This paper investigates the classical buckling problem of rectangular thin plates with two opposite edges free and others rotationally restrained by the finite Fourier integral transform method. The rotationally restrained edges are typically practical boundary conditions in many engineering structures, such as bridge decks. However, these non‐classic edges bring mathematical difficulties in solving boundary value problems of governing partial differential equations of plate. Based on the integral transform theory, the title problem is transformed into solving regular linear algebraic simultaneous equations, which provides a more rational and theoretical solution process than traditional inverse/semi‐inverse approaches. The acquired comprehensive results of critical buckling load factors and mode shapes are in excellent agreement with the ones obtained by finite element method, which verifies the validity and accuracy of the present approach. In addition, classical boundary conditions, such as simply supported and clamped edges, can be investigated by choosing different rotational fixity factors. Furthermore, the features of the employed method that no preselection of trial function and the generality for various boundary conditions enable one to analytically solve static problems for moderately thick plates and thick plates.

中文翻译：

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有限的傅里叶积分变换法对两个相对边自由且旋转受约束的矩形薄板进行屈曲分析

本文研究了矩形薄板的经典屈曲问题，该矩形薄板具有两个相对的自由边，而其他旋转受有限傅里叶积分变换法约束。在许多工程结构（例如桥面板）中，受旋转限制的边缘通常是实际的边界条件。但是，这些非经典边在解决控制板的偏微分方程的边值问题时带来了数学上的困难。基于积分变换理论，标题问题被转化为求解规则线性代数联立方程，与传统的逆/半逆方法相比，它提供了更为合理的理论解决过程。所获得的临界屈曲载荷因子和振型的综合结果与有限元方法获得的结果非常吻合，证明了该方法的有效性和准确性。此外，可以通过选择不同的旋转固定因子来研究经典边界条件，例如简单支撑的边缘和夹紧的边缘。此外，所采用的方法的特点是无需预选试验函数，并且可以针对各种边界条件进行通用性分析，从而能够解析地解决中厚板和厚板的静态问题。可以通过选择不同的旋转固定系数来进行研究。此外，所采用的方法的特点是无需预选试验函数，并且可以针对各种边界条件进行通用性分析，从而能够解析地解决中厚板和厚板的静态问题。可以通过选择不同的旋转固定系数来进行研究。此外，所采用的方法的特点是无需预选试验函数，并且可以针对各种边界条件进行通用性分析，从而能够解析地解决中厚板和厚板的静态问题。