Elizabeth A. Magliula

Directionality of flexural intensity in orthotropic plates

This work investigates composite plates and their ability to direct flexural intensity, which has important implications for noise and vibration control. It is well known that a composite plate supports a flexural wave whose wavenumber depends strongly on its angle of propagation. This suggests that a composite plate will direct more flexural intensity in some directions than others. The present work considers a thin multi-layered plate in which each layer is constructed from an orthotropic material and has a chosen orientation relative to the other layers. Such an approach may be used to design highly directive structures. An analysis is presented in which a two-dimensional Fourier transform is analytically applied to the equation of motion, yielding algebraic expressions for displacements and stress resultants. Next, a two-dimensional discrete inverse Fourier transform is applied to compute displacements and stress resultants at discrete locations. Flexural intensity is computed at these locations.

Far-field approximation for a point-excited anisotropic plate

An analytic approximation is derived for the far-field response of a generally anisotropic plate to a time-harmonic point force acting normal to the plate. This approximation quantifies the directivity of the flexural wave field that propagates away from the force, which is expected to be useful in the design and testing of anisotropic plates. Derivation of the approximation begins with a two-dimensional Fourier transform of the flexural equation of motion. Inversion to the spatial domain is accomplished by contour integration over the radial component of wave number followed by an application of the method of stationary phase to integration over the circumferential component of wave number. The resulting approximation resembles that of an isotropic plate but involves wave numbers, wave amplitudes, and phases that depend on propagation angle. Numerical results for a plate comprised of bonded layers of a graphite-epoxy material illustrate the accuracy of the method compared to a numerical simulation based on discrete Fourier analysis. Three configurations are analyzed in which the relative angles of the layers are varied. In all cases, the agreement is quite good when the distance between force and observation point is greater than a few wavelengths.

Flexural wave dispersion in orthotropic plates with heavy fluid loading

Orthotropic plates support flexural waves with wavenumbers that depend on their angle of propagation. The present work investigates the effect of fluid loading on this angular dependence, and finds that the effect is relatively small for typical composite plate materials in contact with water. This finding results from an analytical model of the fluid-loaded plate, in which the plate is modeled by classical laminated plate theory and the fluid is modeled as an ideal acoustic fluid. The resulting dispersion relation is a tenth-order polynomial in the flexural wavenumber. Direct numerical solution, as well as analysis at frequencies below coincidence, reveals that the angular dependence of wavenumber is magnified but not significantly distorted by the addition of fluid loading.

Finite element modeling of fluid-saturated metallic foams from micro-computed tomography

Open-cell metallic foams are high stiffness-to-weight cellular materials whose microstructure allows for saturation of viscous liquid. Such a composite has advantages for underwater sound absorption over traditional rubbers due to minimal compression from hydrostatic pressure, composite tunability, and potential for specific gravity less than one. Semi-phenomenological and hybrid numerical models have been shown to predict sound absorption performance of metallic foams, however difficulty arises in determining parameters for the numerical models such as tortuosity, viscous characteristic length, thermal characteristic length, and flow resistivity. Such models also assume that the porous frame is rigid, an assumption valid for only a limited frequency range. In this presentation, finite element models of fluid-saturated metallic foams are created from micro-computed tomography scans and analyzed to determine sound absorption performance. The advantage of this method is that the entire foam microstructure and surrounding fluid can be accurately modeled through a finite element mesh. In addition, experimental measurement of model parameters is not required and the rigid frame assumption can be removed.Open-cell metallic foams are high stiffness-to-weight cellular materials whose microstructure allows for saturation of viscous liquid. Such a composite has advantages for underwater sound absorption over traditional rubbers due to minimal compression from hydrostatic pressure, composite tunability, and potential for specific gravity less than one. Semi-phenomenological and hybrid numerical models have been shown to predict sound absorption performance of metallic foams, however difficulty arises in determining parameters for the numerical models such as tortuosity, viscous characteristic length, thermal characteristic length, and flow resistivity. Such models also assume that the porous frame is rigid, an assumption valid for only a limited frequency range. In this presentation, finite element models of fluid-saturated metallic foams are created from micro-computed tomography scans and analyzed to determine sound absorption performance. The advantage of this method is that the entire foam microstructure a...

Design of tunable acoustic metamaterials using 3D computer graphics

The goal of this work is to investigate how the combination of 3D computer graphics and finite element software can be used to rapidly design materials with tunable properties for noise and vibration mitigation applications. Algorithms and software that create three-dimensional objects, known collectively as 3D computer graphics, are widely used artistically for rendering, animation, and game creation. These approaches allow for the design of complex topological structures such as cellular solids. This presentation describes the use of 3D computer graphics to design cellular structures, which can be imported into finite element software in order to determine effective vibrational properties. This approach is advantageous for several reasons. It allows for quick variation of parameters of cellular solids such as porosity and void fraction. It also is time efficient compared to alternative methods such as performing computed tomography scans on physical samples and analyzing the imaged files. Furthermore, r...

Quiet micro boats: An inexpensive acoustic sensing suite

The Quiet Micro Boat [QMB] is an inexpensive acoustic sensing platform constructed from off-the-shelf hardware and software components to allow for a fleet of acoustic sensors that can be deployed into real-world sensing scenarios at a low cost. The QMBs operate using a Beaglebone Black as a central processor, with jet propulsion generated by bilge pumps for robust ocean operation. Acoustic data are collected through a hydrophone which interfaces with the BBB, and data is centralized using the XBee and Zigbee radio mesh configuration. The talk will focus on the hardware costs and performance, discuss the design cycle and decisions, and feature some of the acoustics projects that have been tested on the devices. [Work sponsored by the Naval Sea Systems Command (NAVSEA) Naval Engineering Education Consortium (NEEC) Contract Number N00174-15-C-0022 and by the Raytheon Advanced Studies Fellowship.]

Digital design of cellular solids for noise and vibration mitigation

Cellular solids are of large interest in structural vibration due to their high strength-to-weight ratio and ability for high energy absorption. This presentation describes concepts for digitally designing cellular solids, and demonstrates the ability of this design method for tuning effective material properties for noise and vibration mitigation applications. The designs can be created by defining a complete topology mathematically or by specifying section cut-outs from a solid host material. The digital designs are then analyzed with finite element software to determine effective material properties. This approach is advantageous because it allows for an automated computer procedure for designing and characterizing materials. In addition, resulting designs can be fabricated through either 3D printing processes or CNC milling. In this presentation, the relationship between geometrical/physical properties and effective static material properties (such as Young’s modulus and Poisson ratio) of cellular sol...

Constitutive laws for the design of metallic foam

Cellular materials have recently found attention in structural applications to buffer impacts and for energy absorption. In order to choose the most suitable cellular material based on its intended application, one must understand its mechanical response either through experimentation and/or modeling. Accurate modeling of the response of a material has many advantages, as it helps avoid extensive experimental laboratory tests and provides a fast and efficient avenue to explore the design space and optimize with a specific intent. The problem solved by the present research is as follows: How does one estimate the foam properties, such as porosity and void fraction, to produce a metallic foam with desired mechanical properties, such as Young’s Modulus and Poisson’s ratio? The solution to this problem is vitally important as it will yield an entirely new class of materials with tunable mechanical properties and dramatically improved shock and crack resistance. Therefore, the present work seeks to develop con...

Fundamental studies of zero Poisson ratio metamaterials

As material fabrication advances, new materials with special properties will be possible to accommodate new design boundaries. An emerging and promising field of investigation is to study the basic phenomena of materials with a negative Poisson ratio (NPR). This work seeks to develop zero Poisson ratio (ZPR) metamaterials for use in reducing acoustic radiation from compressional waves. Such a material would neither contract or expand laterally when compressed or stretched, and therefore not radiate sound. Previous work has provided procedures for creating NPR copper foam through transformation of the foam cell structure from a convex polyhedral shape to a concave “re-entrant” shape. A ZPR composite will be developed and analyzed in an effort to achieve desired wave propagation characteristics. Dynamic investigations have been conducted using ABAQUS, in which a ZPR is placed under load to observe displacement behavior. Inspection of the results at 1 kHz and 5 kHz show that the top and bottom surfaces exper...

Optimal design of composite plates based on wave propagation characteristics

The present work is concerned with the design of composite plates that are optimized with respect to their wave propagation characteristics. For example, one may wish to design a composite plate such that the attenuation of a dominant wave is maximized. The optimization proposed here considers a composite plate with a specified number of layers. The material properties and thicknesses of the layers are considered as optimization parameters and these parameters are typically constrained in some way. For each choice of the optimization parameters, complex wave numbers and their associated wave shapes are calculated by using the semi-analytical finite element method developed by others. This method uses a finite element discretization in the thickness coordinate and a propagating wave solution in the lateral coordinates, resulting in a quadratic eigenvalue problem for the complex-valued wave number of each wave that the plate supports. One then computes a scalar cost function based on the complex wave number...