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Symmetry 2018, 10(8), 315; https://doi.org/10.3390/sym10080315

Long Time Behavior and Global Dynamics of Simplified Von Karman Plate Without Rotational Inertia Driven by White Noise

1
Division of Dynamics and Control, School of Astronautics, Harbin Institute of Technology, Harbin 150001, China
2
Division of Dynamics and Control, School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China
3
School of Mathematics, Southwest Jiaotong University, Chengdu 610031, China
*
Authors to whom correspondence should be addressed.
Received: 5 June 2018 / Revised: 20 July 2018 / Accepted: 22 July 2018 / Published: 1 August 2018
(This article belongs to the Special Issue New Trends in Dynamics)
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Abstract

Without the assumption that the coefficient of weak damping is large enough, the existence of the global random attractors for simplified Von Karman plate without rotational inertia driven by either additive white noise or multiplicative white noise are proved. Instead of the classical splitting method, the techniques to verify the asymptotic compactness rely on stabilization estimation of the system. Furthermore, a clear relationship between in-plane components of the external force that act on the edge of the plate and the expectation of radius of the global random attractors can be obtained from the theoretical results. Based on the relationship between global random attractor and random probability invariant measure, the global dynamics of the plates are analyzed numerically. With increasing the in-plane components of the external force that act on the edge of the plate, global D-bifurcation, secondary global D-bifurcation and complex local dynamical behavior occur in motion of the system. Moreover, increasing the intensity of white noise leads to the dynamical behavior becoming simple. The results on global dynamics reveal that random snap-through which seems to be a complex dynamics intuitively is essentially a simple dynamical behavior. View Full-Text
Keywords: Simplified clamped Von Karman plate without rotational inertia; global random attractors; global dynamics; random invariant measure; white noise Simplified clamped Von Karman plate without rotational inertia; global random attractors; global dynamics; random invariant measure; white noise
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Chen, H.; Cao, D.; Jiang, J.; Fan, X. Long Time Behavior and Global Dynamics of Simplified Von Karman Plate Without Rotational Inertia Driven by White Noise. Symmetry 2018, 10, 315.

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