Abstract

In this article, the forward and backward wave frequencies of rotating truncated conical thick shells are investigated. The shell is composed of epoxy as the matrix and functionally graded (FG) graphene nanoplatelets (GPLs) as the reinforcement, which are dispersed with four different patterns through the thickness direction. The effective material properties are estimated using the Halpin-Tsai model and the rule of mixture. The influence of shear deformation in the shell is taken into account based on the third-order shear deformation theory (TSDT). By considering a constant angular velocity, and also considering the effects of the initial hoop tension, Coriolis and centrifugal accelerations, a set of governing equations is derived using Hamilton’s principle and is solved for different boundary conditions using generalized differential quadrature method (GDQM). A parametric study is carried out to investigate the influences of various parameters on the forward and backward traveling wave frequencies with respect to the following cases: the boundary conditions, circumferential wave number, rotating speed, geometrical parameters of the shell as well as the mass fraction, distribution pattern, and width and thickness of the GPLs. The numerical results indicates that dispersing more GPL reinforcements near the inner and outer surfaces of the rotating shells leads to a remarkable increase in both forward and backward wave frequencies.

摘要

在本文中，研究了旋转截锥形厚壳的正向和反向波频率。外壳由环氧树脂作为基体和功能梯度（FG）石墨烯纳米片（GPL）作为增强材料组成，它们在厚度方向上以四种不同的图案分散。使用 Halpin-Tsai 模型和混合规则估计有效材料特性。基于三阶剪切变形理论（TSDT）考虑壳内剪切变形的影响。通过考虑恒定的角速度，并考虑初始环向张力、科里奥利和离心加速度的影响，一组控制方程是使用 Hamilton 原理导出的，并使用广义微分求积法 (GDQM) 针对不同的边界条件求解。针对以下情况，进行了参数化研究，研究了各种参数对前向和后向行波频率的影响：边界条件、周波数、转速、壳的几何参数以及质量分数、分布模式以及 GPL 的宽度和厚度。数值结果表明，在旋转壳的内外表面附近分散更多的 GPL 增强材料会导致前向和后向波频率显着增加。针对以下情况，进行了参数化研究，研究了各种参数对前向和后向行波频率的影响：边界条件、周波数、转速、壳的几何参数以及质量分数、分布模式以及 GPL 的宽度和厚度。数值结果表明，在旋转壳的内外表面附近分散更多的 GPL 增强材料会导致前向和后向波频率显着增加。针对以下情况，进行了参数化研究，研究了各种参数对前向和后向行波频率的影响：边界条件、周波数、转速、壳的几何参数以及质量分数、分布模式以及 GPL 的宽度和厚度。数值结果表明，在旋转壳的内外表面附近分散更多的 GPL 增强材料会导致前向和后向波频率显着增加。