Choudhary, FarhanFree 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.ThesisEngineering, MechanicaldynamicsFree Piston Stirling EngineHopf bifurcationlimit cyclemulticylindernonlinear