This study provides an overview on the effect of porosity on free vibrations and more importantly aeroelastic stability margins of cylindrical shells. A general formulation for cylindrical shells is first developed including the effects of shear deformation and rotary inertia along with Sander’s rigid body rotation modification. Two porosity distributions of even and uneven are considered for functionally graded shells. The most general form of power-law model which is known as four-parameter power-law is utilized to provide a clear understanding for the qualification of functionally graded material. A Ritz-based solution algorithm being capable of representing all combinations of symmetric and asymmetric boundary conditions by a penalty method is also introduced. In addition to the capability of satisfying all boundary conditions, the presented solution method is very fast in terms of convergence and computational effort. Various parametric studies are provided and practical results are reported.

中文翻译：

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使用统一溶液配方的功能梯度多孔圆柱壳的超音速气动弹性和动态不稳定性

本研究概述了孔隙率对自由振动的影响，更重要的是圆柱壳的气动弹性稳定性裕度。首先开发了圆柱壳的一般公式，包括剪切变形和旋转惯性的影响以及 Sander 的刚体旋转修改。对于功能梯度壳，考虑了均匀和不均匀两种孔隙率分布。最通用的幂律模型形式，即四参数幂律，用于为功能分级材料的鉴定提供清晰的理解。还介绍了一种基于 Ritz 的求解算法，该算法能够通过惩罚方法表示所有对称和非对称边界条件的组合。除了满足所有边界条件的能力，所提出的解决方法在收敛和计算量方面非常快。提供了各种参数研究并报告了实际结果。