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Aerospace Engineering

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#### 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.

#### The effect of stiffener parameters on the farfield sound radiation from composite beams: Experiment and theory

The effects of spatial and material variations on farfield sound radiation from carbon/epoxy composite beams were investigated. Specifically, the geometry of a single stiffener of carbon/epoxy embedded in a beam, periodically spaced stiffeners along the length of a beam, and single stiffeners of different materials embedded in beams were all investigated. Because of a lack of methods to sufficiently model the details of spatially varying material properties, experimental data were used to identify important parameters that needed to be included in a model. Vibration testing was performed for three frequency ranges: 500 Hz to 1500 Hz, 1500 Hz to 2500 Hz, and 2500 Hz to 3500 Hz. The geometry of a single stiffener of carbon/epoxy affected the region of the stiffener that radiated sound. Periodically spaced stiffeners tended to have a global stiffening effect at lower frequencies and to act like individual stiffeners for frequencies where the wavelength is shorter than the stiffener. A stiffener of viscoelastic material reduced the sound power radiated from the region of the stiffener, and stiffeners of other materials radiated sound from the ends of the stiffener. Vibration experiments were performed on fiber-reinforced composite beams to verify a cubic spline based solution of a simple Euler-Bernoulli beam model. The model seemed to accurately predict the shape and location of farfield sound radiation from stiffeners. However, limitations on the available boundary conditions prevented accurate prediction of the magnitude of sound radiation. The model was then used to predict sound radiation from beams with varying stiffener bond lengths and these results were experimentally verified. In general a longer stiffener bond length causes less sound radiation. However, there seems to be a critical length at which the sound radiation reaches a maximum.

#### Scattering investigation based on acoustical holography

The objective of this research is to investigate sound scattering by an object using a two-surface measurement technique that separates the incident field and the scattered field. The separation technique is developed in cartesian and cylindrical coordinates. The decomposition method in the cartesian coordinate system is based on the principle that any wave form can be decomposed into plane-wave components by using a two dimensional spatial Fourier transform. For the cylindrical coordinate system, a two plane separation technique is based on decomposing the sound field into cylindrical waves. Numerical simulations are performed and the effect of various parameters are investigated. Specifically, the distance between two measurement surfaces, the distance between measurement points, and the aperture size are investigated. In addition, experimental studies were conducted inside an anechoic chamber with a baffled loudspeaker as a source, illuminating four different scatterers. The decomposed scattered field is then used to estimate the far-field target strength. The experiments demonstrate the feasibility of the field separation technique.

#### An experimental method for structural intensity and source location

This study investigates the structural intensity and the force distribution function as tools to study vibrating plates. A laser Doppler vibrometer is used in measuring the plate normal velocity for the calculation of the structural intensity and the force distribution function. Several examples show the possibility of locating sources and studying the influence of ribs and damping material attached to the plate surface;There have been many studies on structural intensity. This thesis shows that the differences between two commonly used formulations are the assumptions that are used in deriving the formulas;The force distribution function is introduced in this thesis as an additional tool for source location. From Mindlin's plate motion equation, a force distribution function is solved for based on the measured plate normal velocity (or displacement). It is shown that the force distribution is an effective tool to locate sources;A large part of the dissertation research focused on implementing the experimental determination of the structural intensity and the force distribution function. Since the calculations are implemented in wavenumber domain by Fast Fourier Transform (FFT), signal processing techniques such as windowing and filtering are needed to get reasonable results. The influence of windowing and filtering on the calculation of the structural intensity and force distribution function is studied;The rib and damping material that are attached to plates influence the plate vibration and the energy transmission in the plates. Results show that the rib absorbs the vibrational energy when the vibration waves pass through it. A constraint force is applied by the rib to the plate that restricts the plate vibration. Results also show that the damping material is more effective in absorbing bending and shearing vibration energies than in absorbing twisting energy, and that the damping material does not apply a normal force to the plate.

#### Minimizing the radiated sound power with minimal structural modification

In cases where a structure's excitation cannot be altered, the sound radiation from the structure must be minimized by modifying the structure within given design constraints. This dissertation considers minimizing sound radiated by an existing structure with minimal changes to the structure itself. To accomplish this the sound power radiated by a structure was written as a function of the normal surface velocity using the boundary element method. The feasibility of reducing radiated sound power with small patches of constrained layer damping material is proved. Small patches of constrained layer damping material are placed on the structure to effectively reduce radiated sound using reactive structural shearing intensity. The size, shape, and number of patches is explored. Two gradient methods are then used to minimize sound power radiated by a structure as a function of the area covered by constrained layer damping. The method of simulated annealing was used to minimized sound power as a function of damping patch area in cases where gradient methods proved unsuccessful. Reductions in sound power radiated at a single frequency of over 10 dB were achieved by covering just 1.1 percent of the total structural surface area with constrained layer damping material.