We present a computational method for designing compliant mechanical systems that exhibit large-amplitude oscillations. The technical core of our approach is an optimization-driven design tool that combines sensitivity analysis for optimization with the Harmonic Balance Method for simulation. By establishing dynamic force equilibrium in the frequency domain, our formulation avoids the major limitations of existing alternatives: it handles nonlinear forces, side-steps any transient process, and automatically produces periodic solutions. We introduce design objectives for amplitude optimization and trajectory matching that enable intuitive high-level authoring of large-amplitude motions. Our method can be applied to many types of mechanical systems, which we demonstrate through a set of examples involving compliant mechanisms, flexible rod networks, elastic thin shell models, and multi-material solids. We further validate our approach by manufacturing and evaluating several physical prototypes.

中文翻译：

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一种用于设计具有非线性周期性运动的柔顺机械系统的谐波平衡方法

我们提出了一种用于设计具有大振幅振荡的顺应机械系统的计算方法。我们方法的技术核心是一种优化驱动的设计工具，它结合了用于优化的灵敏度分析和用于仿真的谐波平衡法。通过在频域中建立动态力平衡，我们的公式避免了现有替代方案的主要限制：它处理非线性力，避开任何瞬态过程，并自动生成周期解。我们介绍了幅度优化和轨迹匹配的设计目标，以实现大幅度运动的直观高级创作。我们的方法可以应用于多种类型的机械系统，我们通过一组涉及柔顺机构、柔性杆网络、弹性薄壳模型和多材料实体。我们通过制造和评估几个物理原型进一步验证了我们的方法。