TY - GEN
T1 - A nonlinear normal mode approach for studying waves in nonlinear monocoupled periodic systems
AU - Vakakis, A. F.
AU - King, M. E.
N1 - Funding Information:
This work was supported by an NSF Graduate Fellowship, and by NSF Grant No MSS 92-07318. Dr. Devendra Garg is the Grant monitor.
Publisher Copyright:
© 1995 American Society of Mechanical Engineers (ASME). All rights reserved.
PY - 1995
Y1 - 1995
N2 - The free dynamics of a mono-coupled layered nonlinear periodic system of infinite extent is analyzed. It is shown that, in analogy to linear theory, the system possesses nonlinear attenuation and propagation zones (AZs and PZs) in the frequency domain. Responses in AZs correspond to standing waves with spatially attenuating, or expanding envelopes, and are synchronous motions of all points of the periodic system. These motions are analytically examined by employing the notion of "nonlinear normal mode," thereby reducing the response problem to the solution of an infinite set of singular nonlinear partial differential equations. An asymptotic methodology is developed to solve this set. Numerical computations are carried out to complement the analytical findings. The methodology developed in this work can be extended to investigate synchronous attenuating motions of multi-coupled nonlinear periodic systems.
AB - The free dynamics of a mono-coupled layered nonlinear periodic system of infinite extent is analyzed. It is shown that, in analogy to linear theory, the system possesses nonlinear attenuation and propagation zones (AZs and PZs) in the frequency domain. Responses in AZs correspond to standing waves with spatially attenuating, or expanding envelopes, and are synchronous motions of all points of the periodic system. These motions are analytically examined by employing the notion of "nonlinear normal mode," thereby reducing the response problem to the solution of an infinite set of singular nonlinear partial differential equations. An asymptotic methodology is developed to solve this set. Numerical computations are carried out to complement the analytical findings. The methodology developed in this work can be extended to investigate synchronous attenuating motions of multi-coupled nonlinear periodic systems.
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U2 - 10.115/DETC-1995-0324
DO - 10.115/DETC-1995-0324
M3 - Conference contribution
AN - SCOPUS:85103461155
T3 - Proceedings of the ASME Design Engineering Technical Conference
SP - 825
EP - 832
BT - 15th Biennial Conference on Mechanical Vibration and Noise - Vibration of Nonlinear, Random, and Time-Varying Systems
PB - American Society of Mechanical Engineers (ASME)
T2 - ASME 1995 Design Engineering Technical Conferences, DETC 1995, collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium
Y2 - 17 September 1995 through 20 September 1995
ER -