26. Computing Nonlinear Normal Modes of Aerospace Structures Using the Multi-harmonic Balance Method

The extreme environments that hypersonic vehicles experience during flight expose the thin structural panels to high aerodynamic pressure loading and large temperature gradients, leading to a highly nonlinear structural response. Reduced order models (ROMs) provide an efficient means to compute nonlinear response, however, the accuracy of a ROM is highly dependent on how it is made: the number of modes included within the basis set and the load scaling factors used. The authors have previously proposed to validate ROMs by computing the Nonlinear Normal Modes (NNMs) of the ROMs and using them to compare ROMs of increasing order. The NNMs are a useful metric because they are independent of a specific loading scenario, yet if the NNMs are reproduced accurately then the response to various resonant inputs will also be accurate. This framework has proven challenging to apply to curved structures because they can exhibit complex softening-hardening behavior as well as many nested internal resonance branches. The numerical integration and shooting method that has been used to compute the NNMs typically tracks all the internal resonances, and so it becomes slow and tends to require manual intervention. This work seeks to address these challenges by applying a Multi-Harmonic Balance (MHB) method rather than the shooting algorithm used previously. One attractive feature of the MHB method is the fact that one can filter out internal resonance branches from the solution by limiting the number of harmonics included. This filtering property will be explored, to ascertain the extent to which it can be used to skip internal resonances and identify the primary backbone branch of the NNMs. Particular attention will be paid to balancing the number of harmonics required to obtain an accurate primary backbone branch, including modal interactions that occur along the backbone. The method is applied to a clamped-clamped flat beam, a complex aerospace panel structure and a curved beam to demonstrate the capabilities.