TY - GEN
T1 - Localization of vibration in disordered multi-span beams with damping
AU - Bouzit, Djamel
AU - Pierre, Christophe
N1 - Publisher Copyright:
© 1993 American Society of Mechanical Engineers (ASME). All rights reserved.
PY - 1993
Y1 - 1993
N2 - The combined effects of disorder and structured damping on the dynamics of a multi-span beam with slight randomness in the spacing between supports are investigated. A wave transfer matrix approach is chosen to calculate the free and forced harmonic responses of this nearly periodic structure. It is shown that both harmonic waves and normal modes of vibration that extend throughout the ordered, undamped beam become spatially attenuated if either small damping or small disorder is present in the system. The physical mechanism which causes this attenuation, however, is one of energy dissipation in the case of damping but one of energy confinement in the case of disorder. The corresponding rates of spatial exponential decay are estimated by applying statistical perturbation methods. It is found that the effects of damping and disorder simply superpose for a multi-span beam with strong interspan coupling, but interact less trivially in the weak coupling case. Furthermore, the effect of disorder is found to be small relative to that of damping in the case of strong interspan coupling, but of comparable magnitude for weak coupling between spans. The adequacy of the statistical analysis to predict accurately localization in finite disordered beams with boundary conditions is also examined.
AB - The combined effects of disorder and structured damping on the dynamics of a multi-span beam with slight randomness in the spacing between supports are investigated. A wave transfer matrix approach is chosen to calculate the free and forced harmonic responses of this nearly periodic structure. It is shown that both harmonic waves and normal modes of vibration that extend throughout the ordered, undamped beam become spatially attenuated if either small damping or small disorder is present in the system. The physical mechanism which causes this attenuation, however, is one of energy dissipation in the case of damping but one of energy confinement in the case of disorder. The corresponding rates of spatial exponential decay are estimated by applying statistical perturbation methods. It is found that the effects of damping and disorder simply superpose for a multi-span beam with strong interspan coupling, but interact less trivially in the weak coupling case. Furthermore, the effect of disorder is found to be small relative to that of damping in the case of strong interspan coupling, but of comparable magnitude for weak coupling between spans. The adequacy of the statistical analysis to predict accurately localization in finite disordered beams with boundary conditions is also examined.
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U2 - 10.1115/DETC1993-0166
DO - 10.1115/DETC1993-0166
M3 - Conference contribution
AN - SCOPUS:85104184578
T3 - Proceedings of the ASME Design Engineering Technical Conference
SP - 43
EP - 57
BT - 14th Biennial Conference on Mechanical Vibration and Noise
T2 - ASME 1993 Design Technical Conferences, DETC 1993
Y2 - 19 September 1993 through 22 September 1993
ER -