Graduation Semester and Year




Document Type


Degree Name

Doctor of Philosophy in Aerospace Engineering


Mechanical and Aerospace Engineering

First Advisor

Frank Lu


The dynamics of a pulse detonation engine driven linear power generator were studied. For an ideal pulse detonation engine, the thrust generated is in the form of a piecewise function given by the Endo-Fujiwara model. Nonlinear electromagnetic damping is also introduced in the system due to the rare earth permanent magnets present in the linear generator architecture. Various linear generator topologies were studied using static magnetic analysis. Two configurations of a single degree-of-freedom oscillator system, one with a linear spring restoring force and another with geometric nonlinear spring restoring force, were investigated to study any potential advantages of using nonlinear spring restoring force. The governing equations for the coupled system in both cases are nonsmooth, nonautonomous, and nonlinear. As closed-form solutions for the governing equations do not exist, numerical simulations are required to understand the dynamics and power generation characteristics of the system. Special treatment is needed in the neighborhood of the discontinuity hypersurface to locate the discontinuity and continue the integration of the governing equations. The governing equations for two configurations of the coupled pulse detonation engine and linear generator were numerically integrated using adaptive Runge--Kutta method. The power generated using the geometric nonlinear spring was considerably higher compared to the configuration with linear springs for low values of non-dimensional parameter beta. The study of the stability of the coupled system under unsteady and intermittent loading is carried out using a Poincare map and its Jacobians. As the dynamical system is characterized by a multi-segment problem, a Poincare map attached to each discontinuity surface is first generated. Then, using the notions of embedding and projection, a composite differentiable Poincare map is generated and its Jacobian is used to determine the stability characteristics of the coupled system. The results of stability analysis are verified using Lyapunov exponents derived from the time-series simulation data. For all the configurations studied, the maximal Lyapunov exponent approached a value of zero, indicating a critically stable system. In lieu of carrying out numerical simulations for each set of parameter values, bifurcation analysis enables the study of the persistence of periodic solutions under variation of parameters. Using the Poincare maps, Jacobians and continuation methods, a bifurcation analysis was carried out. In all the cases studied, period doubling, and Neimark-Sacker bifurcations were observed. Tangent bifurcation was not observed in any of the cases studied.


Nonlinear dynamics, Pulse detonation engine, Linear power generator


Aerospace Engineering | Engineering | Mechanical Engineering


Degree granted by The University of Texas at Arlington