The analytical solutions of supersonic flutter of porous functionally graded plates are investigated. The material properties of the plates (stiffness and density) vary according to a power law across the thickness and axial coordinates depending on the volume fraction of constituent materials. Their equilibrium and stability equations are derived based on the classical plate theory. The solution of the problem is derived using the Rayleigh–Ritz method and the Mathematica package. An optimization problem is formulated and solved for plates of infinite width.

中文翻译：

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优化受超音速颤振约束的无限宽多孔 FGM 板的厚度/刚度分布

研究了多孔功能梯度板超声速颤振的解析解。板的材料特性（刚度和密度）根据厚度和轴向坐标的幂律变化，具体取决于组成材料的体积分数。它们的平衡和稳定性方程是基于经典板块理论推导出来的。问题的解决方案是使用 Rayleigh-Ritz 方法和 Mathematica 包推导出来的。为无限宽度的板制定并解决了优化问题。