发表机构
The Hong Kong University of Science and Technology; Tongji University; Southwest Jiaotong University; Université Paris-Saclay; Chongqing University; Cardiff University（香港科技大学; 同济大学; 西南交通大学; 巴黎萨克雷大学; 重庆大学; 卡迪夫大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出DSM-PINN框架，结合Wittrick-Williams算法求解特征值问题，用频域-PINN分析结构动态响应，解决神经网络相关局限，验证了方法的实用性与有效性。
AI 中文摘要
本文介绍了一种将动态刚度矩阵（DSM）与物理信息神经网络（PINN）相结合的框架。DSM-PINN在模型中嵌入物理约束，展现出鲁棒性，尤其适用于各类研究中有限数据集的情况。在该方法中，深度神经网络的输出近似单元节点的位移场。与有限元法（FEM）不同，单元形函数是控制偏微分方程的齐次解，构成了精确动态刚度矩阵的基础，从而避免了高阶导数项。该矩阵还充当频域谱元，形成强形式PINN。损失函数通过将神经网络与动态刚度矩阵连接生成。我们专注于利用PINN结合Wittrick-Williams算法求解特征值问题，该算法克服了神经网络无法收敛到高阶特征值的挑战。此外，频域-PINN方法用于分析移动和脉冲载荷下的结构动态响应，解决了神经网络处理复数的局限性。即使在施加边界条件后DSM为不定矩阵，本文也分析了所提方法的理论收敛稳定性。数值结果验证了所推荐方法的实用性和有效性。
英文摘要
This paper introduces a framework that integrates the dynamic stiffness matrix (DSM) with physics-informed neural networks (PINN). The DSM-PINN embeds physical constraints within the model and demonstrates robustness, particularly when addressing limited datasets across diverse investigations. In this approach, deep neural network outputs approximate the displacement fields of element nodes. Unlike the finite element method (FEM), the element shape functions are homogeneous solutions to the governing partial differential equation, forming the basis of the exact dynamic stiffness matrix, thereby avoiding high-order derivative terms. This matrix also serves as a frequency-domain spectral element, resulting in a strong-form PINN. The loss function is produced by connecting neural networks with dynamic stiffness matrices. We focus on utilising PINNs to resolve eigenvalue problems by employing the Wittrick-Williams algorithm, which overcomes the challenge of neural networks failing to converge to higher-order eigenvalues. Additionally, the frequency domain-PINN method is used to analyse structural dynamic responses under moving and impulsive loads, addressing the limitation of neural networks in handling complex numbers. Theoretical convergence stability of the suggested approach is also analysed even DSM is an indefinite matrix after implementing the boundary condition. The numerical results validate the practicality and efficacy of the recommended approach.
