A Harmonic Balance Approach for Designing Compliant Mechanical Systems with Nonlinear Periodic Motions

摘要

We present a computational method for designing compliant mechanicalsystems that exhibit large-amplitude oscillations. The technical core of ourapproach is an optimization-driven design tool that combines sensitivityanalysis for optimization with the Harmonic Balance Method for simulation.By establishing dynamic force equilibrium in the frequency domain, ourformulation avoids the major limitations of existing alternatives: it handlesnonlinear forces, side-steps any transient process, and automaticallyproduces periodic solutions. We introduce design objectives for amplitudeoptimization and trajectory matching that enable intuitive high-level authoringof large-amplitude motions. Our method can be applied to manytypes of mechanical systems, which we demonstrate through a set of examplesinvolving compliant mechanisms, flexible rod networks, elastic thinshell models, and multi-material solids. We further validate our approach bymanufacturing and evaluating several physical prototypes.