| This thesis addresses specific modeling aspects of turboprop engines and ways to reduce and control vibration. Accordingly, three areas are examined: modeling, passive vibration optimization, and active vibration control. A mathematical formulation of a turboprop installation is developed. The proposed model takes into account the rigid body of the engine, the flexibility of the blade, the resilience of the mounting system, and the effects of the aerodynamic forces. By utilizing Lagrange's technique, equations of motion are established. The employment of the Multi-blade Coordinates Transformation eliminates periodic coefficients, which appear in the equations of motion due to blade flexibility. Also, a stability study is performed on the model, and two types of self-excited unstable motion are identified: mechanical instability and whirl flutter instability. Mechanical instability is caused by the coupling of the blades' motions with the transverse vibration of the engine, which transforms rotational energy into unstable vibration; whirl flutter instability emanates from aerodynamic energy being converted into engine lateral vibration.; The design of the engine mounting system is viewed as an optimization problem. A two degrees of freedom model representing the engine and wing dynamics is adopted to determine the best mount stiffness and damping coefficient. The optimization problem is solved analytically by using the frequency response functions of the system. The method seeks to minimize the root mean square of the engine absolute acceleration with respect to the root mean square of the relative displacement. The results, which are presented graphically, facilitate the selection of the optimal mount characteristics when the allowable relative displacement is given. A numerical example demonstrates the optimality of the obtained solution.; In order to expand on the optimization method, a Genetic Algorithm is developed to numerically optimize the mounting system. First, the method is developed for a single degree of freedom model of an engine mount system. Next, the algorithm is extended to the two degree of freedom model of the engine and wing. The results of the GA optimization match the analytical solution.; In addition, this thesis presents a preliminary investigation of the effect of a nonlinear mounting system on the imbalance response of the rotor. The Harmonic Balance and the Averaging method are used to derive a closed form solution of a simplified version of the equations of motion. The influence of the system parameters on the steady state motion is discussed, and the analytical solution is compared to the direct integration of the system equations. The numerical solution reveals the limitation of the presented analytical approach.; An experimental investigation of active vibration control is also carried on a laboratory model of an engine. First, natural frequencies and mode shapes of the apparatus are identified by using modal analysis. Second, the influence of the rotating imbalance on the system response is explored at various rotational speeds. Finally, a direct output feedback active vibration control is implanted. A significant reduction in vibration amplitude is achieved using the MIMO strategy. |
