Background <p>Diaphragm couplings have small axial and bending stiffness, which can absorb axial, radial, and angular misalignment of the shaft system. Therefore, they are commonly used in equipment with foundation deformation such as aircraft engines, helicopters, and ships. As a key component of the coupling, the performance of the diaphragm determines the performance of the coupling.</p> Purpose <p>Under the same structural dimensions, using the graphene nanoplatelets (GPLs) reinforced composite with functional gradients as diaphragm materials can improve the stiffness of the coupling, reduce membrane disk stress, and also generate new dynamic characteristics of the coupling. Therefore, further research is needed on the dynamic characteristics of the coupling.</p> Methods <p>In this article, the GPLs reinforced composite flexible coupling containing multiple diaphragm model is established. The bending-swing-axis coupling dynamics model was established by Finite element method, Lumped-parameter method and Lagrange method. The Runge-Kutta method is used to solve the coupling dynamic response. Based on the dynamics model of the flexible diaphragm, the effects of different GPL weight fractions and non-inertial frame angular velocity on the vibration characteristics of the diaphragm coupling are examined.</p> Results <p>The research shows that due to the influence of the non-inertial frame, the rotation of the platform will lead to the axial and radial coupling of the stiffness matrix and damping matrix of the rotor system have a certain impact. With the increase of GPL content in the diaphragm coupling, the natural frequency of the coupling increases, the axial resonance region shifts to the right, and the resonance peak value increases. In the case of low speed, the content of GPL in the diaphragm coupling increases, which can reduce the vibration response amplitude of the diaphragm coupling, and reduce the vibration trajectory and offset of the shaft center. The larger the non-inertial system lateral angular velocity, the more obvious the effect. However, when the GPL content in the diaphragm coupling is large, the increase of the vertical angular velocity of the non-inertial system will cause the vibration of the diaphragm coupling to appear chaotic in advance.</p> Conclusions <p>The findings from this study shows that GPLs reinforced composite can expand the operating speed range of couplings below the critical speed and have smaller vibration amplitudes. The research provides a certain theoretical and reference basis for the application of GPL reinforced composites in flexible diaphragm couplings.</p>