Comprehensive Analysis of Static, Buckling, and Free Vibration Behavior of Carbon Nanotube Reinforced Composite Plates on Pasternak's Elastic Foundation

Purpose This paper presents an in-depth analysis of the static, buckling, and free vibration behavior of carbon nanotube reinforced composite (CNTRC) plates resting on Pasternak's elastic foundation. The displacement field for the analysis is formulated using a secant function-based non-polynomial shear deformation theory, which captures the effects of transverse shear deformation more accurately than traditional polynomial-based theories. The governing differential equations are derived using Hamilton's principle and subsequently solved using Navier's solution method for CNTRC plates with simply supported boundary conditions. The novelties of this study include a comprehensive exploration of various parametric conditions, such as different volume fractions and distributions of carbon nanotubes, and variations in the foundation stiffness parameters (shear layer and Winkler modulus), providing deeper insights into the mechanical behavior of CNTRC plates under realistic loading conditions. Methods The study incorporates various parametric conditions, including different volume fractions and distributions of carbon nanotubes, and variations in the foundation stiffness parameters (shear layer and Winkler modulus). The influence of these parameters on the mechanical behavior of CNTRC plates is systematically investigated. Results Results demonstrate the significant impact of the Pasternak's foundation parameters and carbon nanotube reinforcement on the static deflection, critical buckling load, and natural frequencies of the plates. The analysis reveals that an appropriate selection of the foundation stiffness and nanotube distribution can significantly enhance the structural performance of CNTRC plates. Conclusion This research provides valuable insights into the design and optimization of CNTRC plates on Pasternak's foundations, highlighting their potential applications in advanced engineering structures where enhanced mechanical properties and stability are crucial.