A harmonic balance approach for large-scale problems in nonlinear structural dynamics

Harmonic balance (HB) methods allow for rapid computation of time-periodic solutions for nonlinear dynamical systems. We present a filtered high dimensional harmonic balance (HDHB) approach, which operates in the time domain, and provide a framework for implementation into an existing finite element solver. To demonstrate its capabilities, the method is used to solve a set of nonlinear structural dynamics problems related to the field of flapping flight. For each example, the HDHB approach produces accurate steady-state solutions orders of magnitude faster than a traditional time-marching scheme.