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Title: Homoclinic behaviors and chaotic motions of double layered viscoelastic nanoplates based on nonlocal theory and extended Melnikov method

The nonlinear dynamical equations are established for the double layered viscoelastic nanoplates (DLNP) subjected to in-plane excitation based on the nonlocal theory and von Kármán large deformation theory. The extended high dimensional homoclinic Melnikov method is employed to study the homoclinic phenomena and chaotic motions for the parametrically excited DLNP system. The criteria for the homoclinic transverse intersection for both the asynchronous and synchronous buckling cases are proposed. Lyapunov exponents and phase portraits are obtained to verify the Melnikov-type analysis. The influences of structural parameters on the transverse homoclinic orbits and homoclinic bifurcation sets are discussed for the two buckling cases. Some novel phenomena are observed in the investigation. It should be noticed that the nonlocal effect on the homoclinic behaviors and chaotic motions is quite remarkable. Hence, the small scale effect should be taken into account for homoclinic and chaotic analysis for nanostructures. It is significant that the nonlocal effect on the homoclinic phenomena for the asynchronous buckling case is quite different from that for the synchronous buckling case. Moreover, due to the van der Walls interaction between the layers, the nonlocal effect on the homoclinic behaviors and chaotic motions for high order mode is rather tiny under themore » asynchronous buckling condition.« less
Authors:
;  [1] ;  [1] ;  [2]
  1. School of Astronautics, Harbin Institute of Technology, P. O. Box 137, Harbin 150001 (China)
  2. (China)
Publication Date:
OSTI Identifier:
22402564
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 25; Journal Issue: 6; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 77 NANOSCIENCE AND NANOTECHNOLOGY; BIFURCATION; BUCKLING; CHAOS THEORY; DEFORMATION; DYNAMICS; EXCITATION; KINETIC EQUATIONS; LYAPUNOV METHOD; NANOSTRUCTURES; NONLINEAR PROBLEMS; VAN DER WAALS FORCES