Free Vibration Analysis of Pre-stressed Membrane Using Element Free Galerkin Method

2019 ◽  
pp. 542-550
Author(s):  
K. R. Unnikrishnan ◽  
I. R. Praveen Krishna ◽  
C. O. Arun
Keyword(s):  
Free Vibration ◽  
Galerkin Method ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Element Free

scholarly journals Free Vibration Analysis of Symmetrically Laminated Folded Plate Structures Using an Element-Free Galerkin Method

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
L. X. Peng
Keyword(s):  
Free Vibration ◽  
Galerkin Method ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Laminated Plate ◽  
Element Free Galerkin Method ◽  
Plate Structures ◽  
Element Free Galerkin ◽  
Mass Matrices ◽  
Element Free

An element-free Galerkin method for the solution of free vibration of symmetrically laminated folded plate structures is introduced. Employing the mature meshfree folded plate model proposed by the author, a folded laminated plate is simulated as a composite structure of symmetric laminates that lie in different planes. Based on the first-order shear deformation theory (FSDT) and the moving least-squares (MLS) approximation, the stiffness and mass matrices of the laminates are derived and supposed to obtain the stiffness and mass matrices of the entire folded laminated plate. The equation governing the free vibration behaviors of the folded laminated plate is thus established. Because of the meshfree characteristics of the proposed method, no mesh is involved to determine the stiffness and mass matrices of the laminates. Therefore, the troublesome remeshing can be avoided completely from the study of such problems as the large deformation of folded laminated plates. The calculation of several numerical examples shows that the solutions given by the proposed method are very close to those given by ANSYS, using shell elements, which proves the validity of the proposed method.

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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