Abstract

In the aerospace and automotive applications driveshafts are manufactured using fiber reinforced composite materials. Compared to a conventional metallic driveshaft, a composite driveshaft gives higher natural frequencies and critical speeds, and lower vibration. The design of the driveshaft is dependent on its fundamental natural frequency and its first critical speed, and tapering the driveshaft can substantially improve the values of the natural frequency and first critical speed. In this thesis, the rotordynamic analysis of the tapered composite driveshaft is carried out using three finite element formulations: the conventional-Hermitian finite element formulation, the Lagrangian finite element formulation, and the hierarchical finite element formulation. These finite element models of the tapered composite shaft are based on Timoshenko beam theory, so transverse shear deformation is considered. In addition, the effects of rotary inertia, gyroscopic force, axial load, coupling due to the lamination of composite layers, and taper angle are incorporated in the conventional-Hermitian, the Lagrangian, and the hierarchical finite element models. The strain energy and the kinetic energy of the tapered composite shaft are obtained, and then the equations of motion are developed using Lagrange’s equations. Explicit expressions for the mass matrix, the gyroscopic matrix and the stiffness matrix of the tapered composite shaft are derived to perform rotordynamic analysis. The Lagrangian beam finite element formulation has three nodes and four degrees of freedom per each node while the conventional-Hermitian beam and the hierarchical beam finite element formulations have two nodes. The three finite element models are validated using the approximate solution based on the Rayleigh-Ritz method. A comprehensive parametric study is conducted based on the finite element models, which shows that tapering the composite driveshaft can increase considerably the natural frequency and first critical speed, and that they have nonlinear variation with the taper angle.