An interesting stability property, as fascinating as that of spinning tops and gyroscopes, is observable in the motion of an unbalanced ring spinning on a rough horizontal surface. An analytical and numerical study is performed to investigate the general motion of an unbalanced ring modeled as a thin ring with a particle attached to its rim. The translational motion is represented by the rectangular coordinates of the ring geometric center. The rotational motion is represented by a 1-2-3 set of Euler angles. The kinetic motion equations are derived with the use of Newton's second law and Euler's rotational motion equations. The types of motion considered are the pure-rolling and rolling-with-slipping motions. Given favorable initial conditions, ring properties, and a sufficiently large constraint force in the form of friction, the ring undergoes a pure-rolling motion. For other conditions, however, limitations on the magnitude of the friction force render the pure the mathematical model to allow switching from pure-rolling to rolling-with-slipping motion and vice versa. The general motions of the unbalanced ring, obtained by numerically integrating the governing equations with the use of the seventh-eighth order Runge-Kutta method, are in very good qualitative agreement to those observed during an experiment performed with the use of a high-speed video camera. / Master of Science

Dropped objects are among the top ten causes of fatalities and serious injuries in the oil and gas industry. Objects may be dropped during lifting or any other offshore operation. Concerns of health, safety, and the environment (HSE) as well as possible damages to structures require the prediction of where and how a dropped object moves underwater. This study of dropped objects is subdivided into three parts. In the first part, the experimental and simulated results published by Aanesland (1987) have been successfully reproduced and validated based on a two-dimensional (2D) theory for a dropped drilling pipe model. A new three-dimensional (3D) theory is proposed to consider the effect of axial rotation on dropped cylindrical objects. The 3D method is based on a modified slender body theory for maneuvering. A numerical tool called Dropped Objects Simulator (DROBS) has been developed based on this 3D theory. Firstly, simulated results of a dropped drilling pipe model using a 2D theory by Aanesland (1987) are compared with results from 3D theory when rolling frequency is zero. Good agreement is found. Further, factors that affect the trajectory, such as drop angle, normal drag coefficient, binormal drag coefficient, and rolling frequency are systematically investigated. It is found that drop angle, normal drag coefficient, and rolling frequency are the three most critical factors determining the trajectories. In the second part, a more general three-dimensional (3D) theory is proposed to physically simulate the dynamic motion of a dropped cylindrical object underwater with different longitudinal center of gravity (LCG). DROBS has been further developed based on this 3D theory. It is initially applied to a dropped cylinder with LCG = 0 (cylinder #1) falling from the surface of calm water. The calculated trajectories match very well with both the experimental and numerical results published in Aanesland (1987). Then DROBS is further utilized to simulate two dropped cylinders with positive LCG (cylinder #2) and negative LCG (cylinder #3) in Chu et al. (2005), respectively. The simulated results from DROBS show a better agreement with the measured data than the numerical results given in Chu et al. (2005). This comparison again validates and indicates the effectiveness of the DROBS program. Finally, it’s applied to investigate the effects of varying LCG on the trajectory and landing points. Therefore, the newly developed DROBS program could be used to simulate the distribution of landing points of dropped cylindrical objects, as is very valuable in the risk-free zone prediction in offshore engineering. The third part investigates the dynamic motion of a dropped cylindrical object under current. A numerical procedure is developed and integrated into Dropped Objects Simulator (DROBS). DROBS is utilized to simulate the trajectories of a cylinder when dropped into currents from different directions (incoming angle at 0o; 90o; 180o; and 270o) and with different amplitudes (0m/s to 1.0m/s). It is found that trajectories and landing points of dropped cylinders are greatly influenced by currents. Cylinders falling into water are modeled as a stochastic process. Therefore, the related parameters, including the orientation angle, translational velocity and rotational velocity of the cylindrical object after fully entering the water, is assumed to follow normal distributions. DROBS is further used to derive the landing point distribution of a cylinder. The results are compared to Awotahegn (2015) based on Monte Carlo simulations. Then the Monte Carlo simulations are used for predicting the landing point distribution of dropped cylinders with drop angles from 0o to 90o under the influence of currents. The plots of overall landing point distribution and impact energy distribution on the sea bed provide a simple way to indicate the risk-free zones for offshore operation.

With the aim to understand the synergistic roles played by kinematics, aerodynamics, and inertia in flapping wing maneuvers, this thesis first investigates the plunging motion of a simple flat plate as it is a fundamental motion in the kinematics of many flying animals. A wide range of frequency (k) and amplitude (h) is investigated to account for a robust kinematic characterization in the form of plunge velocity (kh). Leading Edge Vortices (LEVs) are found to be responsible for producing thrust while Trailing Edge Vortices (TEVs) produce drag. The vortex dynamics becomes nonlinear for higher kh and three main vortex-vortex interactions (VVI) are identified in the flow-field. To estimate the sole effect of LEVs on thrust coefficient, TEVs are eliminated by introducing a splitter plate. This resulted in reduced non-linearity in VVI and facilitated a parametrization of aerodynamic thrust coefficient with key kinematic features, frequency (k) and amplitude (h) [C_T= A.k^1.4 h-B where A and B are constants]. This is followed by investigating the more direct problem of bio-inspired MAV research – the interplay of kinematics, aerodynamics, and inertia on maneuvering bat flights. At first, an ascending right turn of a H. pratti bat is investigated to elucidate on the kinematic features and aerodynamic mechanisms used to effectuate the maneuver. Deceleration in flight speed, an increase in flapping frequency, shortening of the upstroke, and thrust generation at the end of the upstroke is observed during this maneuver. The turn is initiated by the synergisytic implementation of roll and yaw rotation where the turning moments are generated by drawing the inside wing closer to the body, by introducing phase lags in force generation between the two wings and by redirecting force production to the outer part of the wing outside of the turn. Upon comparison with a similar maneuver by a H. armiger bat, some commonalities as well as differences were observed. This analysis was followed by a comparative study among different maneuvering flights (a straight flight, two ascending right turns, and a U-turn) in order to establish the complete motion dynamics of a maneuver in action. The individual effects of aerodynamics and wing inertia for maneuvering flights of a H. armiger and H. pratti are investigated. It is found that for both, translation and rotation the overall trajectory trend is mostly driven by the aerodynamic forces and moments, whereas inertial effects drive the intricate intra-cycle fluctuations as well as the vertical velocity and altitude gain during ascent. Additionally, inertial moments play a dominant role for effecting yaw rotations where the importance of the Coriolis and centrifugal moments increase with increasing acuteness of the maneuver, with the largest effect of centrifugal moments being evidenced in the U-turn. / Doctor of Philosophy / The study of flapping wing is of paramount interest in the field of small aerial and aquatic vehicle propulsion. The intricate mechanisms acting behind a flapping wing maneuver can be explained by the synergistic roles played by 3 main components; details of the wing motion or the kinematics, how the air reacts to the wing motion or the aerodynamics, and the effort or force required to move the wings or wing inertia. This dissertation systematically reports the contribution of these components to a flapping flight maneuver. At first, the plunging motion of a simple flat plate is investigated as it is a fundamental motion in the flapping flight of many flying animals. A wide range of frequency and amplitude is investigated and their effect is characterized by a single parameter called "plunge velocity". It is found that, the resultant flow field becomes disorderly for higher plunge velocities which can be characterized by three different types of vortex interactions. The observed results facilitated a robust parametrization of aerodynamic thrust production with key kinematic features, frequency and amplitude. After this, the dissertation focuses on the bio-inspiration aspect of flapping flight by investigating the interplay of kinematics, aerodynamics, and inertia of maneuvering bat flights. At first, an ascending right turn of one species (H. pratti) is investigated to elucidate on the kinematic features and aerodynamic mechanisms used to effectuate the maneuver. Some characteristic features observed are – lowering of flight speed, increase in flapping rate, shortening of upstrokes, and generation of a forward force at the end of the upstroke. It is observed, that the bat turns by using synergistic body rotations in multiple directions which are effected by various techniques such as - drawing the wing inside the turn closer to the body, and changing the timing and location of the forces produced between the two wings. Upon comparison with a similar maneuver by a H. armiger bat, some commonalities as well as differences were observed in the maneuver mechanisms. This analysis was followed by a comparative study among different maneuvering flights (a straight flight, two ascending right turns, and a U-turn) to establish the complete motion dynamics of a maneuver. The individual contributions of aerodynamics and wing inertia for maneuvering flights of a H. armiger and H. pratti are investigated. It is found that for both, translation and rotation the overall trajectory is mostly influenced by the aerodynamic forces and moments, whereas inertial effects are responsible for trajectory fluctuations during a flapping cycle as well contributing to altitude gain during ascent for the H. armiger bat.