# Browsing by Author "Bliss, Donald B"

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Item Open Access Analytical Models for the Structural-Acoustic Response of Elastic Barriers Subject to Acoustic Forcing(2019) Villa, MauricioAnalytical models are developed for the structural-acoustic response of flexible panels to obliquely incident, planar harmonic acoustic waves. These models provide a detailed understanding of the complex effects of structural discontinuities on the reflection and transmission from both isolated and periodically connected panels bounded by two fluid half-spaces. This investigation demonstrates that boundaries and spatial discontinuities redirect part of the structural energy into reverberant structural waves having flexural wavenumbers different from the oblique wave forcing, creating deviations from specular reflection. The dominant mechanisms that characterize the acoustic scattering from the vibrating panels depend on the Mach regime of the structure-to-fluid in vacuo wave speed ratio. Super-critical reverberant flexural waves act as surface radiators that result in pronounced radiation lobes centered at the Mach Angles with localized spreading. The scattering from baffled sub-critical panels exhibit directivities that can be predicted by distributions of acoustic edge radiators, with significant energy redistribution occurring at structural resonances. These insights are both derived from and used to refine the analytical models developed for membranes and 2D plates.

The periodically connected panels interfaced with discrete discontinuities, and modeled by various boundary conditions, are analyzed with the method of Analytical Numerical Matching (ANM). The method is advanced to more efficiently model the influence of the structural discontinues and it is demonstrated that it improves the numerical accuracy and convergence rate of the structural-acoustic response. The ANM approach includes a novel way to handle difficulties associated with coincidence frequencies. The periodic configuration exhibits acoustic cut-off and a finite set of radiation angles dependent on structural and fluid properties.

In the pursuit of models suitable for broadband energy intensity based methods, radiation models for the baffled finite panels are developed by approximate means. The dominant effects of the fluid loading are characterized and introduced as modifications to the in vacuo flexural wavenumber of the structures. Simple, closed-form, far-field acoustic intensity directivity patterns and the corresponding power spectrums are analytically expressed for high frequencies. These approximate models are compared to the periodic configuration, and exhibit considerable agreement for limited fluid loadings and boundary conditions that eliminate structural coupling across bays. The approximate sub-critical models are refined using insight from the radiation mechanisms to improve the agreement to the periodic panels.

An exact benchmark solution for the structural-acoustic response of the acoustically driven baffled finite structure over a full range of parameters is developed and interpreted utilizing a new approach which is largely analytical. This hybrid modal-analytical solution is developed for homogeneous Dirichlet boundary conditions, and then generalized to arbitrary impedance conditions by isolating the influence of the boundaries. In addition to their availability for quantitative use, the benchmark solution offers a high degree of physical insight, and is used for verification and refinement of the approximate high frequency methods developed. Remarkable agreement between the approximate high frequency models and the benchmark solutions is demonstrated for both light and heavy fluid loading cases.

Item Open Access Modeling of High Frequency Broadband Acoustic Fields Inside Cylindrical Enclosures Using an Energy Intensity Boundary Element Method(2018) Raudales, DavidHigh frequency broadband acoustic fields inside three-dimensional enclosures are modeled through an energy-intensity boundary element method (EIBEM). Derived from first principles, this novel approach uses uncorrelated and spreading energy sources as building blocks to solve for steady state interior mean-square pressure distributions. The enclosure boundary is replaced with a distribution of energy intensity sources and discretized into constant strength radiating panels. The directivity function of the radiating panel is expanded into a series of half-space orthogonal spherical harmonics that accounts for both diffuse and specular reflections. Energy transfer between boundary panels and interior sources are formulated into an influence matrix that satisfies the prescribed reflecting boundary conditions and is inverted to solve for the panel powers. The diffuse solution is straightforward while the specular solution is computed through an iterative Lagrangian optimization technique.

Refinements to the energy method are introduced to model reflections in enclosures with more generalized geometries. These include a numerical quadrature scheme which uses interpolating polynomial functions to approximate panel interactions, along with a boundary panel image source procedure for improving specular convergence. The new energy method is verified with a benchmark solution in three rectangular enclosures and compared against a more exact EIBEM algorithm developed specifically for rectangular geometries. The absorption scaling solution, which decomposes the mean-square pressure response into a power series that scales with the average room absorption, is formulated through the panel influence matrices and is shown to produce quick and accurate diffuse solutions for various levels of absorption.

Once verified in a well-understood rectangular geometry, the energy method is then applied to model mean-square pressure fields inside cylindrical enclosures. The curved boundary is discretized into trapezoidal energy intensity panels and examined for its effect on panel radiation. An analytical benchmark solution is derived for a cylindrical enclosure with rigid flat end caps and a uniform impedance assigned to the cylindrical wall. Through an innovative approach which combines a linear image source array with a modal scattering decomposition, the pressure field is solved at a given frequency which is then numerically band averaged to obtain the broadband solution. Results are computed for both a high and low aspect ratio cylindrical enclosure with an interior dipole source. Excellent agreement is observed when compared with the specular EIBEM solution for three different absorption cases at various trajectories, however the diffuse solution is found to produce substantially incorrect pressure distributions which do not capture the specular focusing effects of the curved geometry.

The EIBEM is also experimentally verified inside of a large cylindrical tank with absorption placed along the cylindrical wall in the form of modular absorbing panels. A custom-built broadband source with monopole and dipole configurations is placed inside the tank and used to generate the steady state response. The normal incidence reflection coefficients of the absorbing materials are measured through both an impedance tube and a free-field panel method. Interior sound pressure levels are recorded along an axial trajectory for six different one-third octave bands ranging from 3kHz to 10kHz, and are compared with the diffuse and specular EIBEM results for an equivalent enclosure. Comparison of the experimental pressure levels for different center frequencies reveals the transition from the mid frequency region to the uncorrelated high frequency limit which produces smooth mean-square pressure variations that show agreement with the diffuse EIBEM predictions.

Item Open Access Modeling Specular and Diffuse Reflection Sound Fields in Enclosures with an Energy-Intensity Boundary Element Method(2011) Michalis, KristaSteady-state sound fields in enclosures, with specular and diffuse reflection boundaries, are modeled with a first-principle energy-intensity boundary element method using uncorrelated broadband directional sources. The specular reflection field is represented by a limited set of spherical harmonics that are orthogonal on the half-space. The amplitudes of these harmonics are determined by a Lagrange multiplier method to satisfy the energy conservation integral constraint. The computational problem is solved using an iterative relaxation method starting from the 3-D diffuse reflection solution. At each iteration, directivity harmonics are estimated by post-processing and the influence matrix is refined accordingly. For internal sources, simple first reflection images improve accuracy with virtually no penalty on computation time. Monotonic convergence occurs in relatively few relaxation steps. Extrapolating to an infinite number of boundary elements and iterations gives very accurate results. The method is very computationally efficient. Results are compared to exact benchmark solutions obtained from a frequency-by-frequency modal analysis, and a broadband image method, demonstrating high accuracy. The method of absorption scaling is verified for complicated 3-D cases, and showing that the spatial variation in rooms is largely determined by source position and the relative distribution of absorption, but not the overall absorption level.

Item Open Access Reflection and Transmission of Oblique Acoustic Waves by a Sub-Critical Elastic Barrier with Discontinuities Using Analytical Numerical Matching(2017) Villa, MauricioThis work focuses on developing models for the coupled structural-acoustic vibration of boundaries that reflect and transmit sound. First, the case of a infinitely long, fluid-loaded, sub-critical membrane that is periodically fixed and forced by oblique incident acoustic waves is considered. The method of Analytical Numerical Matching (ANM) is applied and extended to deal with the resulting phase-shifted periodic forcing. The high resolution content of the solution near the constraints is analytically treated with a polynomial known as the Local Solution. The remaining, rapidly converging, part of the solution is treated modally and is known as the Global Solution.The Composite ANM Solution is then determined for the motion of the structure, and the far-field acoustic fields can be described. It is shown that the use of ANM effectively addresses the sensitivity of the acoustic fields and structure motion to the accuracy of which the local region near the structural discontinuities is resolved. The use of ANM is extended to demonstrate a method to deal with the mathematical difficulty of acoustic coincidence.The second part of this thesis presents ongoing work on the development of a model for a finite membrane in an infinite baffle. Corrections to the in-vacuo structural wavenumber are developed to model the additional inertance and dissipative effects of the surrounding fluid mediums. The resulting dissipated energy as a function of frequency of the modified finite membrane is compared to energy radiated of the infinite, periodically fixed, fluid loaded membrane to motivate further refinements of the finite model.

Item Open Access Rotor Vibration Reduction Using Multi-Element Multi-Path Design(2013) Su, KeyeMulti-Element Multi-Path (MEMP) structural design is a new concept for rotor vibration reduction. This thesis explores the possibility of applying MEMP design to helicopter rotor blades. A conceptual design is developed to investigate the MEMP blade's vibration reduction performance. In the design, the rotor blade is characterized by two centrifugally loaded beams which are connected to each other through linear and torsional springs. A computer program is built to simulate the behavior of such structures. Detailed parametric studies are conducted. The main challenges in this thesis involve the blade hub load vibration analysis, the blade thickness constraint and the blade parameter selection. The results show substantial vibration reduction for the MEMP design but the large relative deflection between the two beams, conceptualized as an internal spar and airfoil shell, remains a problem for further study.

Item Open Access Vibration Transmission Reduction Through Multi-Element Multi-Path Structural Design in Thin Beams and Cylindrical Shells(2015) Raudales, DavidUnwarranted vibrations create adverse effects that can compromise structural integrity, precision and stability. This thesis explores an attenuation technique that rethinks the design of simple lightweight flexible structures, providing an alternative to the current methods of active controllers and heavy damping. Through multi-element/multi-path (MEMP) design, a structure is divided up into several constituent substructures with separate, elastically coupled, wave transmission paths that utilize the inherent dynamics of the system to achieve substantial wide-band reductions in the low frequency range while satisfying constraints on static strength and weight. Attenuation is achieved through several processes acting in concert: different subsystem wave speeds, mixed boundary conditions at end points, interaction through elastic couplings, and stop band behavior. The technique is first introduced into thin beams coupled with discrete axial and torsional springs, resulting in wide-band attenuation and agreement between analytical simulations and experimental studies. MEMP design is then implemented into concentric thin cylindrical shells, providing a more three-dimensional study with axially discrete azimuthally-continuous elastic connectors. By employing a modal decomposition of the governing shell equations, simulations reveal more opportunities for attenuation when subjected to various forcing conditions. Future work examines the effect of MEMP shell design on acoustic scattering reduction.