Inherent resonance of carbon and graphene-based nanocomposite coupled single-span arch beams

•A novel combination of CNTs, GNPs, and GOPs improves vibration behavior in curved-curved beams, indicating a breakthrough in material engineering.•The application of the GDQ method to complex equations reveals a smart and efficient mathematical approach for composite materials.•A comparison of the RoM and Halpin-Tsai techniques gives insights into frequency behavior, allowing for more educated material selection.•Revealing how beam curvature and nanofiller distribution affect vibration behavior, providing critical insights for personalized design techniques. In recent decades, there has been a significant rise in the utilization of composite materials for various engineering applications. These advanced materials offer the potential to improve the mechanical properties and vibration characteristics of structural components. This particular study is dedicated to enhancing the vibration performance of coupled curved-curved beams that feature a linear elastic mid-layer, achieved through the incorporation of carbon nanotubes (CNTs), graphene nanoplates (GNPs), and graphene oxide powder (GOPs). The governing equations of the system are solved using the generalized differential quadrature (GDQ) method. While previous research primarily focused on the use of CNTs to enhance the vibration behavior of coupled-curved beams, this study delves into the utilization of multiple nanofillers for this purpose. An essential aspect of modeling composite materials lies in determining their equivalent mechanical properties. This research undertakes a comparison between the rule of mixture (RoM) and Halpin-Tsai methods for calculating these properties, revealing that frequencies derived from the RoM method are higher than those obtained through the Halpin-Tsai approach. Additionally, the study highlights that systems incorporating GNPs demonstrate higher frequencies at lower nanofiller volumes, with CNTs and GOPs following in ranking. However, this hierarchy shifts at higher nanofiller volumes. The arrangement of nanofillers within the system is influenced by its boundary conditions, with the curvature of the bottom beam playing a significant role in affecting vibration behavior. Increasing the radius of the bottom beam (R2) leads to higher system frequencies, which subsequently decrease with higher R2 values.