PhD Oral Exam - Mohsen Najafi, Mechanical Engineering

When studying for a doctoral degree (PhD), candidates submit a thesis that provides a critical review of the current state of knowledge of the thesis subject as well as the student’s own contributions to the subject. The distinguishing criterion of doctoral graduate research is a significant and original contribution to knowledge.

Once accepted, the candidate presents the thesis orally. This oral exam is open to the public.

Abstract

The dynamic behavior and stability of rotating composite shaft–disk systems have received increasing attention due to their widespread application in high-speed rotating machinery such as aerospace driveshafts, turbomachinery, energy systems, and advanced mechanical transmissions. The increasing demand for lightweight and high-efficiency rotating components has encouraged the adoption of laminated composite shafts, which provide superior specific stiffness, improved damping characteristics, and extensive design flexibility through material tailoring. However, their anisotropic nature and material coupling mechanisms introduce complex systems that require comprehensive investigation. This thesis presents a comprehensive investigation into the linear, transient, nonlinear and dynamic stability characteristics of spinning tapered composite shaft–disk systems. The research develops advanced theoretical formulations and analytical models to investigate system response during acceleration through first critical speed, nonlinear steady-state dynamics and system stability.

The first phase of this thesis investigates the linear and transient vibration behavior of rotating tapered composite shaft–disk systems during acceleration through the first critical speed. The tapered shaft is modeled using an equivalent single-layer laminated composite formulation based on Timoshenko beam theory, including rotary inertia, transverse shear deformation, and gyroscopic effects. The governing equations of motion are derived using Hamilton’s principle from the kinetic and potential energy expressions of the tapered composite shaft–disk system. The equations of motion are solved using the finite element method employing combined Lagrange–Hermite interpolation functions to ensure displacement and slope continuity along the shaft. The transient response assuming constant angular acceleration is obtained using the Newmark direct time-integration method. The developed formulation is validated through comparison with previously published results and an additional parametric study, confirming the accuracy of the proposed model. A detailed parametric study evaluates the influence of rotational acceleration, taper angle, laminate configuration, fiber orientation, and bending–twisting coupling mechanisms on transient system behavior. The results demonstrate that increasing the angular acceleration drops maximum vibration amplitude during critical speed passage, indicating improved dynamic stability. Tapered composite shafts consistently exhibit higher natural frequencies and lower vibration amplitudes compared with uniform shafts.

The second phase examines the nonlinear forced vibration and stability characteristics of spinning tapered composite shaft–disk systems subjected to an unbalance force. A coupled three-dimensional nonlinear model is developed in which longitudinal, lateral, and rotational motions are derived using Hamilton’s principle. The formulation incorporates geometric nonlinearities, rotational inertia and gyroscopic effects, while shear deformation is neglected. The governing equations are discretized using the Galerkin method and analyzed through the method of multiple scales, allowing analytical characterization of primary resonance, steady-state response, and stability boundaries. Frequency response curves, phase trajectories, and bifurcation diagrams reveal that the system exhibits a pronounced hardening-type nonlinear response. Internal damping acts as the primary destabilizing mechanism in supercritical operation, yet nonlinear hardening stiffness delays the instability threshold and constrains post-resonant vibration growth, producing a stabilizing–destabilizing interaction governing overall dynamics.

The third phase provides a detailed investigation of nonlinear frequency response evolution and laminate-dependent rotordynamic behavior under unbalance excitations. The nonlinear forced vibration of the tapered composite shaft–disk system, incorporating bending–twisting coupling mechanisms, rotational inertia, and gyroscopic effects, is analyzed. A parametric study including taper angle, laminate stacking sequence, fiber orientation, unbalance excitation, and external damping are performed. It has been shown that increasing taper angle substantially enhances both linear and nonlinear stiffness, producing higher flexural natural frequencies. Nonlinear stiffness components associated with torsional and bending–twisting coupling coefficients influence resonance curvature and bifurcation development, particularly under large excitation amplitudes. Linear theory predicts a reduction in vibration amplitude with increased stiffness. In contrast, nonlinear analysis demonstrates simultaneous increases in natural frequency and vibration amplitude due to taper-induced hardening and geometric nonlinear effects.