Vibration analysis of nonuniform hyperboloidal and barrel helices made of functionally graded material

Abstract

This study is in investigation of free vibration behavior of functionally graded hyperboloidal and barrel helices with variable cross section. Material and geometric variations of noncylindrical helices are assumed to be along the rod axis. Governing differential equations of motion, including rotatory inertia, axial and shear deformations are derived by the Timoshenko beam theory. Then, transfer matrix and stiffness matrix methods are employed for the numerical solution of obtained ordinary differential equations. Effects of material gradient index $({\beta }_{\mathrm{mat}}),$ diameter variation parameter $({\beta }_{\text{sec}}$), and ratio of helix radius at end section and middle section $R_2/R_1$ on the natural frequencies are investigated through a parametric study considering barrel and hyperboloidal geometries. Comparisons with available literature studies and ANSYS solutions are made regarding obtained results.

Keywords:

• Functionally graded material
• free vibration
• noncylindrical helix
• variable cross section