TY - JOUR
T1 - Fast computation and characterization of forced response surfaces via spectral submanifolds and parameter continuation
AU - Li, Mingwu
AU - Jain, Shobhit
AU - Haller, George
PY - 2024
Y1 - 2024
N2 - For mechanical systems subject to periodic excitation, forced response curves (FRCs) depict the relationship between the amplitude of the periodic response and the forcing frequency. For nonlinear systems, this functional relationship is different for different forcing amplitudes. Forced response surfaces (FRSs), which relate the response amplitude to both forcing frequency and forcing amplitude, are then required in such settings. Yet, FRSs have been rarely computed in the literature due to the higher numerical effort they require. Here, we use spectral submanifolds (SSMs) to construct reduced-order models (ROMs) for high-dimensional mechanical systems and then use multidimensional manifold continuation of fixed points of the SSM-based ROMs to efficiently extract the FRSs. Ridges and trenches in an FRS characterize the main features of the forced response. We show how to extract these ridges and trenches directly without computing the FRS via reduced optimization problems on the ROMs. We demonstrate the effectiveness and efficiency of the proposed approach by calculating the FRSs and their ridges and trenches for a plate with a 1:1 internal resonance and for a shallow shell with a 1:2 internal resonance.
AB - For mechanical systems subject to periodic excitation, forced response curves (FRCs) depict the relationship between the amplitude of the periodic response and the forcing frequency. For nonlinear systems, this functional relationship is different for different forcing amplitudes. Forced response surfaces (FRSs), which relate the response amplitude to both forcing frequency and forcing amplitude, are then required in such settings. Yet, FRSs have been rarely computed in the literature due to the higher numerical effort they require. Here, we use spectral submanifolds (SSMs) to construct reduced-order models (ROMs) for high-dimensional mechanical systems and then use multidimensional manifold continuation of fixed points of the SSM-based ROMs to efficiently extract the FRSs. Ridges and trenches in an FRS characterize the main features of the forced response. We show how to extract these ridges and trenches directly without computing the FRS via reduced optimization problems on the ROMs. We demonstrate the effectiveness and efficiency of the proposed approach by calculating the FRSs and their ridges and trenches for a plate with a 1:1 internal resonance and for a shallow shell with a 1:2 internal resonance.
KW - Backbone curves
KW - Forced response curves
KW - Invariant manifolds
KW - Reduced-order models
KW - Spectral submanifolds
UR - http://www.scopus.com/inward/record.url?scp=85189878665&partnerID=8YFLogxK
U2 - 10.1007/s11071-024-09482-2
DO - 10.1007/s11071-024-09482-2
M3 - Article
AN - SCOPUS:85189878665
SN - 0924-090X
VL - 112
SP - 7771
EP - 7797
JO - Nonlinear Dynamics
JF - Nonlinear Dynamics
IS - 10
ER -