The general solution was obtained for the free flexural vibrations in the plane of a thin circular ring containing a point mass. As a degenerate case of the general solution, the solution for a uniform ring alone was derived from the general solution by taking the point mass to be zero. Numerical calculations of the frequencies and mode shapes of the first and second flexural modes were made for values of the point mass in the range from zero to infinity. The results are presented in graphical form. The predominant feature of the investigation was the difference in frequency and mode shape found in the symmetrical and antisymmetrical modes, and the particular orientation of the nodes with respect to the point mass. It was noted that similar phenomena were observed experimentally for vibrations of imperfect bodies of revolution. In conclusion, it was brought out that a ring with a point mass offers a convenient mathematical model for a preliminary theoretical investigation of the vibrations of imperfect bodies of revolution. / Master of Science

Results are presented of an experimental and analytical study of the longitudinal vibrational response of a modified Agena-B vehicle. The empty, unpressurized vehicle was excited with sinusoidal loads and the response was measured through a frequency range including the first two classical longitudinal. modes of the structure. Non-axisymmetric shell response (shell vibration modes) was noted extensively during the experimental tests. Comparison of the analytical and results indicates that a one-dimensional analytical model gave good results in comparison with experimental results. / Master of Science

The wake of a bluff body is a representative issue in vortex dynamics that plays a central role in civil engineering, ocean engineering and thermal engineering. In this work, a flowing soap film was used to investigate the wakes of multiple stationary circular cylinders and of a single oscillating cylinder. Corresponding computer simulations were also conducted. Vortex formation of a stationary circular cylinder was analyzed by proper orthogonal decomposition (POD). The POD analysis was used to define an unsteady vortex formation length, which suggests a relationship between the vortex formation length of a single cylinder and the critical spacing of two cylinders in a tandem arrangement. A systematic parametric study of the wake structure was conducted for a controlled transversely oscillating cylinder. Neural network and support vector machine codes assisted the wake classification procedure and the identification of boundaries between different wake regimes. The phase map of the vortex shedding regimes for the (quasi) two-dimensional experiment qualitatively agrees with previous three-dimensional experiments. The critical spacings of two identical tandem circular cylinders in a flowing soap film system were determined using visual inspections of the wake patterns and calculations of the Strouhal frequencies. The dimensionless spacing was both increased and decreased quasi-statically. Hysteresis was observed in the flow patterns and Strouhal numbers. This study appears to provide the first experimental evidence of critical spacing values that agree with published computational results. The wake interaction between a stationary upstream circular disk and a free downstream circular disk was also investigated. With the ability to tie together the wake structure and the object motion, the relationship between energy generation and flow structure in the simplified reduced order model system was studied. The research results find the optimal efficiency of the energy harvesting system by a parametric study. / PHD / The wake of a bluff body is a classic issue in vortex dynamics that has been the subject of much research in civil engineering, ocean engineering and thermal engineering. Bluff bodies, especially circular cylinders, can be found extensively in heat exchangers, cooling systems and offshore structures. Flow-induced vibration of a bluff body due to the formation of a wake is an important problem in many fields of engineering. Flow-induced vibration determines the oscillation of flexible pipes that transfer oil from the seabed to the surface of the ocean, for example [71]. In civil engineering, flow-induced vibration affects the design of bluff structures in wind such as bridges, chimneys and buildings [62]. Flow-induced vibration caused by vortices being shed from a bluff body is also a promising way to extract energy from geophysical flows [10]. FIV energy harvesting systems are especially suitable for slow flow speeds in the range 0.5-1.5m/s which cannot be efficiently harvested by traditional hydroelectric power technologies. When a pair of tandem cylinders is immersed in a flow, the downstream cylinder can be excited into wake-induced vibrations (WIV) due to the interaction with vortices coming from the upstream cylinder. In this work, a flowing soap film was used to investigate the flow-induced vibration of the downstream cylinder of a tandem pair. With the ability to tie together the wake structure and the object motion, we investigate the relationship between energy generation and flow structure in the reduced order model system. The research results find the optimal efficiency of the energy harvesting system by a parametric study. To get deep physical understanding of the flow-induced vibration, wake structures of a circular cylinder undergoing controlled motion and the critical spacing of two identical tandem circular cylinders were also investigated in this research. These research results can help not only the optimization of energy harvesting systems based on flow-induced vibration of the circular-cylinder system, but also will benefit the understanding of wake interactions between multiple bluff bodies such as schooling fish, natural draft cooling towers and wind turbine farms.

This work investigates the use of multi-degree of freedom (MDOF) passive and active vibration absorbers for the control of structural vibration as an improvement to conventional single degree of freedom (SDOF) vibration absorbers. An analytical model is first used to compare passive two degree of freedom (2DOF) absorbers to SDOF absorbers using point impedance as the performance criterion. The results show that one 2DOF absorber can provide the same impedance at two resonance frequencies as two SDOF absorbers for equal amounts of total mass. Experimental testing on a composite cylindrical shell supports the assertion that a 2DOF absorber can attenuate two resonance frequencies. Further modeling shows that MDOF absorbers can utilize the multiple mode shapes that correspond to their multiple resonance frequencies to couple into modes of a distributed primary system to improve the attenuation of structural resonance. By choosing the coupling positions of the MDOF absorber such that its mode shape mirrors that of the primary system, the mass of the absorber can be utilized at multiple resonance frequencies. For limited ranges of targeted resonance frequencies, this technique can result in MDOF absorbers providing attenuation equivalent to SDOF absorbers while using less mass. The advantage gained with the MDOF absorbers is dependent on the primary system. This work compares the advantage gained using the MDOF absorbers for three primary systems: MDOF lumped parameter systems, a pinned-pinned plate, and a cylindrical shell. The active vibration absorber study in this work is highly motivated by the desire to reduce structural vibration in a rocket payload fairing. Since the efficiency of acoustic foam is very poor at low frequencies, the target bandwidth was 50 to 200 Hz. A 2DOF active vibration absorber was desired to exhibit broad resonance characteristics over this frequency band. An analytical model was developed to facilitate the design of the mechanical and electrical properties of the 2DOF active vibration absorber, and is supported by experimental data. Eight active vibration absorbers were then constructed and used in a multiple-input multiple-output (MIMO) feed-forward control system on a mock payload fairing under high level acoustic excitation. The results show significant levels of global attenuation within the targeted frequency band. / Master of Science

No description available.

Modern lightweight floor systems are susceptible to annoying vibrations induced by the forcing action of human locomotion. This investigation considered several experimental methods to reduce unwanted floor motion as well as analytical procedures aimed at a better understanding of the phenomenon. A series of test floors were designed and constructed expressly for vibration experiments. Various viscoelastic treatments and second mass damper devices were applied to each test floor and the resulting reduction of vibration tendency was measured. These results are compared and the best-performing treatments and devices are discussed and investigated in detail. The relationship of frequency ratios of structural components was investigated analytically and reasonable design precautions necessary to avoid beating vibrations are discussed. A mathematical model of the forcing function of human locomotion is presented, as well as its implications for statistically-based design criterion. Finally, recommendations for future research are discussed based on the experimental and analytical results of the investigation. / Master of Science

A theoretical method for extracting the rotational degrees of freedom from a reconstructed three-dimensional velocity field has been developed. To extract the angular velocities the curl of the translational velocities must be performed. The three-dimensional velocity field is to be equally spaced so that the DFT-IDFT technique of taking partial derivatives of the translational velocities is used. A program was written in C along with MATLAB® which performed the theoretical calculations. Two proposed methods of experimentally verifying the angular velocity data is developed using a Kistler translational/angular piezobeam accelerometer to compare against the DFT-IDFT partial derivative technique for calculating the angular velocities. / Master of Science

The purpose of this research is to analyze a new type of vibration isolator consisting of two pre-bent struts which are clamped at both ends and intermediately bonded with a viscoelastic filler. The proposed isolation device has the ability to support a relatively large static load with little deflection and offers a low axial resistance under dynamic excitation, making it ideal for isolating vertical vibrations. In this research, four of these vibration isolators are used to support a rigid, square plate. The symmetric case is analyzed first. Then the plate has a center of mass which is located at some distance from the geometric center of the plate. When the system is subjected to vertical harmonic base excitations, this eccentric weight introduces rotational as well as vertical motions of the plate. This research will investigate the effects of various eccentricities on the efficiency of the vibration isolators in the configuration described. The displacement transmissibility will be the measure of the isolators' effectiveness at mitigating vibrations transmitted from the base to the rigid plate. For each case, the nonlinear equilibrium equations and the governing equations of motion for small vibrations about equilibrium are numerically solved, and the transmissibility is calculated and plotted over a wide range of frequencies. These plots are used to recognize ranges of frequencies for which isolation is achieved and frequencies at which resonance occurs in the system. At the resonant frequencies, the physical behavior of the system is analyzed to determine the types of vibration modes which occur in the system. A free vibration analysis is also performed to obtain a better understanding of resonances in the system. / Master of Science

This study evaluates the vibration isolation effect of various mounting systems in a heavy freight locomotive cab, and provides an analytical method for the prediction of structural vibration. The cab is set up in a controlled laboratory environment in a manner similar to the installation on a locomotive. Field measurements are used to emulate actual vibration input to the cab structure. A 16-channel data acquisition system is used to collect vibration data at various points on and inside the cab structure. The cab was isolated from the sill structure through six elastomeric mounts fixed at the base of the cab and at the crash posts. The mounts at the base were selected such that they support the static weight of the cab and offer good lateral and longitudinal stability. Two cylindrical elastomeric mounts were placed between the cab structure and the crash posts which attach to the front of the sill structure. Upon establishing the baseline for laboratory vibration measurements and correlating them with field data, acceleration data was collected at discrete locations, both inside and outside of the cab. The data was used in conjunction with an analytical formulation to generate vibration approximations of the discrete locations. To validate the analytical approximations, experimental results were compared with the analytical predictions using simulated field input to the cab The test results from the analytical model approximations proved to have a strong correlation with experimental results. Vibration approximations of locations outside the cab had a higher correlation to the experimental data than the points on the inside. Although the model did not yield exact results for several positions inside the cab, it resulted in several recommendations for future work. / Master of Science

This thesis investigates the damping effects of a metamaterial, on structural vibration, by inducing periodic voids in the base damping material as opposed to infusing the damping material with other material. Metamaterials have been used previously to improve the damping of vibrational waves and acoustic waves through wave scattering and wave reflection at periodic impedance changes. Impedance changes can occur at both material boundaries and geometric changes of the medium. Impedance changes cause wave scattering, wave reflection, and changing of wave speed. The low frequency region of the vibration spectrum is generally harder to dampen due to the longer wavelengths. By slowing the waves down, the wavelength can be shortened and the viscoelastic material will be more effective at damping the waves. The metamaterial in the thesis has one, two, three, and four periodically located voids in the viscoelastic damping material to determine the effectiveness of the damping compared to the same beam with no damping material applied and the beam covered completely with the standard viscoelastic damping material. This research will include both finite element models of the beam and concept testing to explore the damping effects of the metamaterial. / Master of Science / In the field of mechanical engineering vibrations are one of the main causes of failure of machinery components. Reducing vibrations greatly effects the longevity and effectiveness of a machine. The research in this thesis focuses on how to reduce the vibration in a beam by using a metamaterial. Standard damping materials provide damping, reduction of vibration, at various quantities depending on the frequency and wavelength of the vibrational wave. Metamaterials are particular materials designed to reduce vibration by influencing the physical phenomena of a wave as it travels through the material usually by periodic wave scatters. The metamaterial in this research is designed to slow the flexural waves down, therefore shortening the wavelength, making it easier to dampen the vibration compared to a standard damping material. The damping effectiveness of the metamaterials explored in this research will be quantified via finite element modeling and testing in a laboratory.