A Coupled Improved Element Free Galerkin-Finite Strip (IEFG-FS) Method for Free Vibration Analysis of Plate

2019 ◽  
Vol 11 (10) ◽  
pp. 1950103 ◽  
Author(s):  
Hamed Mousavi ◽  
Mojtaba Azhari ◽  
Mohammad Mehdi Saadatpour ◽  
Saeid Sarrami-Foroushani
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Complex Geometry ◽  
Free Vibration Analysis ◽  
Delta Function ◽  
Thin Plates ◽  
Finite Strip ◽  
Element Free Galerkin ◽  
Element Free

In this paper, a coupling of improved element-free Galerkin (IEFG) method and semi-analytical finite strip (FS) method is presented for free vibration analysis of thin plates. This method is very easy to implement and has advantages of both IEFG and FS methods, so that IEFG method is used in sub-domain with complex geometry, and FS method is used for the remaining domains. The use of the FS method considerably reduces the analysis time, and the essential boundary conditions are easily enforced in FS sub-domain. In the IEFG method, the shape function does not have the Kronecker delta function property. Therefore, Lagrange multipliers method is used to satisfy the boundary conditions. Finally, five examples are presented to show the effectiveness of this work.

scholarly journals Free Vibration Analysis of L-Shaped Folded Thin Plates

2019 ◽  
Vol 2 (1) ◽  
pp. 67-73
Author(s):  
Koji Sekine
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Energy Functional ◽  
Thin Plates ◽  
Mode Shapes ◽  
Width Ratio ◽  
Various Boundary Conditions

Free vibration analysis of L-shaped folded thin plates having various boundary conditions is presented. Vibration properties of the folded plates are analyzed by means of the Ritz method. Displacement functions satisfying the geometric boundary conditions are assumed in the form of double power series. The interconnection of plate elements of the folded plates is defined by translational and rotational coupling springs. The generalized eigenvalue problem, which is derived by means of minimizing the energy functional, is solved to determine the natural frequencies and mode shapes. The accuracy and validity of the present solutions are demonstrated through convergence studies and comparisons with the results from the literature and FEM (finite element method) analysis solutions. Numerical results are presented for different conditions, such as width ratio, length ratio and the four types of boundary condition.

A semi-analytical element-free galerkin method for the 3D free vibration analysis of multilayered FGM circular hollow cylinders

2011 ◽  
Vol 22 (17) ◽  
pp. 1993-2007 ◽  
Author(s):  
Chih-Ping Wu ◽  
Shih-Wei Yang
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Reproducing Kernel ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Weak Formulation ◽  
Element Free Galerkin ◽  
Hollow Cylinders ◽  
Element Free

A semi-analytical element-free Galerkin (EFG) method in conjunction with an earlier proposed differential reproducing kernel (DRK) interpolation is developed for the three-dimensional (3D) free vibration analysis of simply supported, multilayered composite and functionally graded material (FGM) circular hollow cylinders. Based on the Reissner’s mixed variational theorem (RMVT), the weak formulation of this 3D dynamic problem is derived, in which the material properties of each individual FGM layer are assumed to obey the power-law distributions of the volume fractions of the constituents through the thickness coordinate of the layer. A parametric study of the influence of some geometric and material parameters, such as the radius-to-thickness and length-to-radius ratios, thickness ratio for each layer, and material-property gradient index, on the natural frequency parameters of multilayered FGM circular hollow cylinders is undertaken.

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