TY - JOUR
T1 - Modal analysis-based reduced-order models for nonlinear structures-an invariant manifold approach
AU - Shaw, Steven W.
AU - Pierre, Christophe
AU - Pesheck, Eric
PY - 1999
Y1 - 1999
N2 - An approach is outlined that can be used to define and construct normal modes of motion for a wide class of nonlinear vibratory systems. Furthermore, an extension of these ideas is used to develop a mode-based model reduction method for multidegree-of-freedom nonlinear systems. The approach makes use of invariant manifolds in the system phase space, and it reduces to the well-known results in the linearized case. An explicit construction method for weakly nonlinear systems allows for the automated generation of a set of reduced-order equations of motion for the nonlinear modes and, in the single-mode case, it systematically produces the amplitude dependent mode shapes. Results from some illustrative examples are presented. The paper closes with a discussion of some topics of current and future interest and some conclusions.
AB - An approach is outlined that can be used to define and construct normal modes of motion for a wide class of nonlinear vibratory systems. Furthermore, an extension of these ideas is used to develop a mode-based model reduction method for multidegree-of-freedom nonlinear systems. The approach makes use of invariant manifolds in the system phase space, and it reduces to the well-known results in the linearized case. An explicit construction method for weakly nonlinear systems allows for the automated generation of a set of reduced-order equations of motion for the nonlinear modes and, in the single-mode case, it systematically produces the amplitude dependent mode shapes. Results from some illustrative examples are presented. The paper closes with a discussion of some topics of current and future interest and some conclusions.
KW - Invariant manifolds
KW - Modal analysis
KW - Nonlinear vibration
KW - Normal modes
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U2 - 10.1177/058310249903100101
DO - 10.1177/058310249903100101
M3 - Article
AN - SCOPUS:0031599011
SN - 0583-1024
VL - 31
SP - 3
EP - 16
JO - Shock and Vibration Digest
JF - Shock and Vibration Digest
IS - 1
ER -