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Aerospace Engineering

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#### 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.

#### Structural wave propagation and sound radiation study through time and spatial processing

This work explores new usages of experimental and analysis tools to study the relationship between the wave propagation and sound radiation in a structure with inhomogeneities. The focus of the research is to develop and test new and merged techniques. The analysis tools used in the research include: time domain analysis, k-space analysis, and wave speed tracking. With the time domain analysis, one can study the response of any synthetic excitation with only one set of experimental data. The k-space analysis provides insight into locating areas on a vibrating structure that radiate sound to the acoustic farfield. The wave speed tracking technique was developed to estimate the phase speed of propagating waves in a structure. In addition, the reflection coefficient of a boundary can be computed from the wave speed tracking results. The chirp signal, used in the experiments, provides a concentrated power signal which can excite every mode in the interested frequency range. In addition, the transient property of the chirp signal also provides information in the time domain. A very consistent experimental setup and a repeatable experimental procedure were designed and tested to minimize the errors caused by the setup or mishandling of the equipment;A plate equation with a spatially distributed stress was used to model a structure with inhomogeneities. The results of simulations show that the spatially distributed stress can change the amplitude and wavenumbers of the waves in the plate. A HY-80 steel beam with a T-bar welded to it was investigated experimentally with the proposed tools. The T-bar shows a significant contribution to the radiated sound power, and the existence of the T-bar decreases the phase speed of the propagating waves around the T-bar by 4% to 7%. The heat treatment did not have much influence on the sound radiation or wave phase speed change in this study. The experimental results have proven that the proposed techniques are very useful in the study of wave propagation and sound radiation for structures.

#### Determination of secondary sources in noise cancellation with boundary element method

The direct boundary element method is proposed in this thesis to solve acoustic radiation problems as well as to achieve regional noise cancellation in half space with uniform finite impedance over the surface. The boundary integral equation and half space Green's function were derived to accomplish these goals. Those formulations were verified by comparing numerical simulations with theoretical solutions as well as experimental results. In addition, the above formulations were extended to achieve regional noise cancellation in half space by applying the boundary element method;Two methods were investigated to obtain noise cancellation in desired regions. They are the iterative control method and the coupled equation method. A set of Fortran programs including discretizing of geometries, incorporating boundary integral equations, and accommodating the noise cancellation technique were developed. Various problems concerning ill-conditioned matrices in numerical simulation and practical application of noise cancellation technique were discussed as well. Finally, data banks for various configurations of sound sources were set up for quick reference of the locations and driving functions of secondary sources. Thus, noise reduction in a designated area is shown to be feasible;A 6" speaker was used to simulate a noise source with uniform surface velocity. In addition, a ribbed aluminum plate with the dimension 71.12cm x 60cm was used to simulate a noise source with variable surface velocity. Four 10" speakers were used as secondary sources to achieve noise reduction in desired regions at certain frequencies. A multi-channel digital/analog converter was used in order to control desired driving functions for each individual secondary sources. The computer-controlled scanning system including a 2-channel controller, 2-D scanner, and stepping motors was used to place a quarter-inch microphone at certain locations. The acoustic pressure on a 120cm by 120cm plane at various distances above the source plane was measured. A Bruel and Kjaer model 2032 FFT analyzer was used to acquire and process signals from the microphone. The experimental results agreed well with numerical simulations. This indicated that the proposed noise cancellation technique attenuated the acoustic noise level successfully.

#### 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.

#### 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.