Parametric Analysis of Porous FGM Core and CNT Distribution Effects on Vibration Behavior of Truncated Conical Sandwich Shells

Abstract

This study investigates the free vibration behavior of a three-layer sandwich truncated conical shell featuring a functionally graded porous (FG-porous) core between carbon nanotube (CNT)-reinforced composite face sheets. To model material behavior, five CNT distribution profiles and three porosity patterns—symmetric, non-symmetric, and uniform—are considered. Temperature-dependent material properties are incorporated using established micromechanical relations. The structural modeling is based on first-order shear deformation theory (FSDT), which accounts for transverse shear effects through a correction factor. Governing equations are derived using the energy method in conjunction with Hamilton’s principle. A comprehensive parametric analysis is performed to assess the influence of CNT gradation, porosity distribution, and key geometric parameters such as cone angle, radii, layer thicknesses, and shell length on the vibrational response. Numerical results show that increasing CNT volume fraction and adopting the AV distribution model lead to higher natural frequencies, while increased porosity and core thickness generally reduce them. Boundary conditions also significantly influence the dynamic response. These insights contribute to the design optimization of advanced composite conical structures in aerospace, marine, and mechanical applications.