MS03.8: Computational Methods

We introduce a numerical analysis framework for controlling isolated response curves (isolas), i.e., curves that form closed loops and are not connected to the main branch of solutions. The methodology relies on bifurcation tracking analyses to monitor the evolution of node-collocation bifurcations in a codimension-2 space. Singularity theory is employed to differentiate points of isolas formation and merger from codimension-2 bifurcations. An optimization problem is defined to advance or delay the formation or merger of isolas.

Spectral submanifolds (SSMs) have been used to construct low-dimensional reduced-order models (ROMs) for highdimensional mechanical systems. These SSM-based ROMs enable efficient and accurate analysis of nonlinear dynamics of the high-dimensional systems. We show how to perform explicit sensitivity analysis of these SSMs and their associated ROMs truncated at cubic order expansion. The obtained sensitivity provides insight into how the SSMs are affected by system parameters. Moreover, it lays the foundation for optimization design of nonlinear dynamics and model updating of nonlinear finite element analysis for the high-dimensional mechanical systems via the SSM-based model reduction.