This work examines the application of sensor arrays to structures. The wave equation solution of Euler-Bernoulli beam theory provides the structural model for this study. A review of basic array theories for the enhancement of signal-to-noise ratio (SNR) and determination of angle of arrival (AOA) leading to source localization is given. Array techniques are considered with applications to dispersive flexural waves where the propagation velocity is not constant but dependent on frequency. The theory is validated through experiments with harmonic and broad band applications. The test apparatus consisted of a long thin beam with anechoic terminations to emulate an infinite beam for frequencies above 300 Hz and a finite beam below 200 Hz. The beam was excited by a shaker (with a force transducer) mounted on one end of the beam. Measurements were taken with accelerometers and a laser velicometer at the other end of the beam. The infinite beam case was used to isolate the travelling wave response to single harmonic excitation. The finite case was used to consider transient response of the beam to an impulse. The harmonic response experiments on the infinite beam is used to demonstrate two things. First they show that the SNR increases by the square root of the number of sensors. Secondly they show that AOA can be determined explicitly from the phase between sensors for single frequency applications. The measured values of AOA were within ±3 degrees for these experiments. This technique applies to harmonic signals in a highly damped medium. The technique developed for transient applications uses the magnitude and the variance of the correlation coefficient of a densely populated array to determine AOA. This technique is based on correlation between measurements along a wave front. It does not assume a phase relationship between sensors but instead exploits the spread of the signal as it travels. The spread is characteristic of a dispersive medium. This resolution of this technique is directly linked to the population of the array and the angular relationship between elements. The experiments verified that this technique measures the AOA for within the resolution of the array. For arrays from 3x4 to 7x10 resolution of ± 6 to 9 degrees was possible. This work has developed array theory for application to dispersive waves in structures. It highlights the differences in the phase relationship between elements for dispersive versus non dispersive media. It shows improvement of SNR using structural arrays. The potential for AOA determination on highly damped structures using harmonic signals was demonstrated. AOA determination was also shown for finite structures using impact excitation. / Ph. D.

Friction induced vibration of an epoxy coated shaft rotating in an elastomeric bushing is investigated. This study investigates the manner in which system dynamics and friction mechanisms are responsible for friction induced vibration and noise generation. A test method was developed to measure the friction torque and the system and acoustic response of the sliding system. Several materials including a fluorocarbon elastomer, a polydimethylsiloxane, and a natural rubber were tested. Three friction regimes were observed which were stick-slip oscillations, quasi-harmonic oscillations, and steady sliding. System stiffness and load were varied to observe changes in the critical velocities bounding each regime. System parameters were varied to determine sliding conditions leading to self-induced vibration, to establish how the character of vibration is affected, and to correlate friction torque with system and acoustic vibration for each elastomeric material. A two degree-of-freedom, lumped parameter model was developed to simulate the effect of system dynamics on the sliding behavior of the elastomeric bushing. The comparison of simulated and experimental response using analyses in the time and frequency domain indicate the predictive model provides an excellent representation of stick-slip behavior at various operating conditions. / Master of Science

This work discusses the use of Positive Position Feedback (PPF) for Active Vibration Control as part of an Active Damage Control System (ADCS). Vibration control increases the fatigue life of a structure and decreases the in-plane stresses that can cause delamination in a composite. PPF is a collocated direct-output feedback control method that increases the effective damping in a structure. A simply-supported beam was used as the testbed which used strain gages as the sensing element and piezoelectric ceramics as the actuator. Initial investigations into sampled-data systems using PPF are presented. The issues addressed are: stability of the sampled system, the effects of the sampling rate on the system, and degradation from predicted analog performance. A digital design procedure for the tuning filters in the Z-plane is suggested if the sampling rate to be used is known. If the sampling rate varies significantly, to avoid redesigning the filters for each new sampling rate, they should be designed in the continuous-time and transformed to the Z-plane. The Tustin transformation was found to adequately map the poles and zeros of the compensator to the Z-plane for digital control. Experimental implementation of PPF on a simply-supported beam resulted in vibration suppression of three modes with a S180 controller. The beam was subjected to both a single-frequency harmonic disturbance and a broadband harmonic disturbance. One, two, and three-mode controllers were designed with disturbance suppression up to 15dB achieved. / Master of Science

The flexural vibration of two incomplete circular rings, approximately 360º, fixed at one end and free at the other, is investigated. One ring lies in the thin ring range. The other ring lies in the borderline range between a thick and thin ring. A theoretical approach is used in an attempt to approximate the first three natural frequencies of the rings. These theoretical results are then compared with the results obtained from an experimental investigation. In an attempt to simplify the general equation of motion of the ring an assumption was made that the tangential inertia term had a negligible effect on the natural frequencies of a thin ring. The frequencies obtained from the resulting frequency equation were found to be poor approximations for the system. Good approximations were obtained for the first two frequencies of the thin ring, using the method of Rayleigh -Ritz. / Master of Science

The response of one- and two-degree-of-freedom (SDOF and 2DOF) systems with quadratic and cubic nonlinearities to fundamental, principal, and combination harmonic parametric excitations is investigated theoretically and experimentally. The method of multiple scales (MMS) is used to determine the equations that describe to first and second order the amplitude- and phase-modulations with time. These equations are used to determine the fixed points and their stability. The perturbation results are verified by integrating the governing equations on a digital computer. The analytical results are in excellent agreement with the numerical solutions. In the SOOF systems with quadratic and cubic nonlinearities, the large responses that oscillate about three equilibrium positions are investigated on the digital and analogue computers. The analogue computer is used to generate a bifurcation diagram in the excitation amplitude versus excitation frequency domain. The digital computer is used to obtain Poincare maps of strange attractors, to investigate larger amplitude responses, and to show the transition to a fractal basin of attraction. The system exhibits 2T, 3T, 4T, ST, 6T, 7T, 8T, 12T, 16T, and ∞T period-multiplying bifurcations. The response of a flexible cantilever beam with a concentrated mass to principal parametric base excitation of the first bending mode is analyzed theoretically. The model takes into account the geometric nonlinearities due to large displacements. Galerkin's method is used to reduce the fourth-order nonlinear POE to a second-order ODE having periodic coefficients and cubic nonlinearities. The MMS is used to determine steady-state responses and their stability. Experiments are performed on metallic and composite beams; the results show good qualitative agreement with the theory. Chaotic responses are observed in the response of the composite beam. The response of 2DOF systems with quadratic nonlinearities to a combination parametric resonance in the presence of 2:1 internal resonances is investigated using the MMS. The first-order perturbation solution predicts qualitatively the stable steady-state solutions and illustrates the quenching and saturation phenomena. The reduced equations also predict a transition from periodic to quasi-periodic responses (i.e., Hopf bifurcation). 359 pages, 110 figures. / Ph. D.

Submerged turbines which harvest energy from ocean currents are an important potential energy resource, but their harsh and remote environment demands an automated system for machine condition monitoring and prognostic health monitoring (MCM/PHM). For building MCM/PHM models, vibration sensor data is among the most useful (because it can show abnormal behavior which has yet to cause damage) and the most challenging (because due to its waveform nature, frequency bands must be extracted from the signal). To perform the necessary analysis of the vibration signals, which may arrive rapidly in the form of data streams, we develop three new wavelet-based transforms (the Streaming Wavelet Transform, Short-Time Wavelet Packet Decomposition, and Streaming Wavelet Packet Decomposition) and propose modifications to the existing Short-TIme Wavelet Transform. ... The proposed algorithms also create and select frequency-band features which focus on the areas of the signal most important to MCM/PHM, producing only the information necessary for building models (or removing all unnecessary information) so models can run on less powerful hardware. Finally, we demonstrate models which can work in multiple environmental conditions. ... Our results show that many of the transforms give similar results in terms of performance, but their different properties as to time complexity, ability to operate in a fully streaming fashion, and number of generated features may make some more appropriate than others in particular applications, such as when streaming data or hardware limitations are extremely important (e.g., ocean turbine MCM/PHM). / by Randall David Wald. / Thesis (Ph.D.)--Florida Atlantic University, 2012. / Includes bibliography. / Mode of access: World Wide Web. / System requirements: Adobe Reader.

D. Tech. Mathematical Technology. / Investigates hyperbolic and pseudohyperbolic equations and the results are applied to higher-order rod approximations for the propagation of the longitudinal stress waves in elastic rods. The main objectives of this thesis are: 1. Provide a unified approach to the derivation of the families of one-dimensional hyperbolic differential equations simultaneously with the associated natural and essential boundary conditions describing longitudinal vibration of finite length rods. 2. Establish a new theoremto shorten the derivation of equations of motion and the corresponding boundary conditions, modelling longitudinal wave propagation in the rod. 3. Prove that, when deriving the higher-order rod equations, the lower-order are still included, thus increasing the number of deformations in the rod or the accuracy of the model. 4. Provide mathematical tools for the classification of the obtained equations. 5. Compare the accuracy of the above-mentioned vibration theories in elastic rods based on the investigation of their frequency spectrums which are not available in the literature. 6. Show how two of the above vibration theories, the Rayleigh-Bishop and Mindlin-Herrmann theories, can be applied to predict wave propagation in a piezoelectric circular cylinder and isotropic conical rod. In both cases a numerical example is given as a simulation of the solution.7. Find general methods for solving problems of longitudinal vibration of finite length rods for all of the above-mentioned theories.

No description available.

Dynamic instrumentation and a series of ambient vibration tests were performed on a four storey strengthened R/C building within the scope of this study. Traffic load and wind load were accepted as natural dynamic loads and the vibrations were recorded by sensitive accelerometers.For that study, 12 uniaxial, 1 triaxial accelerometers and a 15 channel data logger system were used. Four sets of dynamic measurements were recorded over a period of 6 months. Recorded readings were analyzed using UPC, PC and CVA algorithms and Artemis software. The natural freqeuncies, mode shape of the tested building were determined. The experimental results were compared against each other. A 3D-FE model of the building was prepared and analytical results were also compared against experimental results.The calibration (updating) of the analytical model was carried out using the experimentally obtained mode shapes and freqeunices. The results of the study indicate that first few mode shapes and freqeuncies of the building can be obtained successfully within zero to 10 Hz range using ambient monitoring. Field calibrated FE models can effectively simulate the first translational and torsional modes of the building. Calibration studies indicate that the upper floor is more flexible than the nominal model and there are weaknesses between the shear wall and roof slab connections.

The limiter is a commonly used device in communication receiving systems to remove the amplitude variations of the received signal, but it is usually observed that limiter degrades the envelope detection performance of a single tone. In this thesis, it is demonstrated that the limiter-generated third harmonic can be used to improve the envelope detection performance of a single tone over that of the linearly processed fundamental. Differences in the probability distributions of the limiter-generated harmonics cause differences in their detection probabilities, which lead to differences in the performance of subsequent envelope detection. Comparison of the envelope detection performance of the limiter-generated third harmonic and the input to the limiter shows a maximum detection probability gain of 1.12 and also error probability gain of 2.4 in linear scale, whereas the fundamental harmonic does not show any practically significant gain. The envelope detection performance of the vector sum of the limiter-generated fundamental and third harmonics is also evaluated. This combination provides better performance than do the individual harmonics, especially for a large clipping parameter of the limiter. The combined harmonics shows a maximum detetction probability gain of 1.15 and error probability gain of 14, over that of the envelope detection performance of a tone without limiter. It is also observed that the envelope detection performance of a tone with limiter-generated higher harmonics shows non-monotonic behaviour as functions of either noise or the limiter-clipping parameter, which is a signature of stochastic resonance. The theoretical results from earlier research on the envelope detection of a single tone embedded in additive white Gaussian noise, both with and without a limiter, are presented and shown to match our simulation results. In previous work when a limiter was used in the envelope detection of a single tone, only the envelope of the fundamental harmonic was considered under very specific conditions. By contrast we also take notice of the limiter-generated higher harmonics and obtain improved envelope detection performance in the detection of a single tone.