tmdsimpy.roms.vprnm

Module for reduced order models (ROMs) based on Variable Phase Resonance Nonlinear Modes (VPRNM) for capturing superharmonic resonances.

This module utilizes precalculated VPRNM and EPMC solutions.

See Also

tmdsimpy.VibrationSystem.epmc_res

EPMC residual method that can be used to solve the set of EPMC equations.

tmdsimpy.VibrationSystem.vprnm_res

VPRNM residual method that can be used to solve the set of VPRNM equations.

tmdsimpy.VibrationSystem.vprnm_amp_phase_res

VPRNM residual method that can be used to solve the set of VPRNM equations with some extra constraints to allow for easier convergence.

tmdsimpy.VibrationSystem.hbm_res :

Harmonic balance method residual function for calculating truth solutions.

tmdsimpy.Continuation.continuation :

Method of obtaining solutions to EPMC/VPRNM at multiple points with continuation.

Notes

The formulation of VPRNM and VPRNM based ROMs are described in [1], [2], [3].

References

[1]

Porter, J. H., and M. R. W. Brake. 2024. “Tracking Superharmonic Resonances for Nonlinear Vibration of Conservative and Hysteretic Single Degree of Freedom Systems.” Mechanical Systems and Signal Processing 215:111410. https://doi.org/10.1016/j.ymssp.2024.111410. arXiv:2401.08790

[2]

Porter, J. H., and M. R. W. Brake. Under Review. “Efficient Model Reduction and Prediction of Superharmonic Resonances in Frictional and Hysteretic Systems.” Mechanical Systems and Signal Processing. arXiv:2405.15918.

[3]

Porter, J. H. 2024. Modal Interactions and Jointed Structures. PhD Thesis. Rice University.

Functions

constant_h1_displacement(epmc_fund_bb, ...)

Reduced order model (ROM) for a superharmonic resonance based VPRNM, EPMC, and on constant first harmonic amplitude.