Nonlinear Bending Analysis of FG Porous Beams Reinforced with Graphene Platelets Under Various Boundary Conditions by Ritz Method

2021 ◽  
pp. 72-86
Author(s):  
Dang Xuan Hung ◽  
Huong Quy Truong ◽  
Tran Minh Tu
Keyword(s):  
Boundary Conditions ◽  
Ritz Method ◽  
Nonlinear Bending ◽  
Bending Analysis ◽  
Various Boundary Conditions ◽  
Graphene Platelets

Nonlinear bending analysis of fgp plates under various boundary conditions using an analytical approach

Structures ◽  
2021 ◽  
Vol 34 ◽  
pp. 4803-4813
Author(s):  
Pham Thanh Tung ◽  
Nguyen Van Long ◽  
Tran Minh Tu ◽  
Nguyen Thi Bich Phuong ◽  
Le Thanh Hai ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Analytical Approach ◽  
Nonlinear Bending ◽  
Bending Analysis ◽  
Various Boundary Conditions

Vibration of Stiffened Rectangular Plates

1963 ◽  
Vol 67 (629) ◽  
pp. 305-307 ◽  
Author(s):  
S. Mahalingam
Keyword(s):  
Boundary Conditions ◽  
Present Note ◽  
Ritz Method ◽  
Arbitrary Parameter ◽  
Rectangular Plates ◽  
Various Boundary Conditions ◽  
Beam Function ◽  
Rayleigh Method ◽  
The Given ◽  
Free Edges

The free flexural vibrations of rectangular plates with various boundary conditions have been considered by Warburton. The natural frequencies were calculated by the Rayleigh method, the mode assumed being the product of the characteristic beam functions for the given boundary conditions. Comparison with experimental results shows that the method gives reasonably good approximations. The present note describes a method of obtaining the approximately equivalent characteristic beam functions to enable Warburton's method to be extended to plates having one or more stiffeners parallel to an edge. As a numerical example expressions for the frequencies are derived for a plate, simply supported along two opposite edges, and having a central stiffener parallel to the other two free edges. The results are compared with those given in a recent note by Kirk, who solved the same problem by the Rayleigh-Ritz method, using a mode with one arbitrary parameter. In the case of the fundamental frequency of the unstiffened plate, the characteristic beam function in a direction perpendicular to the free edges is simply a constant, and the solution is less accurate than that given by the Rayleigh-Ritz method. However, numerical analysis of a square plate shows that above a certain stiffener depth the characteristic beam function method is more accurate than the Rayleigh-Ritz method. The two methods are also compared for the 2/2 mode.

FREE VIBRATION ANALYSIS OF DISCRETELY STIFFENED SKEW PLATES

2001 ◽  
Vol 01 (01) ◽  
pp. 125-144 ◽  
Author(s):  
HUAN ZENG ◽  
CHARLES W. BERT
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Vibration Characteristics ◽  
Skew Angle ◽  
Various Boundary Conditions ◽  
Skew Plate ◽  
Convergence Study

Stiffened skew plates find application in various engineering fields. The free vibration characteristics of such plates have been studied by various methods. An orthogonally stiffened skew plate is a skew plate with stiffeners running orthogonal to two opposite edges. To the best knowledge of the present investigators, no previous work has been done for free vibration characteristics of skew plates of such stiffening geometry. The present work studies the free vibration of such plates. The pb-2 Rayleigh–Ritz method was employed due to its accuracy and computational efficiency. The conventional finite element method was also used as a comparative check. A convergence study was first performed for various boundary conditions. Then the vibration of orthogonally stiffened skew plates with different boundary conditions was studied. Close agreement was found between these two methods. The variations of natural frequencies with different parameters, including skew angle ϕ, edge ratio b/a, and height-thickness ratio f/h, were investigated for three types of boundary conditions.

Vibration of Rectangular Mindlin Plates with Intermediate Stiffeners

1994 ◽  
Vol 116 (4) ◽  
pp. 529-535 ◽  
Author(s):  
K. M. Liew ◽  
Y. Xiang ◽  
S. Kitipornchai ◽  
M. K. Lim
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Torsional Rigidity ◽  
Ritz Method ◽  
Rectangular Plates ◽  
Vibration Frequencies ◽  
Algebraic Polynomials ◽  
Plate Structures ◽  
Various Boundary Conditions ◽  
Vibrational Response

A first known investigation into the vibratory characteristics of rectangular Mindlin plates with intermediate stiffeners is presented. The Rayleigh-Ritz method is used, with displacement and rotational functions assumed in the form of mathematically complete algebraic polynomials. Sets of numerical frequency parameters for rectangular plates of various boundary conditions, thicknesses and plate dimensions are presented. In the study, the effects of shear deformation and rotary inertia on the vibrational response of the plate structures are investigated. The influence of torsional rigidity and geometric properties of stiffeners on the natural frequency parameters are included. To validate the proposed formulation, numerical results for some simplified problems have been determined where existing literature for these problems can be found. Finally sets of new vibration frequencies for plates with one or more stiffeners in various directions are presented.

Bending analysis of moderately thick functionally graded conical panels with various boundary conditions using GDQ method

2013 ◽  
Vol 103 ◽  
pp. 68-74 ◽  
Author(s):  
J. Abediokhchi ◽  
M. Shakouri ◽  
M.A. Kouchakzadeh
Keyword(s):  
Boundary Conditions ◽  
Functionally Graded ◽  
Bending Analysis ◽  
Various Boundary Conditions

Free vibration analysis of rectangular sandwich plates with compressible core and various boundary conditions

2020 ◽  
pp. 109963622097927
Author(s):  
Sajjad Riahi Farsani ◽  
Arash Ramian ◽  
Ramazan-Ali Jafari-Talookolaei ◽  
Paolo S Valvo ◽  
Maryam Abedi
Keyword(s):  
Boundary Conditions ◽  
Plate Theory ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Thickness Ratio ◽  
Quadratic Functions ◽  
Sandwich Plates ◽  
Various Boundary Conditions ◽  
Rectangular Sandwich Plates

Extended higher-order sandwich plate theory is used to analyze the free vibrations of rectangular sandwich plates with compressible core. Accordingly, first-order shear deformation theory is used to model the laminated face sheets. Besides, the in-plane and transverse displacements of the core are assumed to be cubic and quadratic functions of the thickness coordinate, respectively. To deduce the governing equations, Hamilton’s principle is used. Then, based on the Rayleigh-Ritz method, single series expansions with two-variable orthogonal polynomials – namely, the orthogonal plate functions – are considered to approximate the displacement components. Lastly, a generalized eigenvalue problem is solved to obtain the free vibrational characteristics of sandwich plates with both symmetric and anti-symmetric lay-ups subjected to various boundary conditions. The method is validated against the results obtained by different methods in the literature. Finally, the effects of the plate side-to-thickness ratio, in-plane aspect ratio, and core-to-face sheets thickness ratio on the natural frequencies are discussed.

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