Authors: Davis Wing
Mentors: Matt Allen
Insitution: Brigham Young University
When thin structures vibrate under large forces, can exhibit geometric nonlinearity, which makes it very hard to compute their motion and the stresses they undergo. This work builds on prior efforts, which used a small number of computations derived from detailed models, together with machine learning techniques, to train a reduced order model (ROM). This ROM could then be simulated efficiently to estimate the dynamic, nonlinear response of the structure in a fraction of the time it takes to compute the full-order model.
This reduced order modeling technique is called Gaussian Process ROM or GPR ROM, and was developed by Park et al. [MSSP, vol. 184, p. 109720, 2023]. The GPR-ROM approach works by applying a number of static loads to the detailed model of the thin structure, and then by integrating those loads over time, it produces an understanding of the dynamics. In addition to its speed, this approach also provides confidence bounds on its findings, meaning that researchers can gauge a number of plausible values for the nonlinear responses of the system being measured.
This research further develops this approach to computing the dynamics of structures by applying the GRP-ROM to a more complicated structure than previously studied, namely, a gong. The gong as a test structure is significant, as the signature sound of a gong is produced through geometric nonlinearities. In order to capture the behavior of the gong, and thereby its sound, several modes need to be studied simultaneously, and thus more degrees of freedom are required to capture its behavior in a ROM. This work evaluates the GPR-ROM process for the gong by computing various ROMs for different load states, thereby capturing the geometric variability of the gong’s responses. Then, the non-linear normal modes (NNMs) of the system are calculated within 95% confidence, which allows for a reasonable understanding of the dynamics of the system. These will be compared to the NNMs computed, at great expense, from the full-order model to validate the method.