功能梯度开孔板是工程中常见的承力结构，研究其动力行为具有重要意义。针对规则形状开孔板，通过辛叠加方法结合子域分解技术已能系统解析求解，但是当研究对象扩展至应用更加广泛的任意四边形开孔板时，解析求解因边界更加复杂而面临巨大挑战。尽管存在近似/数值方法进行求解，但可能存在计算耗时长、网格依赖性强等问题，常导致结果精度不足。如能利用已有解析解推知任意四边形开孔板振动问题的高效高精度解，则可为类似复杂问题的求解提供一种新思路。本文建立了结合辛叠加方法与迁移学习技术的求解框架，利用可解析求解的功能梯度矩形开孔板自振频率进行知识迁移，从而高效高精度求解功能梯度任意四边形开孔板自由振动问题。首先，基于多层感知机神经网络对大样本解析解数据集进行预训练，提取不同几何形状间几何参数的复杂映射关系；其次，基于小样本有限元仿真数据对预训练模型进行迁移，将矩形开孔板自振频率数据集中的知识有效迁移至任意四边形开孔板自由振动问题；最后，利用均方误差和决定系数等指标，验证了所提方法用于功能梯度任意四边形开孔板自振频率预测的准确性及适用性。
Functionally graded plates with cutouts are common load-bearing structures in engineering, making the study of their dynamic be-havior crucial. For plates with regularly shaped cutouts, the symplectic superposition method combined with subdomain decomposi-tion technique has established a comprehensive analytical solution framework. However, when the research object is extended to plates with arbitrarily shaped cutouts, which have broader applications, the analytical solution faces significant challenges due to the increased complexity of the boundary conditions. While approximate or numerical methods exist, they may suffer from time-consuming computations and strong mesh dependency, often leading to insufficient accuracy in results. If an efficient and high-precision solution for the vibration problem of plates with cutouts could be derived from existing analytical solutions, it would pro-vide a new approach for solving similar complex problems. This paper establishes a novel solution framework that integrates the symplectic superposition method with the transfer learning technique. It leverages the analytically solvable natural frequencies of functionally graded rectangular plates with rectangular cutouts for knowledge transfer, thereby achieving efficient and highly accurate solutions for the free vibration problems of functionally graded plates with arbitrary quadrilateral cutouts. First, a multi-layer percep-tron neural network is pre-trained on large-scale analytical solution dataset to extract the complex mapping relationships of geometric parameters between different shapes. Second, the pre-trained model is transferred based on few-shot finite element simulation data, effectively transferring knowledge from the natural frequency dataset of the rectangular plates with rectangular cutouts to the free vibration of plates with arbitrary quadrilateral cutouts. Finally, the accuracy and applicability of the proposed method for predicting the natural frequencies of functionally graded plates with arbitrary quadrilateral cutouts are validated, using metrics such as mean squared error and coefficient of determination.
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