Data-driven modeling of subharmonic forced response due to nonlinear resonance

Area of Science:

• Nonlinear Dynamics
• Fluid Mechanics
• Complex Systems Analysis

Background:

• Complex behavior in nonlinear dynamical systems often stems from resonances enabling energy transfer between modes.
• Classical linear analysis can detect resonances among linearized modes, but nonlinear modal interactions remain poorly understood.
• Existing methods lack systematic approaches to detect and model nonlinear resonant interactions directly from data.

Purpose of the Study:

• To develop a data-driven methodology for identifying and modeling nonlinear resonant interactions.
• To specifically address subharmonic responses in forced nonlinear systems, particularly those lacking linear resonances.
• To provide a generalizable approach applicable to various nonlinear dynamical systems.

Main Methods:

• Developed a data-driven methodology to identify nonlinear resonant response on low-dimensional spectral submanifolds (SSMs).
• Employed analytical methods to demonstrate the origin of subharmonic response from nonlinear resonances in the conservative limit.
• Validated the approach by isolating and modeling unexplained response patterns in fluid sloshing experiments.

Main Results:

• Successfully identified and modeled nonlinear resonant interactions from experimental and numerical data.
• Demonstrated the capability to detect subharmonic responses not predictable by linear analysis.
• Isolated and explained previously unexplained phenomena in fluid sloshing dynamics.

Conclusions:

• The developed data-driven methodology offers a systematic way to detect and model nonlinear resonances.
• This approach enhances the understanding of complex behaviors arising from nonlinear modal interactions.
• The findings have significant implications for analyzing and predicting responses in various nonlinear systems, including fluid dynamics.