The elastically line-hinged orthotropic rectangular plates with rotationally restrained edges are commonly used in engineering applications such as deployable structures. However, it is intractable to obtain the analytical solutions for the free vibration problems of such structures owing to the challenges in processing the high-order partial differential equations. Here, we make a first attempt to deal with such issues within the Hamilton system-based symplectic space. The problem of a plate is transformed into the symplectic space from the Euclidean space, and the subplates that may be analyzed analytically by the symplectic superposition method are then obtained with the division of the entire plate. The complex boundary and connection forms are achieved by enforcing mechanical quantities with undetermined expansion coefficients on the edges of the subplates. By integrating the solutions of the subplates, the final solution of an elastically line-hinged orthotropic rectangular plate with rotationally restrained edges is accessible. The proposed solution scheme is performed with rational derivations, with no requirement for pre-defined solution forms. Comprehensive results with validations under various boundary and hinge connection cases are presented. Moreover, detailed parametric investigations are conducted, which could facilitate the engineering design of deployable structures.

中文翻译：

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具有旋转限制边缘的弹性线铰接正交各向异性矩形板自由振动的辛解析解


具有旋转限制边缘的弹性线铰接正交各向异性矩形板通常用于可展开结构等工程应用中。然而，由于处理高阶偏微分方程的挑战，获得此类结构自由振动问题的解析解是很困难的。在这里，我们首次尝试在基于汉密尔顿系统的辛空间内处理此类问题。将板块问题从欧几里得空间转化为辛空间，然后将整个板块进行划分，得到辛叠加法可以解析分析的子板块。复杂的边界和连接形式是通过在底板边缘强制施加具有未确定的膨胀系数的机械量来实现的。通过整合子板的解，可以获得具有旋转约束边缘的弹性线铰接正交各向异性矩形板的最终解。所提出的解决方案通过理性推导来执行，不需要预定义的解决方案形式。给出了在各种边界和铰链连接情况下经过验证的综合结果。此外，还进行了详细的参数研究，这可以促进可展开结构的工程设计。