Abstract In this paper, the free vibration characteristics of Sigmoid Functionally Graded Material (S-FGM) Levy-type plates are investigated by developing the Dynamic Stiffness Method (DSM) through the application of the Wittrick-Williams algorithm, as solution technique. Kirchoff-Love Plate Theory (KLPT) and Hamilton principle are utilised to derive the governing equation of motion and associated natural boundary conditions. Based on two power-law distribution functions, the material properties are gradually varied along the thickness direction. Using the proposed theory, a substantial number of numerical examples showing the natural vibration characteristics of plates made of sigmoid functionally graded material are illustrated to demonstrate the accuracy of the method. Some numerical results are compared with published results and found to be in excellent agreement. An extensive investigation is carried out and the results are examined and discussed in detail. The variations of material properties such as the Young’s modulus ratio and density ratio are seen to affect the natural frequencies of S-FGM plates significantly. The proposed method is not only accurate but also, quite simple and straightforward to compute the natural frequencies and mode shapes of S-FGM plates. The results presented can be used as benchmark solution for further investigation of FGM plates.

中文翻译：

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使用动态刚度方法和 Wittrick-Williams 算法的 sigmoid 功能梯度板的自由振动

摘要 在本文中，通过应用 Wittrick-Williams 算法开发动态刚度法 (DSM) 作为求解技术，研究了 Sigmoid 功能梯度材料 (S-FGM) Levy 型板的自由振动特性。Kirchoff-Love Plate Theory (KLPT) 和 Hamilton 原理用于推导运动控制方程和相关的自然边界条件。基于两个幂律分布函数，材料特性沿厚度方向逐渐变化。使用所提出的理论，大量的数值例子显示了由 sigmoid 功能梯度材料制成的板的自然振动特性，以证明该方法的准确性。一些数值结果与公布的结果进行了比较，发现非常一致。进行了广泛的调查，并对结果进行了详细的检查和讨论。杨氏模量比和密度比等材料特性的变化显着影响 S-FGM 板的固有频率。所提出的方法不仅准确，而且计算 S-FGM 板的固有频率和振型非常简单和直接。所呈现的结果可用作进一步研究 FGM 板的基准解决方案。杨氏模量比和密度比等材料特性的变化显着影响 S-FGM 板的固有频率。所提出的方法不仅准确，而且计算 S-FGM 板的固有频率和振型非常简单和直接。所呈现的结果可用作进一步研究 FGM 板的基准解决方案。杨氏模量比和密度比等材料特性的变化显着影响 S-FGM 板的固有频率。所提出的方法不仅准确，而且计算 S-FGM 板的固有频率和振型非常简单和直接。所呈现的结果可用作进一步研究 FGM 板的基准解决方案。