scholarly journals Analytical bending solutions of clamped rectangular thin plates resting on elastic foundations by the symplectic superposition method

2013 ◽  
Vol 26 (3) ◽  
pp. 355-361 ◽  
Author(s):  
Baofeng Pan ◽  
Rui Li ◽  
Yewang Su ◽  
Bo Wang ◽  
Yang Zhong
Keyword(s):  
Thin Plates ◽  
Superposition Method ◽  
Elastic Foundations

scholarly journals Analytic bending solutions of free rectangular thin plates resting on elastic foundations by a new symplectic superposition method

2013 ◽  
Vol 469 (2153) ◽  
pp. 20120681 ◽  
Author(s):  
Rui Li ◽  
Yang Zhong ◽  
Ming Li
Keyword(s):  
Finite Element Method ◽  
Symplectic Geometry ◽  
Analytic Solutions ◽  
Thin Plates ◽  
Superposition Method ◽  
The Finite Element Method ◽  
Simple Derivation ◽  
Elastic Foundations ◽  
Winkler Model ◽  
Geometry Method

Analytic bending solutions of free rectangular thin plates resting on elastic foundations, based on the Winkler model, are obtained by a new symplectic superposition method. The proposed method offers a rational elegant approach to solve the problem analytically, which was believed to be difficult to attain. By way of a rigorous but simple derivation, the governing differential equations for rectangular thin plates on elastic foundations are transferred into Hamilton canonical equations. The symplectic geometry method is then introduced to obtain analytic solutions of the plates with all edges slidingly supported, followed by the application of superposition, which yields the resultant solutions of the plates with all edges free on elastic foundations. The proposed method is capable of solving plates on elastic foundations with any other combinations of boundary conditions. Comprehensive numerical results validate the solutions by comparison with those obtained by the finite element method.

Analytical free vibration solutions of fully free orthotropic rectangular thin plates on two-parameter elastic foundations by the symplectic superposition method

2020 ◽  
pp. 107754632096782
Author(s):  
Xin Su ◽  
Eburilitu Bai
Keyword(s):  
Free Vibration ◽  
Fundamental Solutions ◽  
Thin Plates ◽  
Superposition Method ◽  
Elastic Foundations ◽  
Vibration Problem ◽  
Separation Variable ◽  
Vibration Problems ◽  
Two Parameter ◽  
Free Edges

The free vibration of orthotropic rectangular thin plates with four free edges on two-parameter elastic foundations is studied by the symplectic superposition method. Firstly, by analyzing the boundary conditions, the original vibration problem is converted into two sub-vibration problems of the plates slidingly clamped at two opposite edges. Based on slidingly clamped at two opposite edges, the fundamental solutions of these two sub-vibration problems are respectively derived by the separation variable method of the corresponding Hamiltonian system, and then the symplectic superposition solution of the original vibration problem is obtained by superimposing the fundamental solutions of the two sub-problems. Finally, the symplectic superposition solution obtained in this study is verified by calculating the frequencies and mode functions of several concrete rectangular thin plates with four free edges.

Analysis of Clamped Rectangular Plates

1940 ◽  
Vol 7 (4) ◽  
pp. A139-A142
Author(s):  
Dana Young
Keyword(s):  
Middle Surface ◽  
Lateral Loading ◽  
Thin Plates ◽  
Superposition Method ◽  
Rectangular Plates ◽  
Lagrange’S Equation

Abstract This paper attempts to solve the problem of the bending action of rectangular plates clamped at all four edges and subjected to lateral loading. Analytical in nature, the author’s investigation is based upon the ordinary theory of bending of thin plates as treated in Lagrange’s equation of the middle surface. The superposition method is used and applied to a number of loadings not hitherto studied.

New analytic buckling solutions of side-cracked rectangular thin plates by the symplectic superposition method

2021 ◽  
Vol 191 ◽  
pp. 106051
Author(s):  
Zhaoyang Hu ◽  
Xinran Zheng ◽  
Dongqi An ◽  
Chao Zhou ◽  
Yushi Yang ◽  
...  
Keyword(s):  
Thin Plates ◽  
Superposition Method

On the symplectic superposition method for new analytic free vibration solutions of side-cracked rectangular thin plates

2020 ◽  
Vol 489 ◽  
pp. 115695
Author(s):  
Zhaoyang Hu ◽  
Yushi Yang ◽  
Chao Zhou ◽  
Xinran Zheng ◽  
Rui Li
Keyword(s):  
Free Vibration ◽  
Thin Plates ◽  
Superposition Method
Sign in / Sign up

Export Citation Format

Share Document