Mathematical modeling and vibration analysis of rotating functionally graded porous spacecraft systems reinforced by graphene nanoplatelets

Abstract

This paper investigates the theoretical modeling and coupled free vibration behaviors of a rotating double‐bladed shaft assembly resting on elastic supports in a spacecraft system. According to the Kirchhoff plate theory and the Euler–Bernoulli beam theory, the theoretical model is established. The presented rotor is considered to be made of porous foam metal matrix and graphene nanoplatelet (GPL) reinforcement. Nonuniform distributions of porosity and GPLs are taken into account, which leads to the functionally graded (FG) structure. The effective material properties of the double‐bladed shaft assembly are varying along the radius and thickness directions of the shaft and blade, respectively. Moreover, the rule of mixture, the Halpin–Tsai model, and the open‐cell scheme are employed to determine its material properties. Considering the gyroscopic effect, the Lagrange equation is utilized to derive the coupled equations of motion. Then the traveling wave frequencies of the double‐bladed shaft assembly are obtained by applying the assumed modes method and substructure modal synthesis method. A detailed parametric analysis is conducted to examine the effects of the rotating speed, GPL weight fraction, GPL distribution pattern, GPL length‐to‐thickness ratio, GPL length‐to‐width ratio, porosity coefficient, porosity distribution pattern, shaft length‐to‐radius ratio, blade length‐to‐thickness ratio, support stiffness and support location on the free vibration behaviors of the double‐bladed shaft assembly.