Jeffrey Cipolla

Special transformations for pentamode acoustic cloaking

The acoustic cloaking theory of Norris [Proc. R. Soc. London, Ser. A 464, 2411-2434 (2008)] permits considerable freedom in choosing the transformation f from physical to virtual space. The standard process for defining cloak materials is to first define f and then evaluate whether the materials are practically realizable. In this paper, this process is inverted by defining desirable material properties and then deriving the appropriate transformations which guarantee the cloaking effect. Transformations are derived which result in acoustic cloaks with special properties such as (1) constant density, (2) constant radial stiffness, (3) constant tangential stiffness, (4) power-law density, (5) power-law radial stiffness, (6) power-law tangential stiffness, and (7) minimal elastic anisotropy.

A comparison between one‐sided and two‐sided Arnoldi‐based model order reduction (MORe) techniques for fully coupled structural‐acoustic analysis

Reduced order models are developed for fully coupled structural‐acoustic unsymmetric matrix models, resulting from Cragg’s displacement/pressure formulation, using Krylov subspace techniques. The reduced order model is obtained by applying a Galerkin and Petrov‐Galerkin projection of the coupled system matrices, from a higher dimensional subspace to a lower dimensional subspace, while matching the moments of the coupled higher dimensional system. Two such techniques, based on the Arnoldi algorithm, focusing on one‐sided and two‐sided moment matching, are presented. To validate the numerical techniques, an ABAQUS coupled structural‐acoustic Benchmark problem is chosen and solved using the direct approach. First, the physical problem is modeled using ANSYS FE package and compared with closed form solutions. Next, ANSYS results are compared with nodal velocities obtained by generating reduced order models via moment matching. The results show that the reduced order models give a very significant reduction in...

Design of pentamode acoustic materials using homogenization and the adjoint approach.

Acoustic metamaterials need to be realized using subwavelength microstructures. By tailoring the microstructure of the underlying unit cell, different effective properties at the macroscopic scale may be achieved. These macroscopic properties can be related to the microstructure using homogenization theory. The problem of designing a pentamode acoustic metamaterial is formulated as the minimization of an objective functional representing the difference between the homogenized properties and the target pentamode acoustic metamaterial properties. A quasi‐Newton optimization approach is used to solve the optimization problem. Such an approach requires the gradient of the objective function with respect to the microstructural properties at every iteration, and hence the cost of gradient computation must be low. The gradient is calculated efficiently using the adjoint approach which requires the solution of only two (primal and dual) finite element problems, per homogenization deformation field, independent of...

Investigating the fidelity of a pseudo-analytical solution of a rib-stiffened, layered plate structure subjected to high frequency acoustic loading

There is a need for a fast and reliable tool to assist in the analysis, design, and optimization of submarine and UUV coatings due to high frequency incident acoustic pressure loading. An existing pseudo-analytical, frequency domain solution for wave propagation in coated, ribbed, three-dimensional elastic layered plates excited by acoustic plane waves provides fast solutions for high frequency excitations. Weidlinger Associates, Inc. (WAI) is developing an analysis software tool which integrates this solution methodology while adding some technical improvements to the formulation. The solution methodology, which is found to be numerically unstable under certain conditions, contains a fundamental ansatz regarding the set of excited wave forms expressed through a particular wave number expansion in the direction of periodicity. Evidence is presented to show that the numerical instability is due to the specific choice of the wave number basis used in the solution. In order to provide a remedy while retaining the positive aspects of the solution methodology, WAI is implementing a pre-processing step to determine the optimal wave number basis: the set of admissible propagating (and attenuating) waves are predetermined via an eigenvalue analysis and then substituted into the wave number basis in computing the pseudo-analytical solution.

The effect of inertial distribution on dispersive modes in pentamode metamaterials for use in acoustic cloaking

Transformation acoustics uses invertible maps to transform a cloaked region to a region with a smaller scatterer. The “elastic” or Norris class of acoustic cloaking theory is inherently broadband, in that it does not rely on the presence of resonant effects. To achieve the properties required by the transformation theory, we utilize pentamode materials, which admit the use of finite mass but require anisotropic stiffness throughout the material. These types of materials do not exist naturally and must be fabricated through the use of metamaterials. One of the challenges associated with metamaterials for use in dynamic applications is the distribution of mass in a unit cell and its consequences for frequency-dependent behavior in the metamaterial. Various homogenization techniques for recovering wave speed properties of the metamaterial unit cells may predict contradictory wave speed values for pentamodal structures. These disagreements can be explained through the distribution of inertia in the material a...

Microstructure-in-the-loop optimization of acoustic metamaterial structures

The field of acoustic metamaterial research has been driven, first, by transformation acoustics cloaking theory. This and other theoretical approaches optimize an acoustic effect through definition of artificial material properties which at present are only achievable using metamaterial technology. Metamaterials, however, present separate challenges in optimization for any desired acoustic effect: in particular, their dynamic behavior depends on parameters unrelated to acoustics, and exhibits wave propagation behavior more complex than elastic or acoustic continua. Homogenization methods which assume Cartesian symmetry are a staple in metamaterial design, but these only approximate a feasible optimal design. Moreover, total reliance on homogenized continuum models provides no information about the actual microstructure performance, and presents problems in functionally graded applications. To overcome this, we augment our Cartesian homogenization processes with high-resolution finite element models to optimize the design. Comparatively computationally expensive implicit FEM is avoided; specifically tailored time-domain wave propagation codes make the analyses feasible. Examples of the process, combining Cartesian homogenization estimates with high-resolution microstructural wave propagation solutions, will be shown.The field of acoustic metamaterial research has been driven, first, by transformation acoustics cloaking theory. This and other theoretical approaches optimize an acoustic effect through definition of artificial material properties which at present are only achievable using metamaterial technology. Metamaterials, however, present separate challenges in optimization for any desired acoustic effect: in particular, their dynamic behavior depends on parameters unrelated to acoustics, and exhibits wave propagation behavior more complex than elastic or acoustic continua. Homogenization methods which assume Cartesian symmetry are a staple in metamaterial design, but these only approximate a feasible optimal design. Moreover, total reliance on homogenized continuum models provides no information about the actual microstructure performance, and presents problems in functionally graded applications. To overcome this, we augment our Cartesian homogenization processes with high-resolution finite element models to opt...

Adaptive manifold interpolation techniques for acoustic metamaterial characterization in HPC environments

Functionally graded acoustic metamaterials (FGAMs) can be designed to have specific waveguide properties dictated by a theory relevant to the application. Frequently, these material properties do not exist naturally, and must be fabricated by gradually layering manufactured unit cell microstructures, resulting in a (usually smooth) variation of properties. Tailoring these microstructures to the demands of the relevant theory requires assembling microstructures with very specific material properties—a process that often requires haphazardly searching a large domain space of unit cells for desirable parameter combinations. Moreover, the process of determining the material tensor of interest for a specific set of metamaterial cell design parameters typically involves solving a costly high dimensional finite element problem for each new microstructure cell of interest. This work presents a gradient-based, manifold interpolation technique to characterize acoustic metamaterial homogenized elastic tensors. An ad...

Exhaustive optimization of rib-stiffened, layered plate structures for acoustic response

A previously reported structural-acoustic frequency-domain formulation for layered, ribbed structures is used here as the basis for an approach to optimize these systems. We will review a previously reported singular perturbation approach to resolve convergence difficulties in both planar and cylindrical configurations, and discuss verification and validation. The significant successes of topological structural optimization for strength, weight, and efficiency are more challenging to repeat in coupled wave-bearing systems with many modes present. This is due, at least, to the difficulties of defining appropriate cost and regularization functions applicable across frequency ranges of interest and across the orders of magnitude of response characteristic of vibroacoustic systems. We discuss overcoming these difficulties by evading them entirely: the layered ribbed structural-acoustic model we use is sufficiently fast that sophisticated optimization algorithms are not required. To understand the dependence o...

Jacobian-Free Newton Krylov based iterative strategies in frequency-domain analyses

This study examines the theory and performance of Jacobian-Free Newton Krylov (JFNK) methods for the efficient, iterative solution of steady state dynamics of linear vibrating systems in the frequency domain. Currently, most commercial FEM algorithms employ use direct factorization of large system matrices to achieve steady state solution. Such approaches are usually quite demanding on memory and CPU requirements. Some implementations exploit iterative solutions, but still use large, assembled system matrices, requiring significant memory. The methods investigated in this work avoid the formation of a matrix completely, minimizing memory requirements and enabling much larger problems to be performed on desktop computers. Here, the Conjugate-Gradient (CG) and Transpose Free Quasi Minimal Residual (TFQMR) algorithms are studied as possibilities. These methods are of particular interest for adaptation to finite element software which uses explicit transient dynamics, because such softwares optimal architect...

A stochastic inverse solution for functionally graded acoustic layered metamaterial validation

Functionally graded acoustic metamaterials (FGAMs) can be designed to have specific waveguide properties. In sonar applications, FGAMs can be tailored to resist incident wave reflection. As these materials do not exist naturally, they must be fabricated by gradually layering manufactured, resulting in a (usually smooth) variation of properties. Validating material properties of FGAMs is difficult with conventional tests, as the distribution of material properties over the layered structure results in a non-unique solution if typical data (e.g., compressive strain) is measured. This talk will demonstrate an approach to characterize the functionally graded material properties by parameterizing how the functionally graded material changes throughout the specimen. Experiments designed to minimize the uncertainty surrounding the FGM model parameters are formulated and evaluated numerically. The FGM model parameters are estimated by Markov chain Monte Carlo so that a probability distribution surrounding each pa...