Impact of Polymeric Composites on Static and Dynamic Behaviors of Timoshenko Beams Using Spectral and Newmark-\(\beta \) Methods

To address challenges related to optimal shape parameters in various mesh-free methods, this study introduces an efficient and robust mesh-free tool. Unlike other meshless methods, this numerical tool eliminates the need for parametrization and allows for a reduction in the number of nodes, resulting in a substantial decrease in CPU time. Additionally, this paper presents the first analytical-numerical assessment focusing on the vibration of functionally graded-reinforced composite (FG-RC) beams under various boundary conditions. The analytical-numerical approach in this study includes static and dynamic investigations into the behavior of composite beams reinforced with Functionally graded graphene oxide powder (FG-GOP), carbon nanotubes (FG-CNT), and graphene platelets (FG-GPL). The exploration covers a range of boundary conditions, providing a comprehensive analysis of the vibrational characteristics.