The harmonic balance method enables a nonlinear harmonic analysis using multiple harmonics and supporting localized nonlinearities. The nonlinear forces coming from nonlinear elements are calculated in the time domain. An alternating frequency-time (AFT) method is used to link the multiharmonic analysis performed on the linear elements and the sequential transient analyses performed on the nonlinear elements. For details, see Modeling an HBM Analysis.

The nonlinear multiharmonic equations are solved using a trust-region method, which is a gradient-descent type method, based on the Newton-Raphson procedure. A continuation method where the continuation parameter is the excitation frequency is used to follow the solution branch.

When the solution has run successfully, each harmonic response is written on a dedicated results file (.rst). Therefore, each harmonic can be postprocessed using typical harmonic solution postprocessing commands (described in Reviewing the Results in the Structural Analysis Guide). The postprocessing of the total solution, which is the combination of all harmonics, is done using an external macro (see Appendix A: HBM Macros).

HBM Analysis and Parallel Processing

The harmonic balance method procedure automatically partitions the model during solution to run in distributed-memory parallel (DMP) mode using two processors. The nonlinear multiharmonic solution runs on one processor, the master MPI process, while the AFT transient analysis runs on the other processor.