Theses and Dissertations from UMD
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New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a give thesis/dissertation in DRUM
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Item Dynamics, Nonlinear Instabilities, and Control of Drill-strings(2020) Zheng, Xie; Balachandran, Balakumar; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Drill strings are flexible, slender structures, which are many kilometers long. They are used to transmit the rotary motion to the drill bit in the process of drilling a borehole. Due to the flexibility of the drill string and nonlinear interactions between the drill bit and rock, these systems often experience severe vibrations, and these vibrations may cause excessive wear of the drill bit and equipment damage. The aim of this dissertation effort is to further the understanding of the underlying mechanism leading to the undesired vibratory motions of drill strings, as well as to develop a viable control strategy that is applicable for mitigation of harmful vibrations. A reduced-order drill-string model with coupled axial and torsional dynamics is constructed. Nonlinear effects associated with dry friction, loss of contact, and the state-dependent delay, which all arise from cutting mechanics are considered. For the sake of analyses, a non-dimensionalized form of the governing equations is provided. Next, in order to study the local stability of the drill-string system, a linear system associated with the state-dependent delay is derived. The stability analysis of this linearized system is carried out analytically by using the D-subdivision scheme. The obtained results are illustrated in the terms of stability crossing curves, which are presented in the plane of non-dimensional rotation speed and non-dimensional cutting depth; non-dimensional rotation speed and cutting coefficient, respectively. For the nonlinear analysis, a numerical continuation method is developed and used to follow periodic orbits of systems with friction, loss of contact, and state-dependent delay. Bifurcation diagrams are constructed to capture the possible routes from either a nominal stable operational state or a stable limit-cycle motion without stick-slip to a limit-cycle motion with stick-slip. It is shown that the system can experience subcritical Hopf bifurcations of equilibrium solutions and cyclic fold bifurcations. Furthermore, with the preceding work, an observer-based on controller design is proposed by using a continuous pole placement method for time delay systems. The effectiveness of the controller in suppressing stick-slip behavior is shown through simulations. The primary contributions of this dissertation are summarized as follows: i) analytical determination of the stable operational region; ii) revelation of the routes to torsional stick-slip vibrations; and iii) construction of a feasible control scheme to mitigate the destructive vibrations caused by complex nonlinear effects.Item Linear Stability Analysis Using Lyapunov Inverse Iteration(2012) Wu, Minghao; Elman, Howard; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this dissertation, we develop robust and efficient methods for linear stability analysis of large-scale dynamical systems, with emphasis on the incompressible Navier-Stokes equations. Linear stability analysis is a widely used approach for studying whether a steady state of a dynamical system is sensitive to small perturbations. The main mathematical tool that we consider in this dissertation is Lyapunov inverse iteration, a recently developed iterative method for computing the eigenvalue with smallest modulus of a special eigenvalue problem that can be specified in the form of a Lyapunov equation. It has the following "inner-outer" structure: the outer iteration is the eigenvalue computation and the inner iteration is solving a large-scale Lyapunov equation. This method has two applications in linear stability analysis: it can be used to estimate the critical value of a physical parameter at which the steady state becomes unstable (i.e., sensitive to small perturbations), and it can also be applied to compute a few rightmost eigenvalues of the Jacobian matrix. We present numerical performance of Lyapunov inverse iteration in both applications, analyze its convergence in the second application, and propose strategies of implementing it efficiently for each application. In previous work, Lyapunov inverse iteration has been used to estimate the critical parameter value at which a parameterized path of steady states loses stability. We refine this method by proposing an adaptive stopping criterion for the Lyapunov solve (inner iteration) that depends on the accuracy of the eigenvalue computation (outer iteration). The use of such a criterion achieves dramatic savings in computational cost and does not affect the convergence of the target eigenvalue. The method of previous work has the limitation that it can only be used at a stable point in the neighborhood of the critical point. We further show that Lyapunov inverse iteration can also be used to generate a few rightmost eigenvalues of the Jacobian matrix at any stable point. These eigenvalues are crucial in linear stability analysis, and existing approaches for computing them are not robust. A convergence analysis of this method leads to a way of implementing it that only entails one Lyapunov solve. In addition, we explore the utility of various Lyapunov solvers in both applications of Lyapunov inverse iteration. We observe that different Lyapunov solvers should be used for the Lyapunov equations arising from the two applications. Applying a Lyapunov solver entails solving a number of large and sparse linear systems. We explore the use of sparse iterative methods for this task and construct a new variant of the Lyapunov solver that significantly reduces the costs of the sparse linear solves.Item Dynamics of Free Piston Stirling Engines(2009) Choudhary, Farhan; Balachandran, Balakumar; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Free piston Stirling engines (FPSEs) are examples of closed cycle regenerative engines, which can be used to convert thermal energy into mechanical energy. FPSEs are multi-degree-of-freedom dynamical systems that are designed to operate in a periodic manner. Traditionally, the designed periodic orbits are meta-stable, making the system operation sensitive to disturbances. A preferred operating state would be an attracting limit cycle, since the steady-state dynamics would be unique. In this thesis, it is investigated as to how to engineer a Hopf bifurcation of an equilibrium solution in a FPSE. Through a combination of weakly nonlinear analysis and simulations, it is shown that it is possible to engineer a Hopf bifurcation in a FPSE system. Through the analyses, reduced-order-models are developed on the basis of Schmidt formulations and nodal analysis. This thesis effort could serve as a platform for designing FPSEs which take advantage of nonlinear phenomena in either the beta or double acting alpha configuration.