approach. Analytical results are compared with experimental results to determine the utility of existing theory. It was found that existing macro and molecular theory is inadequate to describes measured responses.

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In T1, periodic minimal surfaces in a medium with exclusions (voids) are constructed and in this paper we present two algorithms for computing these minimal surfaces. The two algorithms use evolution of level sets by mean curvature. The first algorithm solves the governing nonlinear PDE directly and enforces numerically an orthogonality condition that the surfaces satisfy when they meet the boundaries of the exclusions. The second algorithm involves h-adaptive finite element approximations of a linear convection-diffusion equation, which has been shown to linearize the governing nonlinear PDE for weighted mean curvature flow.

We discuss application of the FETI-DP linear solver within the Salinas finite element application. An overview of Salinas and of the FETI-DP solver is presented. We discuss scalability of the software on ASCI-red, Cplant and ASCI-white. Options for solution of the coarse grid problem that results from the FETI problem are evaluated. The finite element software and solver are seen to be numerically and cpu scalable on each of these platforms. In addition, the software is very robust and can be used on a large variety of finite element models.