TY - JOUR
T1 - Mode localization and eigenvalue loci veering phenomena in disordered structures
AU - Pierre, C.
PY - 1988/11/8
Y1 - 1988/11/8
N2 - An investigation of the effects of disorder on the modes of vibration of nearly periodic structures is presented. It is shown that, in structures with close eigenvalues, small structural irregularities result in both strong localization of the mode shapes and abrupt veering away, or mutual repulsion, of the loci of the eigenvalues when these are plotted against a parameter representing the disorder in the system. Perturbation methods for the eigenvalue problem are applied to predict the occurrence of strong localization and eigenvalue loci veering, which are shown to be two manifestations of the same phenomenon. Also, perturbation methods that handle the dramatic effects of small disorder are developed to analyze eigenvalue loci veering and strong localization. Two representative disordered nearly periodic structures are studied: a mistuned assembly of coupled oscillators and a multi-span beam with irregular spacing of the supports.
AB - An investigation of the effects of disorder on the modes of vibration of nearly periodic structures is presented. It is shown that, in structures with close eigenvalues, small structural irregularities result in both strong localization of the mode shapes and abrupt veering away, or mutual repulsion, of the loci of the eigenvalues when these are plotted against a parameter representing the disorder in the system. Perturbation methods for the eigenvalue problem are applied to predict the occurrence of strong localization and eigenvalue loci veering, which are shown to be two manifestations of the same phenomenon. Also, perturbation methods that handle the dramatic effects of small disorder are developed to analyze eigenvalue loci veering and strong localization. Two representative disordered nearly periodic structures are studied: a mistuned assembly of coupled oscillators and a multi-span beam with irregular spacing of the supports.
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U2 - 10.1016/0022-460X(88)90226-X
DO - 10.1016/0022-460X(88)90226-X
M3 - Article
AN - SCOPUS:0024282020
SN - 0022-460X
VL - 126
SP - 485
EP - 502
JO - Journal of Sound and Vibration
JF - Journal of Sound and Vibration
IS - 3
ER -