A Finite Element Approach for Forced Dynamical Responses of Porous FG Nanocomposite Beams Resting on Viscoelastic Foundations

In this paper, a comprehensive dynamical analysis of porous-reinforced carbon nanotube (CNT) nanocomposite beams on viscoelastic foundations is presented. Using a three-unknown shear beam theory, the two-nodded finite element model was formulated and adapted for both [Formula: see text] and [Formula: see text] continuities for displacement variables. This model captured the distinct characteristics and interactions of the porous medium, CNT reinforcements, and the intrinsic damping introduced by the viscoelastic foundation. The dynamical investigation incorporates both free and forced vibration analysis, and the Newmark method is employed for time-dependent analysis, ensuring accurate temporal behavior prediction. The study also emphasizes the impact of different CNT distribution patterns and porosity variations on the mechanical properties of the beams, particularly in terms of stiffness and damping characteristics. Further depth is added by analyzing the interactions between beams and both Winkler and Pasternak foundation models, with findings that highlight the importance of foundation parameters in the overall dynamic response. The results shed light on the critical role each component plays in the composite beam’s dynamic response, offering insights for potential innovative designs and applications in both advanced structural engineering and nanotechnology domains.