<p>In the study of complex high dimensional nonlinear systems, the process of simplifying and reducing the order of models inevitably results in the loss of critical nonlinear characteristics. The spectral sub-manifold (SSM) method ensures the preservation of the nonlinear terms of the system when reducing the dimensionality of a high-dimensional nonlinear system to a low-dimensional spectral subspace. In this paper, we propose for the first time to use the SSM method for the dimensionality reduction analysis of a continuous system of the Ring Truss Antenna System obtained by modelling based on the Hamilton principle. The initial step is to construct a parametric mapping of the system, which involves transforming the system’s equations from the rectangular coordinate form to the modal coordinate form. Secondly, the Forced Response(FRC) Curves are plotted based on the reduced system in order to identify the periodic solution of the system and to predict the bifurcation. The location and number of bifurcation points of the system can be directly observed from the FRC. Finally, the computational efficiency of the FRC curves plotted by the SSM method is 10²–10³ times higher than that of collocation methods and harmonic balance approaches. It can conclude that the SSM method is not only an effective method for the dimensionality reduction of high-dimensional nonlinear systems, but also can accurately and efficiently analyse the nonlinear vibration characteristics of the system.</p>