Nonlinear vibration study of a rotor blade based on a novel non-polynomial function

Abstract

This work investigates the nonlinear free vibration of a turbomachinery blade, which is idealized as a rotating, conical, twisted shell of varying thickness reinforced with graphene platelets. Using the von Karman type of nonlinearity, the dynamic equilibrium equation for the twisted panel is obtained and solved by finite element method. The impact of the centrifugal force caused by rotation is taken into account, but the effect of the Coriolis force is neglected. The functionally graded twisted tapering conical shell has two alternative ways in which graphene platelets (GPLs) are reinforced in the thickness direction. The rule of mixture and the modified Halpin-Tsai model are used to compute the effective material properties of the twisted shell. The strain displacement relation is based on a new non-polynomial shear deformation theory. The parametric analysis performed at the endshows that nonlinear frequency increases when twist angle, rotational speed, tapper ratio, and weight fraction of GPLs increase. It is also observed that mode shapes are severely impacted by twist angle and rotational speed.