TY - JOUR
T1 - Large-amplitude non-linear normal modes of piecewise linear systems
AU - Jiang, D.
AU - Pierre, C.
AU - Shaw, S. W.
PY - 2004/5/6
Y1 - 2004/5/6
N2 - A numerical method for constructing non-linear normal modes (NNMs) for piecewise linear autonomous systems is presented. These NNMs are based on the concept of invariant manifolds, and are obtained using a Galerkih-based solution of the invariant manifold's non-linear partial differential equations. The accuracy of the constructed non-linear modes is checked by the comparison of the motion on the invariant manifold to the exact solution, in both time and frequency domains. It is found that this construction approach can accurately capture the NNMs over a wide range of amplitudes, including those with strong non-linear effects. Several interesting dynamic characteristics of the non-linear modal motion are found and compared to those of linear modes. A two-degree-of-freedom example is used to illustrate the technique. The existence, stability and bifurcations of the NNMs for this example are investigated.
AB - A numerical method for constructing non-linear normal modes (NNMs) for piecewise linear autonomous systems is presented. These NNMs are based on the concept of invariant manifolds, and are obtained using a Galerkih-based solution of the invariant manifold's non-linear partial differential equations. The accuracy of the constructed non-linear modes is checked by the comparison of the motion on the invariant manifold to the exact solution, in both time and frequency domains. It is found that this construction approach can accurately capture the NNMs over a wide range of amplitudes, including those with strong non-linear effects. Several interesting dynamic characteristics of the non-linear modal motion are found and compared to those of linear modes. A two-degree-of-freedom example is used to illustrate the technique. The existence, stability and bifurcations of the NNMs for this example are investigated.
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U2 - 10.1016/S0022-460X(03)00497-8
DO - 10.1016/S0022-460X(03)00497-8
M3 - Article
AN - SCOPUS:2142657195
SN - 0022-460X
VL - 272
SP - 869
EP - 891
JO - Journal of Sound and Vibration
JF - Journal of Sound and Vibration
IS - 3-5
ER -