Three-dimensional vibration analysis of carbon nanotube-reinforced composite plates and shell structures considering agglomeration effects using an improved solid–shell element

The novelty of this paper is the use of a unified 3D formulation for free vibration analysis of the free vibrational behavior of carbon nanotube-reinforced composites (CNTRCs) in various forms, including plates, rings, and cylindrical shells. Material properties are obtained through a Mori–Tanaka based micromechanical model, and a three-dimensional finite element formulation. The developed model relies on an enhanced first-order shear deformation theory that incorporates a modified transverse shear strain function into the compatible strain field. This formulation accurately represents shear behavior without increasing the number of kinematic variables, while automatically satisfying the traction-free boundary conditions (zero shear stresses) at the top and bottom surfaces of the shell. To mitigate locking in the present finite element formulation based on three-dimensional constitutive equations the assumed natural strain and enhanced assumed strain methods are employed with a minimal number of internal parameters. Parametric studies explore the influence of nanofiber volume fraction, agglomeration, geometry, and boundary conditions on the vibrational response. The investigation underlines the impact of fiber distribution and agglomeration on structural behavior, offering design insights. Results highlight controlling carbon nanotube agglomeration during manufacturing to maximize reinforcement efficiency and dynamic performance of CNTRC components.