The low frequency (0-500 Hz) automotive noise and vibration behavior is influenced by the rolling dynamics of the tire. Driven by pressing environmental concerns, the automotive industry has strived to innovate fuel-efficient and quieter powertrain systems over the last decade. This has eventually led to the prevalence of hybrid and electric vehicles. With the noise masking effect of the engine orders being absent, the interior structure-borne noise is dominated by the tire pavement interaction under 500 Hz. This necessitates an accurate estimation of rolling tire dynamics. To this date, there is no direct procedure available for modal analysis of rolling tires with tread patterns under realistic operating conditions. The present start-of-art laser vibrometer based non-contact measurements are limited to tread vibration measurement of smooth tires only in a lab environment. This study focuses on devising an innovative strategy to use a wireless Tire Cavity Accelerometer (TCA) and two optical sensors in a tire on drum setup with cleat excitation to characterize dynamics of tread vibration in an appreciably easier, time and cost-effective approach. In this approach, First, the TCA vibration signal in a single test run is clustered into several groups representing an array of virtual sensor position at different circumferential positions. Then modal identification has been performed using both parametric and non-parametric operational modal identification procedures. Furthermore, relevant conclusions are drawn about the observed modal properties of the tire under rolling including the limitations of the proposed method. The method proposed here, as is, can be applied to a treaded tire and can also be implemented in an on-road test setup. / Master of Science / The low frequency(0-500 Hz) interior noise and vibration of an automobile is primarily influenced by the dynamics of the rolling tire. In recent studies, the laser vibrometer with moving mirrors for measurement of vibration on the tread of a rotating tire has been used. However, these are limited to tires without tread pattern. In this study, an innovative experimental way of performing operational modal analysis using the Tire cavity Accelerometer (TCA) and optical sensors is presented. The proposed method is simpler in terms of instrumentation and cost and time-effective. This method, as is, can also be implemented in case of a treaded tire

The transmission line is an underappreciated style of loudspeaker enclosure characterized by an acoustic labyrinth stemming from the rear of the speaker driver. In practice, the transmission line enclosure produces airy sound uncharacteristic of other styles, at the cost of more pronounced resonant peaks. The most important practical drawback of this loudspeaker enclosure design is the difficulty of properly applying damping to these enclosures. Ideally, this difficulty can be mitigated using an analytical model that accurately predicts the SPL frequency response of a transmission line loudspeaker system for a given geometry and mass of damping material. This research takes the first step towards establishing such a model by developing a limited model for a simple enclosure geometry. Through the application of a modal analysis, this research predicts the frequency response of the enclosure for the first five modes, discusses the effect damping has on this response, and experimentally verifies the produced outputs. For the simplified transmission line enclosure, the developed model successfully predicts the target portion of the frequency response. The model produces accurate results for a range of damping levels using experimentally derived damping ratios for the first five modes. The resulting curves for each modal damping ratio allow for a set of novel damping ratios to be produced from an input mass of damping material. Through this process, an input mass of damping material produces the predicted frequency response for a straight, non-tapered transmission line enclosure. This prediction can make damping a transmission line enclosure much more efficient, allowing for transmission line loudspeakers to be more widely available.

In the present study, the author builds upon the single degree of freedom ice-structure interaction model initially proposed by Matlock, et al. (1969, 1971). The model created by Matlock, et al. (1969, 1971), assumed that the primary response of the structure would be in its fundamental mode of vibration. In order to glean a greater physical understanding of ice-structure interaction phenomena, it was critical that this study set out to develop a multi-mode forced response for the pier when a moving ice floe makes contact at a specific vertical pier location. Modal analysis is used in which the response of each mode is superposed to find the full modal response of the entire length of a pier subject to incremental ice loading. This incremental ice loading includes ice fracture points as well as loss of contact between ice and structure. In this model, the physical system is a bottom supported pier modeled as a cantilever beam. The frequencies at which vibration naturally occurs, and the mode shapes which the vibrating pier assumes, are properties which can be determined analytically and thus a more precise picture of pier vibration under ice loading is presented. Realistic conditions such as ice accumulation on the pier modeled as a point mass and uncertainties in the ice characteristics are introduced in order to provide a stochastic response. The impact of number of modes in modeling is studied as well as dynamics due to fluctuations of ice impact height as a result of typical tidal fluctuations. A Poincaré based analysis following on the research of Karr, et al. (1992) is employed to identify any periodic behavior of the system response. Recurrence plotting is also utilized to further define any existing structure of the ice-structure interaction time series for low and high speed floes. The intention of this work is to provide a foundation for future research coupling multiple piers and connecting structure for a comprehensive ice-wind-structural dynamics model. / Master of Science

A lumped parameter model is developed for the analysis of dynamic fluid systems and the techniques of modal analysis are applied. An introduction to the lumped parameter modeling approach is accomplished by a thorough review of the dynamic mechanical system. This review of mechanical system analysis introduces terms such as the natural frequency, damping ratio and the frequency response function. For the analysis of more complex mechanical systems the topic of modal analysis is introduced. Proceeding in a manner analogous to that of the review of the mechanical system, the lumped parameter fluid model is introduced. This introduction includes the definition of the dynamic fluid properties and two relatively simple examples of how these properties may be used in the modeling of fluid systems. As an example of this method an analytical model is developed for a compressor system and the techniques of modal analysis are applied in a fluid sense. / Master of Science

Experimental modal analysis (EMA) techniques have become a popular method of studying the dynamic characteristics of structures. A survey of literature available reveals that experimental modal models resulting from EMA may suffer from inaccuracy due to a host of reasons. Every stage of EMA could be a potential source of errors - from suspension of the test structures, transduction to parameter estimation phase. Though time-domain methods are actively being investigated by many researchers and are in use, fast Fourier transform (FFT) methods, due to their speed and ease of implementation, are the most widely used in experimental modal analysis work. This work attempts to quantify errors that result from a typical modal test. Using a simple beam with free-free boundary conditions simulated, three different modal tests are performed. Each test differs from the other chiefly in the excitation method and FRF estimator used. Using finite element models as the reference, correlation between finite element and experimental models are performed. The ability of the EMA process to accurately estimate the modal parameters is established on the basis of level of correlation obtained for natural frequencies and mode shapes. Linear regression models are used to correlate test and analysis natural frequencies. The modal assurance criterion (MAC) is used to establish the accuracy of mode vectors from the modal tests. The errors are further quantified spatially (on a location-by-location basis) for natural frequencies and mode shapes resulting from the EMA process. Finally, conclusions are made regarding the accuracy of modal parameters obtained via FFT-based EMA techniques. / Master of Science

The Laser Doppler Velocimetry technique has been widely used for dynamic measurements and experimental modal analysis. A laser scanning system that provides position accuracy, speed, and flexibility plays a key role in this technique. This thesis gives an overview of various laser scanning techniques and the requirements of a laser scanning system for the LDV and modal testing. The G3B/DE2488, a most-advanced galvanometer-based laser scanning system manufactured by the General Scanning Inc., is one of the most suitable laser scanning systems for the LDV and modal testing. The focus of this work was to test and calibrate such a scanning system to meet the requirements for modal testing. A new method to determine laser scanning angles was introduced. Based on this test method, a laser scanning system test rig was designed and constructed. To determine a laser bealTI scanning angle, the laser and scanner together were translated in a direction perpendicular to the target plane by using a micrometerdriven translation stage. The translation of the scanned laser spot at the target plane due to the translation of the laser-scanner unit was traced by a photodetector and another set of micrometer-driven translation stages that moved in the target plane. The laser beam scanning angle was calculated from the traveled distances of the laser-scanner unit and of the laser spot at the target plane. The test setup was used to determine the overall performance of the G3B/DE2488 which included the scanning time and accuracy. The errors that affected the scanning accuracy were analyzed. Due to the relatively low precision and quality of the cost-constrained equipment used in the test setup, the accuracy of determining a scanning angle was not very high (around 50 µrad). However, if some high-accuracy and high-resolution equipment such as a beam profiler and a set of motor-driven stages are used, this test method has the potential to determine a laser beam scanning angle with an accuracy in the order of microradians. / Master of Science

In this thesis, we apply nonlinear Koopman mode analysis to decompose the swing dynamics of a power system into modes of oscillation, which are identified by analyzing the Koopman operator, a linear infinite-dimensional operator that may be defined for any nonlinear dynamical system. Specifically, power system modes of oscillation are identified through spectral analysis of the Koopman operator associated with a particular observable. This means that they can be determined directly from measurements. These modes, referred to as Koopman modes, are single-frequency oscillations, which may be extracted from nonlinear swing dynamics under small and large disturbances. They have an associated temporal frequency and growth rate. Consequently, they may be viewed as a nonlinear generalization of eigen-modes of a linearized system. Koopman mode analysis has been also applied to identify coherent swings and coherent groups of machines of a power system. This will allow us to carry out a model reduction of a large-scale system and to derive a precursor to monitor the loss of transient stability. / Master of Science

Civil infrastructure failure is hard to predict, both in terms of occurrence and impact. This is due to combination of many factors, including highly variable environmental and operational conditions, complex construction and materials, and the sheer size of these structures. Often, the mitigation strategy is visual inspection and regular maintenance, which can be time-consuming and may not address root causes of failure. One potential solution to anticipating infrastructure failure and mitigating its consequences is the use of distributed sensors to monitor the physical state of a structure, an area of research known commonly as structural health monitoring, or SHM. This approach can be applied in a variety of contexts: safety during and after natural disasters, evaluation of building construction quality and life-cycle assessment for performance based design frameworks. In one way or another, SHM methods always require a ``baseline,'' a set of physical features which describes the behavior of a healthy structure. Often, the baseline is defined in terms of modal parameters: natural frequencies, damping ratios, and mode shapes. Although changes in modal parameters are indicative of structural damage, they are also indicative of a slew of non-damage factors, such as signal-to-noise ratio, environmental conditions, and the characteristics of forces exciting the structure. In many cases, the degree of observed modal parameter changes due to non-damage factors can be much greater than that due to damage itself. This is especially true of low-frequency modal parameters. For example, the fundamental frequency of a building is more sensitive to global influences like temperature than local structural changes like a cracked column. It has been proposed that extracting modal parameters at higher frequencies may be the key to improving the damage-sensitivity of SHM methods. However, for now, modal analysis of civil structures has been limited to low frequency ambient excitation and sparse sensor networks, due to practical limitations. Two key components for high-frequency modal analysis have yet to be studied: 1) Sufficient excitation at high frequencies and 2) high-resolution (high sensor density) measurements. The unifying goal of this work is to expand modal analysis in these two areas by applying novel instrumentation and experimental methods to two full-scale buildings, Goodwin Hall and Ernest Cockrell Jr. Hall. This enables realistic, practical insights into the limitations and benefits of the high-frequency SHM approach. Throughout, analyses are supported through the novel integration of uncertainty quantification techniques which so far has been under-utilized in the field. This work is divided into three experimental areas, with approaches centering on the identification of modal parameters. The first area is the application of high spacial resolution sensor networks in combination to ambient vibration testing. The second is the implementation of a robust automation and monitoring strategy for complex dynamic structures. The third is the testing of a novel method for performing experimental modal analysis on buildings emph{in situ}. The combination of results from these experiments emphasizes key challenges in establishing reliable high-frequency, high-resolution modal parameter ``baselines'' for structural health monitoring (SHM) of civil infrastructure. The first study presented in this work involved the identification of modal parameters from a five-story building, Goodwin Hall, using operational modal analysis (OMA) on ambient vibration data. The analysis began with a high spacial density network of 98 accelerometers, later expanding this number to 117. A second extensional study then used this data as reference to implement a novel automation method, enabling the identification of long-term patterns in the building's response behavior. Three dominant sources of ambient excitation were identified for Goodwin Hall: wind, human-induced loading, and consistent low-level vibrations from machinery, etc. It was observed that the amplitude of excitation, regardless of source, had significant effects on the estimated natural frequencies and damping ratios. Namely, increased excitation translated to lower natural frequencies and higher damping. In addition, the sources had different characteristics in terms of excitation direction and bandwidth, which contributed to significantly different results depending on the ambient excitation employed. This has significant implications for ambient-based methods that assume that all ambient vibrations are broadband random noise. The third and final study demonstrated the viability of emph{in situ} seismic testing for controlled excitation of full-scale civil structures, also known as experimental modal analysis (EMA). The study was performed by exciting Ernest Cockrell Jr. Hall in Austin, Texas with both vertical and lateral ground waves from seismic shaker truck, T-Rex. The EMA results were compared to a standard operational modal analysis (OMA) procedure which relies on passive ambient vibrations. The study focused on a frequency bandwidth from 0 to 11 Hz, which was deemed high frequency for such a massive structure. In cases were coherence was good, the confidence comparable or better than OMA, with the added advantage that the EMA tests took only a fraction of the time. The ability to control excitation direction in EMA enabled the identification of new structural information that was not observed OMA. It is proposed that the combination of high spacial resolution instrumentation and emph{in situ} excitation have the potential to achieve reliable high-frequency characterization, which are not only more sensitive to local damage but also, in some cases, less sensitive to variations in the excitation conditions. / Ph. D. / Civil structures, like buildings and bridges, become weaker as they age, increasing their risk of collapse due to sever weather, earthquakes, and heavy traffic. Engineers regularly inspect civil structures to ensure they are in good shape, but it is difficult do a full assessment by eye since many defects can be hidden. Structural Health Monitoring, or SHM for short, is an approach that uses permanent vibration sensors to continuously inspect civil structures. Any activity, like blowing wind or moving traffic on bridge, produces small vibrations which can be analyzed to assess the “health” of the structure. This approach can detect some invisible defects, but there is still debate about whether it can detect them when they are small and early on in the life of a structure. If SHM can’t issue early warnings, then there is little incentive to spend large amounts of money on a sensor system. To capture small defects, a sensor system needs a large number of sensors, hence the term high-resolution in the title. In addition, the structure being tested needs to vibrate rapidly (that is at high-frequencies) in order for the high-resolution information to be useful. So far, there have been no tests of this kind on civil structures, especially buildings. Instead, most sensor systems have contained a relatively low number of sensors tested with low-frequency vibrations. This works fills in this gap by testing two different buildings with SHM sensor systems. The first experiment uses a very high number of sensors to analyze the vibrations of Goodwin Hall on the Virginia Tech campus. The vibrations in this building are produced by wind and people walking inside. The second experiment uses a standard number of sensors, but explores a new method of vibrating buildings. This method uses a truck with a large hydraulic piston to shake the ground near the E. Cockrell Jr. building (University of Austin-Texas), essentially creating a tiny earthquake. The experiments show that both testing techniques provide more useful information than standard ones alone. For the first experiment, using more sensors meant the analysis could better distinguish the structural characteristics of the building. For the second, the artificial “earthquake” enabled the measurement of high-frequency vibrations, something which was not possible by relying on wind or people to vibrate the building. Although these new approaches are not used to inspect for damage, they have laid the foundation for improving the early-warning capabilities of SHM systems. This could mean that buildings and other structures can be repaired sooner, remain in operation longer, and cost the owners less money in the end!

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