Thermal Bend of Concrete Rectangular Thin Plate: Two Adjacent Clamped Edges, One Simply Supported Edge, One Free Edge

2018 ◽  
Vol 43 (10) ◽  
pp. 5689-5699
Author(s):  
Xuansheng Cheng ◽  
Lijun Gong ◽  
Xuedong Fu
Keyword(s):  
Thin Plate ◽  
Free Edge ◽  
Rectangular Thin Plate ◽  
Simply Supported ◽  
Clamped Edges

Multi-Pulse Chaotic Motion for a Non-Autonomous Buckled Plate by Using the Extended Melnikov Method

2007 ◽  
Author(s):  
Wei Zhang ◽  
Jun-Hua Zhang ◽  
Ming-Hui Yao
Keyword(s):  
Thin Plate ◽  
Chaotic Dynamics ◽  
Melnikov Method ◽  
Type Equation ◽  
Rectangular Thin Plate ◽  
Governing Equations ◽  
Chaotic Motions ◽  
Simply Supported ◽  
Extended Melnikov Method ◽  
Two Degree Of Freedom

The multi-pulse Shilnikov orbits and chaotic dynamics for a parametrically excited, simply supported rectangular buckled thin plate are studied by using the extended Melnikov method. Based on von Karman type equation and the Galerkin’s approach, two-degree-of-freedom nonlinear system is obtained for the rectangular thin plate. The extended Melnikov method is directly applied to the non-autonomous governing equations of the thin plate. The results obtained here show that the multipulse chaotic motions can occur in the thin plate.

scholarly journals Nontrivial Periodic Solutions of an -Dimensional Differential System and Its Application

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
F. B. Gao
Keyword(s):  
Periodic Solutions ◽  
Thin Plate ◽  
Differential System ◽  
Nonlinear Term ◽  
Periodic Motions ◽  
Rectangular Thin Plate ◽  
Simply Supported ◽  
Nontrivial Periodic Solutions ◽  
Existence Of Periodic Solutions ◽  
Plate System

Two criteria are constructed to guarantee the existence of periodic solutions for a second-order -dimensional differential system by using continuation theorem. It is noticed that the criteria established are found to be associated with the system’s damping coefficient, natural frequency, parametrical excitation, and the coefficient of the nonlinear term. Based on the criteria obtained, we investigate the periodic motions of the simply supported at the four-edge rectangular thin plate system subjected to the parametrical excitation. The effectiveness of the criteria is validated by corresponding numerical simulation. It is found that the existent range of periodic solutions for the thin plate system increases along with the increase of the ratio of the modulus of nonlinear term’s coefficient and parametric excitation term, which generalize and improve the corresponding achievements given in the known literature.

A New Kind of Energy Transfer From the High-Frequency to Low-Frequency Mode in a Composite Laminated Plate

2010 ◽  
Author(s):  
Wei Zhang ◽  
Xiang-Ying Guo ◽  
Qian Wang ◽  
Cui-Cui Liu ◽  
Yun-cheng He
Keyword(s):  
Numerical Simulation ◽  
Natural Frequency ◽  
Thin Plate ◽  
High Frequency ◽  
Low Frequency ◽  
Frequency Mode ◽  
Rectangular Thin Plate ◽  
Chaotic Motions ◽  
Simply Supported ◽  
Low Frequency Mode

This paper focuses on the analysis on a new kind of nonlinear resonant motion with the low-frequency large-amplitude, which can be induced by the high-frequency small-amplitude mode through the mechanism of modulation of amplitude and phase. The system investigated is a simply supported symmetric cross-ply composite laminated rectangular thin plate subjected to parametric excitations. Experimental research has been carried out for the first time. The test plate was excited near the first natural frequency with parametric forces and the above mentioned high-to-low frequency mode has been observed, whose frequency is extremely lower than the first natural frequency. Theoretical job goes to analysis the above phenomenon accordingly. Based on the Reddy’s third-order shear deformation plate theory and the von Karman type equation, the nonlinear governing equations of the simply supported symmetric cross-ply composite laminated rectangular thin plate subjected to parametric excitations are formulated. The Galerkin method is utilized to discretize the governing partial differential equations into a two-degree-of-freedom nonlinear system. Numerical simulation is conducted to investigate this non-autonomous system subsequently. The results of numerical simulation demonstrate that there is a qualitative agreement between the experimental observation and the theoretical result. Besides, the multi-pulse chaotic motions are also reported in numerical simulations.

scholarly journals Multipulse Chaotic Dynamics for a Laminated Composite Piezoelectric Plate

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
J. H. Zhang ◽  
W. Zhang
Keyword(s):  
Thin Plate ◽  
Chaotic Dynamics ◽  
Piezoelectric Plate ◽  
Equations Of Motion ◽  
Laminated Composite ◽  
Phase Portraits ◽  
Rectangular Thin Plate ◽  
Governing Equations ◽  
Chaotic Motions ◽  
Simply Supported

We investigate the global bifurcations and multipulse chaotic dynamics of a simply supported laminated composite piezoelectric rectangular thin plate under combined parametric and transverse excitations. We analyze directly the nonautonomous governing equations of motion for the laminated composite piezoelectric rectangular thin plate. The results obtained here indicate that the multipulse chaotic motions can occur in the laminated composite piezoelectric rectangular thin plate. Numerical simulations including the phase portraits and Lyapunov exponents are used to analyze the complex nonlinear dynamic behaviors of the laminated composite piezoelectric rectangular thin plate.

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