Frequency analysis of FG-CNT–reinforced composite doubly curved panels on visco-Pasternak medium

Abstract

In this paper, the free damped vibration behavior of doubly curved panels is investigated, while reinforcements are aligned and straight single-walled carbon nanotubes with uniform and functionally graded distributions under four different patterns through thickness. The extended rule of mixtures is employed to achieve effective material properties. Hamilton principle and third-order shear deformation theory of Reddy are used for governing equations of motions of spherical, cylindrical, hyperboloid and paraboloid panels resting on visco-Pasternak medium. A semi-analytical approach with an iterative numerical algorithm is implemented to figure out frequencies and modal loss factors of eigenvalue problem. To verify, the present results are compared with those that are obtained via first-order shear deformation theory for flat, cylindrical, and spherical panels. Also, the influence of shallowness, thickness, curvature, aspect ratios, distribution and content of carbon nanotubes, and viscoelastic medium on natural frequency and damping capability of panels are examined via numerical examples. For the first time, the crossing phenomena of natural frequencies and modal loss factors of FG-CNT–reinforced composite panels with external damping under higher-order theory assumptions are presented. Results show that hyperboloid panels with high aspect, shallowness, and low thickness ratios are susceptible to follow inharmonic motion rather than a harmonic one.