Nonlinear dynamic analysis of the coupling structure between FG-CNTC beams and DVA

Beams, as essential supporting and load-bearing structures in fields such as aerospace and defense, are frequently subjected to complex and variable loads. This often leads to nonlinear vibrations induced by large structural deformations and excessive noise, whereas dynamic vibration absorption provides a viable solution for the safety and comfort design of structures. Aiming to establish an efficient semi-analytical framework for the nonlinear vibration control of advanced composite structures, this study couples a Dynamic Vibration Absorber (DVA) to a Functionally Graded Carbon Nanotube Composite (FG-CNTC) beam. Within the framework of the First-order Shear Deformation Theory (FSDT) and incorporating geometric nonlinearity, the displacement field is formulated using a spectral-geometric series expansion. Subsequently, the Incremental Harmonic Balance (IHB) method is employed to solve the free and forced vibration responses of the coupled system, yielding the beam's nonlinear frequency parameters and frequency-domain response curves. Comparisons of the present results with existing literature and finite element simulations validate the convergence and accuracy of the proposed coupled system model. Through comprehensive numerical examples, the influences of material properties, geometric parameters, and DVA characteristics on the nonlinear dynamic response of the beam are extensively investigated. This work expands the nonlinear dynamic analysis methodology for DVA-coupled FG-CNTC beams and provides fundamental support for the vibration attenuation design of FG-CNTC beam structures.