The Kirchhoff model is derived from the vibration problem of stretchable strings. In this paper, we focus on the longtime dynamics of higher-order (m1, m2) - coupled Kirchhoff system with higher-order rotational inertia and nonlocal Damping. We first obtained the state of the model's solutions in different spaces through prior estimation, After obtaining the state of the solutions, we immediately proved the existence and uniqueness of their solutions in different spaces through the Faedo-Galerkin method. Subsequently, we proved their family of global attractors using the compactness theorem. At the end of the paper, we reflected on the subsequent research of the model, which pointed out relevant directions for further research on the model. In this way, we systematically studied the longtime dynamic of higher-order $(m_1,m_2)-$coupled Kirchhoff model with higher-order Rotational Inertia, thus enriching the related conclusions of higher-order coupled Kirchhoff models and laying a theoretical foundation for future practical applications.
MR(2010) Subject Classi cation 35B41,35G31