A vibration analysis model for carbon nanotube reinforced composite conical shells

This article systematically investigates the vibration characteristics of functional gradient carbon nanotube reinforced composite truncated conical shells under arbitrary boundary conditions. First, a structural dynamic model is developed based on the first-order shear deformation theory. The mid-surface displacement field is constructed using Jacobi polynomials to accurately capture the deformation behavior of the shell under complex boundary constraints. Subsequently, the governing equations for free vibration are derived via the Lagrange energy method, and a solution framework for the forced vibration response under single-point pulse excitation is established using the modal superposition approach. The proposed model is validated through comparison with existing literature and finite element results, confirming its accuracy and effectiveness and providing a solid theoretical basis for subsequent vibration analysis. Finally, the effects of carbon nanotube distribution patterns, weight fractions, and fiber laying angles on the structural vibration response are systematically analyzed, yielding a set of engineering-relevant conclusions with practical significance for structural design and vibration control.