航空学报2026，Vol.47Issue(5)：171-182,12.DOI:10.7527/S1000-6893.2025.32453
基于辛叠加方法与迁移学习的功能梯度任意四边形开孔板自由振动问题求解
Free vibration solution of functionally graded plates with arbitrary quadrilateral cutouts based on symplectic superposition method and transfer learning
摘要
Abstract
Functionally graded plates with cutouts are common load-bearing structures in engineering,making the study of their dynamic behavior crucial.For plates with regularly shaped cutouts,the symplectic superposition method combined with subdomain decomposition technique can be used to establish 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 bound-ary 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.A novel solution framework that inte-grates the symplectic superposition method with the transfer learning technique is established.It leverages the analyti-cally solvable natural frequencies of functionally graded rectangular plates with rectangular cutouts for knowledge trans-fer,thereby achieving efficient and highly accurate solutions for the free vibration problems of functionally graded plates with arbitrary quadrilateral cutouts.First,a multi-layer perceptron neural network is pre-trained on large-scale analytical solution dataset to extract the complex mapping relationships of geometric parameters between different shapes.Sec-ond,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 solution framework 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.The transfer learning technique is used to lever-age small-sample data and existing analytical solutions to efficiently and accurately solve free vibration problems of functionally graded with arbitrary quadrilateral plates cutouts.The proposed framework,adaptable to various working conditions through model parameter adjustments,offers a novel strategy for the mechanical analysis of complex-shaped plates.关键词
四边形开孔板/自由振动/辛叠加方法/迁移学习Key words
quadrilateral plates with cutouts/free vibration/symplectic superposition method/transfer learning分类
航空航天引用本文复制引用
程超宇,徐典,郭程洁,李进宝,李锐..基于辛叠加方法与迁移学习的功能梯度任意四边形开孔板自由振动问题求解[J].航空学报,2026,47(5):171-182,12.基金项目
国家自然科学基金(12372067,12502071) （12372067,12502071）
国防基础科研计划(JCKY2021205B003) （JCKY2021205B003）
大连市杰出青年科技人才项目(2024RJ005) （2024RJ005）
辽宁省自然科学基金杰出青年基金(2025JH6/101100005) National Natural Science Foundation of China(12372067,12502071) （2025JH6/101100005）
National Defense Basic Scientific Research Program of China(JCKY2021205B003) （JCKY2021205B003）
Dalian Science Fund for Distinguished Young Scholars(2024RJ005) （2024RJ005）
Liaoning Science Fund for Distinguished Young Scholars(2025JH6/101100005) （2025JH6/101100005）
