Basic equations of the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with variable thickness

2004 ◽  
Vol 25 (7) ◽  
pp. 812-816 ◽  
Author(s):  
Huang Jia-yin
Keyword(s):  
Thin Plate ◽  
Variable Thickness ◽  
Rectangular Thin Plate ◽  
Basic Equations ◽  
Nonlinear Unsymmetrical Bending

Design of a Variable Thickness Plate to Focus Bending Waves

2012 ◽  
Author(s):  
Noah H. Schiller ◽  
Sz-Chin Steven Lin ◽  
Randolph H. Cabell ◽  
Tony Jun Huang
Keyword(s):  
Numerical Simulations ◽  
Thin Plate ◽  
Traveling Waves ◽  
Variable Thickness ◽  
Focal Point ◽  
Frequency Range ◽  
Additional Energy ◽  
Broad Frequency Range ◽  
Bending Waves ◽  
Energy Dissipated

This paper describes the design of a thin plate whose thickness is tailored in order to focus bending waves to a desired location on the plate. Focusing is achieved by smoothly varying the thickness of the plate to create a type of lens, which focuses structure-borne energy. Damping treatment can then be positioned at the focal point to efficiently dissipate energy with a minimum amount of treatment. Numerical simulations of both bounded and unbounded plates show that the design is effective over a broad frequency range, focusing traveling waves to the same region of the plate regardless of frequency. This paper also quantifies the additional energy dissipated by local damping treatment installed on a variable thickness plate relative to a uniform plate.

Nonlinear Oscillations of a Composite Laminated Plate with Parametrically and Externally Excitations

2013 ◽  
Vol 699 ◽  
pp. 641-644
Author(s):  
Xiao Li Bian ◽  
Shuang Bao Li
Keyword(s):  
Thin Plate ◽  
Nonlinear Oscillations ◽  
Plate Theory ◽  
Laminated Plate ◽  
Rectangular Thin Plate ◽  
Third Order ◽  
Composite Laminated Plate ◽  
Strain Relationship ◽  
Relationship Of ◽  
Equations Of Motions

Nonlinear oscillations of a simply-supported symmetric cross-ply composite laminated rectangular thin plate are investigated in this paper. The rectangular thin plate is subjected to the transversal and in-plane excitations. Based on the Reddy’s third-order shear deformation plate theory and the stress-strain relationship of the composite laminated plate, a two-degree-of-freedom non-autonomous nonlinear system governing equations of motions for the composite laminated rectangular thin plate is derived by using the Galerkin’s method. Numerical simulations illustrate that there exist complex nonlinear oscillations for composite laminated rectangular thin plate.

Mulit-Pulse Orbits and Chaotic Motion of Composite Laminated Plates

2008 ◽  
Author(s):  
Xiangying Guo ◽  
Wei Zhang ◽  
Ming-Hui Yao
Keyword(s):  
Numerical Simulation ◽  
Normal Form ◽  
Differential Equations ◽  
Thin Plate ◽  
Equations Of Motion ◽  
Laminated Plates ◽  
Phase Method ◽  
Rectangular Thin Plate ◽  
Partial Differential ◽  
Chaotic Motions

This paper presents an analysis on the nonlinear dynamics and multi-pulse chaotic motions of a simply-supported symmetric cross-ply composite laminated rectangular thin plate with the parametric and forcing excitations. Firstly, based on the Reddy’s three-order shear deformation plate theory and the model of the von Karman type geometric nonlinearity, the nonlinear governing partial differential equations of motion for the composite laminated rectangular thin plate are derived by using the Hamilton’s principle. Then, using the second-order Galerkin discretization approach, the partial differential governing equations of motion are transformed to nonlinear ordinary differential equations. The case of the primary parametric resonance and 1:1 internal resonance is considered. Four-dimensional averaged equation is obtained by using the method of multiple scales. From the averaged equation obtained here, the theory of normal form is used to give the explicit expressions of normal form. Based on normal form, the energy phase method is utilized to analyze the global bifurcations and multi-pulse chaotic dynamics of the composite laminated rectangular thin plate. The results obtained above illustrate the existence of the chaos for the Smale horseshoe sense in a parametrical and forcing excited composite laminated thin plate. The chaotic motions of the composite laminated rectangular thin plate are also found by using numerical simulation. The results of numerical simulation also indicate that there exist different shapes of the multi-pulse chaotic motions for the composite laminated rectangular thin plate.

Discussion of “Discharge Characteristics of Rectangular Thin-Plate Weirs”

1958 ◽  
Vol 84 (3) ◽  
pp. 21-30
Author(s):  
Steponas Kolupaila ◽  
Ralph W. Powell ◽  
John W. Paull ◽  
Iwao Oki
Keyword(s):  
Thin Plate ◽  
Rectangular Thin Plate ◽  
Discharge Characteristics
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