Measurement of phase velocity in the functionally graded concrete systems via improved higher-order shear deformation theory

Abstract The measurement of phase velocity (PV) in concrete systems is critically important for civil engineers as it provides essential insights into the material properties and structural integrity of concrete. PV, which refers to the speed at which a wave phase propagates through a medium, is directly related to the stiffness and density of the material. By accurately measuring PV, civil engineers can assess the quality and homogeneity of concrete, detect potential flaws, and predict the material’s behavior under various load conditions. This information is crucial for ensuring the safety and durability of concrete structures, from bridges and buildings to pavements and dams. Moreover, understanding PV helps in the optimization of mix designs and the development of new, advanced concrete materials, ultimately leading to more resilient and cost-effective construction practices. For this issue, in this work, for the first time, the measurement of PV in the concrete doubly curved panel reinforced by graphene oxide powders (GOPs) via improved higher-order shear deformation theory is presented. Hamilton’s principle and analytical method are used for extracting and solving the higher-order equations. Finally, some recommendations for improving the efficiency and stability of the concrete structures are presented for related engineering industries. The findings underscore the potential of combining state-of-the-art theoretical models with cutting-edge material reinforcements to push the boundaries of structural engineering and material performance.