This study delves into the vibrational characteristics of concrete annular plates reinforced with graphene oxide powders (GOP), underpinned by an innovative auxetic-elastic foundation. By applying Hamilton’s principle, the governing dynamic equations are meticulously derived, incorporating the effects of internal forces and GOP geometrical properties. The Differential Quadrature Method (DQM) is utilized to solve these equations, providing a robust and efficient numerical approach for analyzing the system’s complex dynamic behavior. GOP reinforcement significantly enhances the mechanical properties of the concrete plates, yielding improved stiffness and superior damping capabilities. The auxetic-elastic foundation, known for its unique property of becoming thicker perpendicular to the applied force, plays a pivotal role in altering the vibrational response of the system. The study meticulously examines the influence of this foundation on the system’s vibrational behavior, highlighting its potential to enhance performance under varying operational conditions. A comprehensive analysis is conducted to understand the effects of different boundary conditions on the vibrational characteristics of the reinforced concrete annular plates. The results underscore the importance of integrating advanced materials like GOP and innovative foundation designs in optimizing structural components. This study provides valuable insights into the design and application of reinforced concrete structures, emphasizing the effectiveness of GOP reinforcement and auxetic-elastic foundations in enhancing vibrational performance. These findings offer a significant contribution to the field of structural engineering, paving the way for future innovations in the design of resilient and efficient structural systems.