Vibration and stability of thin-walled composite shafts of variable cross-section with different end constaints

A dynamic model is proposed to study the vibration and stability of thin-walled composite shafts of variable cross-section with different end constraints. The variational asymptotic method and Lagrange equations are employed to derive the free vibration equations for thin-walled composite shafts of variable cross-section. The structural model of the shafts is developed considering warping effects on the cross section caused by torsion, tension, and bending. Natural frequencies and critical spinning speeds are analyzed by the Galerkin method for tapered shafts having a cross-section varying linearly or parabolically, with the consideration of two types of end constraints, i. e. clamped-free and clamped-hinged support, as well as the effect of the ply angle of the composite laminates. Additionally, the analytical model presented in this work is verified and validated to a decisive extent by comparing its results with those obtained from the commercial finite element software ANSYS.