Effect of graphene nanoplatelet reinforcements on the dynamics of rotating truncated conical shells

Abstract

In this paper, a parametric study is presented for free vibration analysis of rotating truncated conical shells reinforced with graphene nanoplatelets (GNPs). The composite shell is considered to be composed of epoxy as the matrix and the GNPs which are distributed along the thickness direction based on the various distribution patterns. The shell is modeled based on the first-order shear deformation theory (FSDT), and effective material properties are calculated based on the Halpin-Tsai model and the rule of mixture. Incorporating centrifugal and Coriolis accelerations along with initial hoop tension, the set of the governing equations and boundary conditions are derived using Hamilton's principle and are solved numerically using generalized differential quadrature method. Convergence and accuracy of the presented solution are confirmed, and influences of various parameters on the forward and backward frequencies are investigated including circumferential mode number, boundary conditions, rotational speed, semi-vertex angle and also mass fraction, distribution pattern, width and thickness of the GNPs. It is noteworthy that for the first time, the initial hoop tension is incorporated for a rotating conical shell modeled based on the FSDT.

Frequency response of rotating two-directional functionally graded GPL-reinforced conical shells on elastic foundation

“…Three cases of one-directional dispersion of GPLs through the thickness direction are considered: uniform dispersion (UD) (type 1, p = q = 0), FG-V (type 1, p = 1, q = 0) and FG-A (type 2, p = 1, q = 0). For n = 1, 2, 3 and 4, values of the first three natural frequencies are presented in Table 1 against corresponding ones reported by Afshari [36]. As observed, the present results are in high agreement confirming the accuracy of the present model.…”

“…and they can be stated by utilizing Eqs. ( 9) and (10) as where Due to the initial hoop tension, the following potential energy is created [36,39]: in which with the following definitions, 0 and NL are the initial hoop stress and the nonlinear part of circumferential strain [46][47][48]:…”

“…They studied the influences of some involved parameters such as the weight fraction and dispersion pattern of the GPLs on the natural frequencies. Using first-order shear deformation theory (FSDT), Afshari [36,37] presented semi-analytical solutions for GPLreinforced non-rotating and rotating truncated conical shells. Arshid et al [38] studied the free vibrational characteristics of rectangular sandwich microplates consisted of a honeycomb core and two GPL-reinforced composite face sheets.…”

Vibration characteristics of rotating truncated conical shells reinforced with agglomerated carbon nanotubes

“…It was shown by them that the natural frequencies increase by a reduction in the length-to-radius ratio of the shell and an increase in boundary spring stiffness. Afshari (2020a) presented a parametric study to investigate the free vibration characteristics of rotating GNP-reinforced conical shells. He studied the individual effect of Coriolis and centrifugal accelerations and initial hoop tension on the natural frequencies.…”

The Vibration Study of A Sandwich Conical Shell With A Saturated FGP Core

“…He examined the effects of the percentage of the CNTs and heterogeneity on the buckling and free vibrational characteristics of the shell. The free vibration characteristics of rotating polymeric truncated conical shells enriched by graphene nanoplatelets (GNPs) were investigated by Afshari [2]. It was shown by him that the sequence of vibrational modes can be affected by the variation of semi-vertex angle.…”