Vibration of tapered composite driveshaft based on the hierarchical finite element analysis

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. They are also lightweight structures, especially when they are tapered. The design of the driveshaft is based on its fundamental natural frequency, and tapering the driveshaft can substantially improve the value of this natural frequency. In this study, the vibration analysis of the tapered composite driveshaft is carried out using the hierarchical finite element formulation, and for this purpose, the Timoshenko beam theory is used. In addition, the effects of rotary inertia, transverse shear deformation, gyroscopic force, axial load, coupling due to the lamination of composite layers, and taper angle are incorporated in the hierarchical finite element model. The potential energy and the kinetic energy of the tapered composite shaft are obtained, and then the equations of motion are developed using Lagrange's equation. The finite element solution is validated using the approximate solution based on the Rayleigh-Ritz method. A comprehensive parametric study is conducted based on the hierarchical finite element formulation.