This paper aims to analyze the forced vibration (FV) behavior of polymer matrix (PM) composite material beams (PMCBs), incorporating functionally graded boron nitride nanotubes (FG-BNNT) and carbon fibers (CF) reinforcements, supported on viscoelastic foundations (VEFs). The PMCBs are subjected to dynamic mechanical loading (DMLs) under various boundary conditions (BCs). The viscoelastic foundations supporting the PMCBs are used to simulate the interaction between the composite beams and their surrounding media. The Visco-Winkler-Pasternak (VWP) elastic foundation model is adopted to represent these foundations. The structural behavior of PMCBs is analyzed based on the first-order shear deformation theory (FSDT). The effective material properties are determined through a combination of the modified Halpin-Tsai model (MHTM), the rule of mixtures (ROM), and a fiber micromechanics method (FMM). The governing equations of motion are derived using Hamilton’s principle (HP) and solved numerically via the finite element method (FEM) combined with the Newmark implicit time integration numerical method (NITINM). After validation studies, parametric analyses are conducted to analyze the impact of multiple factors on the dynamic behavior of FG-BNNT/CF-reinforced PMCBs. This study highlights the vibration behavior of advanced composite structures and their potential use in designing and controlling smart materials and structures.
