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 studied rotor is considered to be made of porous
foam metal matrix and graphene nanoplatelet (GPL) reinforcement.
Non-uniform distributions of porosity and graphene nanoplatelets (GPLs)
are taken into account and lead to functionally graded (FG) structures.
The effective material properties of the double-bladed shaft are varying
along the radius and thickness direction of the shaft and blade,
respectively. Moreover, the rule of mixture, the Halpin-Tsai model, and
the open-cell scheme are used 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 is obtained by employing
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.