一维非线性力定律的AFT神经函数逼近器

中文摘要 AI 辅助

非线性接触和摩擦强烈影响装配结构的振动响应，但其精确数值处理计算成本高昂。谐波平衡法广泛用于计算周期稳态响应，然而所需的交替频率-时间方案对于非光滑和滞回非线性变得昂贵，且必须在非线性求解过程中重复进行。在此，我们表明该过程可由神经网络替代，这些网络直接将位移傅里叶系数映射到非线性力系数，并通过自动微分提供相应的雅可比矩阵。周围的求解器和延续算法在计算频率响应曲线时保持不变。神经网络仅学习单个非线性单元，而非完整系统响应。基于物理的无量纲化和相位归一化促进了学习过程，并使单个训练网络能够覆盖广泛的参数组合。基于本文考虑的立方弹簧、单边弹簧和Jenkins单元，该方法指向一个可重用的非线性单元代理库，可在机械系统中任意数量和位置组合。通过绕过时域中的迭代力评估，该方法为高分辨率分析和具有许多非线性单元的系统提供了有利的计算扩展性。

英文摘要

Nonlinear contacts and friction strongly influence the vibration response of assembled structures, but their accurate numerical treatment is computationally demanding. The harmonic balance method is widely used to compute periodic steady-state responses, yet the required alternating frequency-time scheme becomes costly for nonsmooth and hysteretic nonlinearities and must be repeated throughout the nonlinear solution process. Here we show that this procedure can be replaced by neural networks that directly map displacement Fourier coefficients to nonlinear force coefficients and provide the corresponding Jacobian through automatic differentiation. The surrounding solver and continuation algorithms remain unchanged for the computation of frequency response curves. The neural networks exclusively learn individual nonlinear elements rather than complete system responses. Physics-based nondimensionalization and phase normalization facilitate the learning process and enable a single trained network to cover a wide range of parameter combinations. Building on the cubic spring, unilateral spring, and Jenkins elements considered here, the approach points toward a reusable library of nonlinear-element surrogates that can be combined in arbitrary number and location within a mechanical system. By bypassing the iterative force evaluation in time domain, the method offers favorable computational scaling for high-resolution analyses and systems with many nonlinear elements.

发表机构

• Technische Universität Berlin（柏林工业大学）
• University of Stuttgart（斯图加特大学）

机构由 AI 辅助整理，请以论文原文为准。

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20 pages, 6 figures, 6 tables