TY - JOUR
T1 - A momentum subspace method for the model-order reduction in nonlinear structural dynamics
T2 - Theory and experiments
AU - Sinha, Kautuk
AU - Singh, Niels K.
AU - Abdalla, Mostafa M.
AU - De Breuker, Roeland
AU - Alijani, Farbod
PY - 2020
Y1 - 2020
N2 - The article proposes a method developed for model order reduction in a Finite Element (FE) framework that is capable of computing higher order stiffness tensors. In the method, a truncated third order asymptotic expansion is used for transformation of an FE model to a reduced system. The basis matrix in the formulation of the reduced-order model (ROM) is derived from linear mode shapes of the structure. The governing equations are derived using Hamilton's principle and the method is applied to geometrically nonlinear vibration problems to test its effectiveness. An initial validation of the numerical formulation is obtained by comparison of results from time domain nonlinear vibration analyses of a rectangular plate using Abaqus. Subsequently, a stiffened plate is modeled to test a more complex structure and a continuation algorithm is used in combination with the ROM to compute nonlinear frequency response curves. The validation of the stiffened plate has been performed through comparisons with the results of nonlinear vibration experiments. The experiments are conducted with Polytec Laser Doppler Vibrometer and PAK MK-II measurement systems for large amplitude vibrations to validate the nonlinear vibration analyses.
AB - The article proposes a method developed for model order reduction in a Finite Element (FE) framework that is capable of computing higher order stiffness tensors. In the method, a truncated third order asymptotic expansion is used for transformation of an FE model to a reduced system. The basis matrix in the formulation of the reduced-order model (ROM) is derived from linear mode shapes of the structure. The governing equations are derived using Hamilton's principle and the method is applied to geometrically nonlinear vibration problems to test its effectiveness. An initial validation of the numerical formulation is obtained by comparison of results from time domain nonlinear vibration analyses of a rectangular plate using Abaqus. Subsequently, a stiffened plate is modeled to test a more complex structure and a continuation algorithm is used in combination with the ROM to compute nonlinear frequency response curves. The validation of the stiffened plate has been performed through comparisons with the results of nonlinear vibration experiments. The experiments are conducted with Polytec Laser Doppler Vibrometer and PAK MK-II measurement systems for large amplitude vibrations to validate the nonlinear vibration analyses.
KW - Finite element method
KW - Hamiltonian mechanics
KW - Model order reduction
KW - Nonlinear vibrations
UR - http://www.scopus.com/inward/record.url?scp=85074137938&partnerID=8YFLogxK
U2 - 10.1016/j.ijnonlinmec.2019.103314
DO - 10.1016/j.ijnonlinmec.2019.103314
M3 - Article
AN - SCOPUS:85074137938
SN - 0020-7462
VL - 119
JO - International Journal of Non-Linear Mechanics
JF - International Journal of Non-Linear Mechanics
M1 - 103314
ER -