Abstract

This paper investigates the free vibration behavior of a rotating functionally graded conical shell, reinforced by an anisogrid lattice structure. The material properties of the shell are assumed to be graded in the thickness direction. The governing equations have been derived based on classical shell theory and considering the effects of centrifugal and Coriolis accelerations as well as initial hoop tension due to shell rotation. The smeared method is also employed to superimpose the stiffness contribution of the stiffeners with those of the shell to obtain the whole structure's equivalent stiffness parameters. The resulting equations, which are the coupled set of three variable coefficient partial differential equations in terms of displacement components, are solved by the Galerkin method for different boundary conditions. The obtained frequencies are compared with the available literature and the finite element software results. Finally, new results are discussed to show the effect of various parameters such as shell geometrical and material properties, stiffeners, rotating speed, and boundary conditions on natural frequencies.

摘要

本文研究了由各向异性网格结构增强的旋转功能梯度锥壳的自由振动行为。假设壳的材料属性在厚度方向上是渐变的。控制方程是根据经典壳理论导出的，并考虑了离心和科里奥利加速度的影响以及由于壳旋转引起的初始环向张力。还采用涂抹法将加强筋的刚度贡献与壳体的刚度贡献叠加，以获得整个结构的等效刚度参数。所得到的方程是位移分量方面的三个变系数偏微分方程的耦合集，通过 Galerkin 方法求解不同的边界条件。将获得的频率与现有文献和有限元软件结果进行比较。最后，讨论了新的结果以显示各种参数的影响，例如壳的几何和材料特性、加强筋、转速和边界条件对固有频率的影响。