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Aerospace Engineering

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#### Solution of viscous flow problems by using the boundary element method

A scheme based on the Boundary Element Method (BEM) for solving the problem of steady flow of an incompressible viscous fluid is presented in this thesis. The problem is governed by both Navier-Stokes (N-S) equations and the continuity equation. The fundamental solution of the two-dimensional N-S is derived, and the partial differential equations are converted to an integral equation;The computer code is flexible enough to handle a variety of boundary and domain elements with different degrees of interpolation polynomial. Boundary and domain integrals over corresponding elements are evaluated analytically. The Newton Raphson iteration scheme accompanied by a relaxation factor is used to solve the nonlinear equations. The code includes a post processor that calculates the velocity components at any point inside the domain;The scheme has been applied to three test problems. The first concerns Couette flow, which has been used as a test case for testing the rate of convergence and accuracy. The second and the third concern the driven cavity and the flow in a stepped channel, respectively;In the integral equation formulation, the primary unknowns are tractions on the domain boundary and velocities in the interior. Because the shear stress, drag, and lift can be simply computed from the values of tractions along the boundary, such a formulation is markedly superior to either the finite-difference or the finite-element formulation. In customary pressure-velocity or streamfunction-vorticity formulations, employed in the finite-difference or finite-element methods, calculation of stress, drag, and lift involves extensive postprocessing.

#### The effect of rib attachment properties on structural acoustics

Sound Pressure measurements were taken of several 2.44m long thin beams which had 0.635cm wide t-ribs centered on them. The beams were excited by a chirp signal with the frequency range of 500Hz to 1500Hz. Two rib attachment methods were used on the beams. One group of beams were machined out of thick stock to the geometry of a rib welded to a beam to ensure that the rib and attachment were one continuous media. The other group of beams had ribs that were welded on. Fillets from the welding process were subjected to heat-treatment and machining to determine the effect of static stress in fillets. Farfield sound radiation from the beam and phase speeds of waves propagating through the beam were used to investigate the effects of the rib and its attachment properties on the beam response;The experimental results showed that the geometry and stress state of the attachment are the main parameters that alter wave propagation and sound radiation. Also, the maximum sound radiation from the rib was not centered directly over the rib, but rather ahead of the rib location. Furthermore, substantial phase speed increases were observed around the shaker location and the rib location;Attachment geometry and stress information were incorporated into a Euler-Bernoulli wave-based model. This wave-based model reproduced the static stress effect on the farfield sound radiation, but didn't reproduce the position of the sound radiation from the rib nor the experimental phase speed increases around the shaker or rib locations;An energy-based model was derived that included the geometry of the rib and attachment. The model used the Extended Hamilton's Principle. Cubic spline weighting functions were applied via Galerkin's method of weighted residuals. This energy-based model did reproduce both the position and the magnitude of the peak in the sound radiation field from the rib. It also reproduced the phase speed increases around the shaker and the rib locations.

#### Application of the boundary element method to coupled fluid-structure interaction problems

The direct boundary element method (BEM) is used to formulate and numerically simulate the interaction of acoustic waves with submerged elastic structures and subsequently specialized to model finite beam transmission through locally curved elastic surfaces. These are structural-acoustic or fluid-solid interaction problems coupling scalar (acoustic) and vector (elastic) media. The problem is formulated in the frequency domain and modelled in three dimensions, and the elasto-acoustic phenomenon described by the acoustic and elastodynamic boundary integral equations (BIE) with pressure and displacement serving as the primarily variables;The general problem deals with a closed solid domain surrounded by an unbounded fluid medium so that with the well known radiation condition, the integral formulation requires modelling only the fluid-solid interface. This formulation is valid for both the exterior scattering/radiation behavior and the field transmitted into the elastic domain. A FORTRAN program (FS3D) was developed and implements the BEM approach using point collocation and isoparametric quadratic shape functions and provides pressure and displacements on the surface of the structure. The code includes separate acoustic and elastic post-processors to generate the far-field fluid pressure and the transmitted interior elastic displacements. Incident wave or the acoustic source is arbitrary but is normally taken to be either a plane or spherical wave or a bounded beam of any given form. The accuracy of the BEM approach is tested for simple shapes like spheres, spheroids and cylinders. Examples illustrate the structural response and acoustic field due to solids of different elastic properties and fluids of different impedances;The capability developed for the general problem is extended to a specific application, namely the reflection and transmission of an ultrasonic beam through an open interface. Wave mechanics of this type is an important part of nondestructive ultrasonic immersion testing where the interface is the surface of the component being probed. That surface, if locally flat, can be modelled as a flat half-space or it might have local curvature. Infinite domains, under certain assumptions, are readily approximated with an easy modification of the BEM formulation. The formalism is verified by an exact analysis of a Gaussian beam transmitted through a flat interface and by studying the ability of the solutions to satisfy the elastodynamic reciprocity relations for concave and convex interfaces;Various features of the coupling phenomenon and the BIE formalism are discussed, including instability of the coupled matrix at special eigenfrequencies (fictitious eigenfrequencies). The accuracy to be expected in a scattering problem at or near these frequencies is investigated and illustrated for the case of an elastic sphere in a fluid. Surface wave phenomenon encountered during non-normal incidence on an interface is also analyzed and various aspects of their modelling discussed.

#### Vibrational and acoustic response of ribbed plates

A self-consistent mathematical formulation, using the Fourier transform method and a direct Gaussian numerical integration scheme, is developed and verified for analysis of both vibrational and acoustic responses of infinite submerged ribbed plates. Further steps developed from standard theories make structural intensity, acoustic intensity, and acoustic power calculations possible in the nearfield and farfield, and are demonstrated in this work;The direct numerical integration scheme adopted to obtain responses has proved to be straightforward and reliable. Although the double integration expression in some responses makes the technique infeasible, a practical way to overcome that difficulty is demonstrated using a standard branch-cut integration to eliminate one integration step analytically. The model and numerical scheme readily allow investigation of additional interesting topics, like the passband and stopband characteristic and the mode localization phenomenon that are observed in ribbed structures. Furthermore, an extension to comprehension of the mechanisms that generate the mode localization phenomenon on disordered structures has been realized;A secondary effort examines natural modes of vibration and acoustic radiation for finite stiffened multiple-span beams with the efficient transfer matrix method. This model shows that the mode localization phenomenon exists on disordered stiffened beams both under free-free and hinged-hinged end conditions. The sensitivity of the response to attachment disorder (perturbations in rib stiffness and location) has also been examined. An elaborate vibrational and acoustic experiment has been carried out on a baffled, stiffened, two-span, hinged beam to examine the existence of the localized modes and verify the predicted acoustic responses. Moreover, the radiation efficiency of finite beams has been investigated for comparison of the radiation behavior presented by the different stiffened beam arrangements;A thorough investigation of mode localization, frequency passbands and stopbands, structural and acoustic intensities and radiated acoustic power is presented for analysis of submerged infinite ribbed plates, with variable rib materials geometry and spacing (periodic and non-periodic). A second investigation of localized natural modes is demonstrated for analysis and experiment of finite stiffened beams in air.

#### Numerical solution of inverse problems in nondestructive evaluation using the boundary element method and multivariate adaptive regression splines

Flaw identification is an important inverse problem that underlies techniques for nondestructive evaluation (NDE). In this study, a known steady state thermal field is used to identify multiple flaws in a material. The problem is to determine locations and sizes of the multiple flaws if the number of flaws and the temperature at certain probe locations on the boundary are known. The boundary element method (BEM) is used as a computational tool in this task;Earlier work in this area has dealt with the case of a single flaw, while we address the case of multiple flaws. The identification of the multiple flaws is difficult because it is impossible to identify the disturbances caused by each individual fLaw; As a result, the iterative methods, used in the single flaw identification, typically fail to converge unless approximate locations of the multiple flaws are known;In our method, the characterization of flaws is performed in two stages. First, the specimen probe data is compared with a set of known cases of probe data (training set) to predict the approximate locations and sizes of the multiple flaws. Second, the final prediction of flaws is determined using a nonlinear optimization method;To prepare the training set, we need only the information of a single flaw of fixed size at various locations. The superposition principle and a special scaling are used to create the multiple flaws information. This procedure is developed as an extension of the theory of potential flows in fluid mechanics. The distinguishing feature of this technique is that only a small training set is stored in the memory;In this study, the final characterizations are made by two different methods. One of them is an iteration method, which minimizes an error functional. The other is called the multivariate adaptive regression splines (MARS). Various test cases yielded excellent solutions. The tolerance of both methods to experimental errors is also discussed. It is found that the iterative method performs better than MARS.

#### Numerical investigation of Type II non-Newtonian de/anti-icing fluid effects on take-off performance for general aviation aircraft

Ground icing, while preventable with glycol based freezing point depressant fluids, accounts for nearly 40-50 civil accidents a year according to one account. More viscous than Type I fluids, Type II fluids are inherently non-linear in their shear stress-rate of strain relationship having smaller relative viscosity at higher shear rates. The non-linearity makes properly scaled wind-tunnel testing difficult and computational methods are employed in this study to look at the aerodynamic effects of the deicing fluid on global performance during typical take-off maneuvers for general aviation. The method is tested on a two-dimensional NACA 0012 airfoil under typical take-off simulation parameters;A modified PANEL method arrives at potential flow solutions which account for the accelerating freestream, rotation maneuver, and shed vorticity while time-dependent Boundary Layer equations are solved using an implicit finite difference scheme. Viscid-inviscid interaction is accomplished in an inverse method through the specification of normal velocities induced on each panel during potential flow calculations to account for displacement thickness effects. Deicing fluid motion is driven by shear stresses at the interface of the fluid and gas-dynamic boundary layer and pressure gradients based on the outer flow solution. Slip velocities and shear stresses are then matched at the interface to insure kinematic and dynamic continuity. The displacement thickness effect of the deicing fluid is accounted for in the viscid-inviscid interaction;The deicing fluid is assumed Newtonian in this study and exhibits a fluid bucking effect which may point to reasons for reported losses in lift. The large shear stresses toward the leading edge drag the fluid to the center of the airfoil while large pressure gradients in the back push the fluid to the center. The buckling phenomena is shown to be brought on by (1) increased fluid viscosity, (2) deeper initial depths of deicing fluid and (3) higher rotation speeds where shear stresses and pressure gradients are larger. In simulations which did not exhibit fluid buckling, the effect on maximum lift coefficient was found to be minimal. The current programming is not equipped to handle this aspect of fluid stability and remains an issue for further investigation.

#### Effects of stinger axial dynamics and mass compensation methods on experimental modal analysis

A longitudinal bar model that includes both stinger elastic and inertia properties is used to analyse the stinger's axial dynamics as well as the mass compensation that is required to obtain accurate input forces when a stinger is installed between the excitation source, force transducer, and the structure under test. Stinger motion transmissibility and force transmissibility, axial resonance and excitation energy transfer problems are discussed in detail;Stinger mass compensation problems occur when the force transducer is mounted on the exciter end of the stinger. These problems are investigated theoretically, numerically, and experimentally. It is found that the measured Frequency Response Function (FRF) can be underestimated if mass compensation is based on the stinger exciter-end acceleration and can be overestimated if the mass compensation is based on the structure-end acceleration due to the stinger's compliance. A new mass compensation method that is based on two accelerations is introduced and is seen to improve the accuracy considerably. The effects of the force transducer's compliance on the mass compensation are also discussed;A theoretical model is developed that describes the measurement system's FRF around a test structure's resonance. This model shows that very large measurement errors occur when there is a small relative phase shift between the force and acceleration measurements. These errors can be in hundreds of percent corresponding to a phase error on the order of one or two degrees. The physical reasons for this unexpected error pattern are explained. This error is currently unknown to the experimental modal analysis community;Two sample structures consisting of a rigid mass and a double cantilever beam are used in the numerical calculations and experiments.

#### Modeling of ultrasonic scattering experiments with applications to system and transducer characterization

The voltage signal output by the receiver electronics, which represents the observable quantity in an ultrasonic scattering experiment, is written as a product, in the frequency domain, of two factors: the system efficiency and the scattering coefficient. The system efficiency represents the combined electrical properties of both the generator and receiver electronics and is a function of frequency only. The scattering coefficient represents the acoustic nature of the experiment (the radiation, propagation, scattering and reception of ultrasonic waves) and depends on the distributed field properties of the transducers involved and their locations and orientations, on the number and type of scattering obstacles and their locations and orientations, on the acoustic properties of the media through which the waves travel, and on the nature and shape of any interfaces through which the waves pass. Based on a generalized principle of electroacoustic reciprocity, formulae are developed for the evaluation of the scattering coefficient. The most general of these involve an integration over either the volume or the surface of the scattering obstacle. More specific formulae are also developed which express the scattering coefficient in terms of either the spherical wave transition matrix or the plane wave scattering amplitude of the obstacle;In order to demonstrate the use of the formulae developed, the calculation of the scattering coefficient is considered for two common ultrasonic scattering experiments. The first experiment involves the pulse-echo scattering from an infinite, flat elastic plate immersed in water. This arrangement is often used for the measurement of the velocity and attenuation of elastic waves, and also as a reference experiment for the determination of the system efficiency. The second experiment involves the pulse-echo scattering from an elastic sphere immersed in water. Particular attention is given to the specular reflection component of the scattering, which is demonstrated to be approximately equivalent to a point measurement of the pressure field radiated by the transducer. This approximation is subsequently used as the basis for obtaining experimental data for transducer characterization. The characterization itself is based on expanding in a set of basis functions, each weighted by an unknown coefficient, the normal velocity profile across the plane flush with the face of the probe. Values for the coefficients are obtained by determining the best fit between the experimental pressure data and the pressure calculated from the assumed velocity profile. Results are presented for two commercially manufactured immersion transducers, one planar (unfocused) and the other focused.

#### A three-dimensional, dynamic model of the human body for lifting motions

Lower back pain is prevalent in society and manual lifting has been linked as one potential cause of these types of injuries. Therefore, the 3dLift biomechanical model was developed in this research with the goal of quantitatively analyzing lifting motions. The model divided the body into fifteen segments that were connected by fourteen anatomical joints. During experimental trials, a volunteer subject lifted an object using four different lifting combinations: symmetric leglifts, asymmetric leglifts, symmetric backlifts, and asymmetric backlifts. In order to individualize the 3dLift model, anthropometric parameters were estimated using measurements taken on the subject. During the lifting trials, the subject wore reflective markers placed on anatomical landmarks, the motions of which were tracked by five video cameras. The subject also stood with each foot on a separate force platform that was used to determine ground reaction forces and centers of pressure. Signal processing methods were utilized to predict the marker positions that were obscured during the lifting trials, and digital filtering was implemented to attenuate noise in the data. After reducing the experimental errors, the segment coordinate axes, Cardan angles, joint center positions, and mass center positions were calculated. The changes in the segment orientations with respect to time were then analyzed to determine the three-dimensional kinematics of the segments. Anthropometric, video, and force platform information were combined in equations of motion that were derived to predict the forces and moments occurring at the joints during the lifting motions. A lower body formulation was developed that started with the measured ground reactions at the feet and proceeded through the segments to the T10/T11 intervertebral joint. Similarly, an upper body formulation was derived that began with a known lifted load at the hands and continued through the segments to the same T10/T11 intervertebral joint. While predicting joint forces and moments, the two formulations also served as a means of validating the 3dLift model by comparing the results at the T10/T11 joint. While there is much work yet to be done in this research area, the 3dLift model takes the first steps by developing a systematic methodology for studying lifting motions.

#### Development of an acoustic microscope to measure residual stress via ultrasonic Rayleigh wave velocity measurements

High stress in a crucial instrument part can cause failure. Stress detection is one of the aims of nondestructive testing. The velocity change of acoustic waves can be used to detect stress in a material. An acoustic microscope is an instrument which induces and detects acoustic waves and in one mode of operation, is able to measure the velocity of acoustic surface waves. It does this over a very small area and is capable of high spatial resolution;One of the challenges in the measurement of stress is the achievement of high spatial resolution. Since the stress induced velocity shifts are generally small (~0.01%), the required precision of time and distance measurements can be quite high for the short propagation distances required for high spatial resolution. The goal of this dissertation is to measure residual stress via the acoustic wave velocity with spatial resolution on the order of one millimeter or less;There are many types of acoustic waves. The type of interest here are surface waves known as Rayleigh waves. The velocity of these waves are determined by time and distances measurements. The high precision necessary leads to many complications in the measurements. These are described and, for a few cases, overcome;The sound velocity in a material can be used to describe material characteristics other than stress. The instrument was used to measure the velocity of Lamb waves on freestanding diamond films. The possibility of using these velocity measurements as a method of characterizing the diamond films is explored. Attempts at using the acoustic microscope on a variety of materials with a large range of Rayleigh wave velocities led to the discovery of surface waves following the second and third front surface reflections between the lens and the surface of the sample. The explanation of these surface waves and their uses are described;Velocity measurements were made on a sample of silicon carbide during loading in an attempt to measure applied stress. Shifts in the velocity were observed but were not reproducible. The problems with these measurements are described and some possible causes given.

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