Vibration

The periodic structures considered in the dissertation are one-dimensional periodic multi-span beams, and two-dimensional periodic grillages with elastic interior supports. The following specific topics are included: (1) Deterministic Vibration--Exact solutions are obtained for free vibrations of both multi-span beams and grillages, by utilizing the wave propagation concept. The wave motions at the periodic supports/nodes are investigated and the dispersion equations are derived from which the natural frequencies of the periodic structures are determined. The emphasis is placed on the calculation of mode shapes of both types of periodic structures. The general expressions for mode shapes with various boundary conditions are obtained. These mode shapes are used to evaluate the exact dynamic response to a convected harmonic loading. (2) Stochastic Vibration--A multi-span beam under stochastic acoustic loading is considered. The exact analytical expressions for the spectral densities are derived for both displacement and bending moment by using the normal mode approach. Nonlinear vibration of a multi-span beam with axial restraint and initial imperfection are also investigated. In the latter case, the external excitation is idealized as a Gaussian white nose. An expression for the joint probability density function in the generalized coordinates is obtained and used to evaluate the mean square response of a multi-span beam system. (3) Convex Modeling of Uncertain Excitation Field--It is assumed that the parameters of the stochastic excitation field are uncertain and belong to a multi-dimensional convex set. A new approach is developed to determine the multi-dimensional ellipsoidal convex set with a minimum volume. The most and least favorable responses of a multi-span beam are then determined for such a convex set, corresponding to a stochastic acoustic field. The procedure is illustrated in several examples.

This study presents and illustrates a methodology to calculate the capacity of an existing reinforced concrete bridge under a non-conventional blast load due to low and intermediate pressures. ATBlast program is used to calculate the blast loads for known values of charge weight and stand off distance. An excel spreadsheet is generated to calculate ultimate resistance, equivalent elastic stiffness, equivalent elastic deflection, natural period of the beam, the maximum deflection, and the maximum rotation in the support for a simple span solid slab and T-Beam bridges. The allowable rotation could be taken as to two degrees. Naval Facility Engineering Command (NAVFAC) approach was adopted, where the inputs were material properties, span length, and area of reinforcement. The use of the Fiber Reinforced Polymer for increasing the capacity of an existing bridge is also presented in this study. Parametric studies were carried out to evaluate the performance of the solid slab and T-Beam bridges under the assumed blast load.

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).

This thesis describes a method to detect, localize and identify a faulty bearing in a rotating machine using narrow band envelope analysis across an array of accelerometers. This technique is developed as part of the machine monitoring system of an ocean turbine. A rudimentary mathematical model is introduced to provide an understanding of the physics governing the vibrations caused by a bearing with a raceway defect. This method is then used to detect a faulty bearing in two setups : on a lathe and in a dynamometer.

This work incorporates previous work done by Guerra and the application of fluid dynamics. The structure attached to the turbine will cause unsteady fluctuations in the flow, and ultimately affect the acoustic pressure. The work of Guerra is based on a lot of assumptions and simplifications to the geometry of the turbine and structure. This work takes the geometry of the actual turbine, and uses computational fluid dynamic software to numerically model the flow around the turbine structure. Varying the angle of the attack altered the results, and as the angle increased the noise levels along with the sound pulse, and unsteady loading increased. Increasing the number of blades and reducing the chord length both reduced the unsteady loading.

This work seeks to understand water turbine noise generation and to make preliminary estimations of the noise levels. Any structure attached to a turbine upstream its blades will generate unsteady fluctuating loads on the blade's surface, which are proportional to the radiated acoustic pressure. The noise levels of a simplified turbine based on existing designs surpass the ambient noise levels of the ocean at low frequencies (< 20 Hz) by approximately 50 dB ref 1 μPa and stay under the ambient noise levels at higher frequencies for a blade-passing frequency of 0.83 Hz and point of observation (100 m, 45 degrees, 45 degrees) from the hub. Streamlining the cross-section of the upstream structure as well as reducing its width decrease the noise levels by approximately 40 dB ref 1 μPa, at low frequencies and moderately increase them at higher frequencies. Increasing the structure-rotor distance decreases the noise levels with increasing frequencies (> 30 Hz).

Natural frequencies of the double and triple-walled carbon nanotubes are determined exactly and approximately for both types. Approximate solutions are found by using Bubnov-Galerkin and Petrov-Galerkin methods. For the first time explicit expressions are obtained for the natural frequencies of double and triple-walled carbon nanotubes for different combinations of boundary conditions. Comparison of the results with recent studies shows that the above methods constitute quick and effective alternative techniques to exact solution for studying the vibration properties of carbon nanotubes. The natural frequencies of the clamped-clamped double-walled carbon nanotubes are obtained; exact solution is provided and compared with the solution reported in the literature. In contrast to earlier investigation, an analytical criterion is derived to establish the behavior of the roots of the characteristic equation. Approximate Bubnov-Galerkin solution is also obtained to compare natural frequencies at the lower end of the spectrum. Simplified version of the Bresse-Timoshenko theory that incorporates the shear deformation and the rotary inertia is proposed for free vibration study of double-walled carbon nanotubes. It is demonstrated that the suggested set yields extremely accurate results for the lower spectrum of double-walled carbon nanotube. The natural frequencies of double-walled carbon nanotubes based on simplified versions of Donnell shell theory are also obtained. The buckling behavior of the double-walled carbon nanotubes under various boundary conditions is studied. First, the case of the simply supported double-walled carbon nanotubes at both ends is considered which is amenable to exact solution.