Free vibration analysis of functionally graded conical shell panels by a meshless method

2011 ◽  
Vol 93 (2) ◽  
pp. 649-664 ◽  
Author(s):  
X. Zhao ◽  
K.M. Liew
Keyword(s):  
Free Vibration ◽  
Conical Shell ◽  
Meshless Method ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Functionally Graded

scholarly journals Static bending and free vibration analysis of functionally graded porous plates laid on elastic foundation using the meshless method

2021 ◽  
Vol 15 (2) ◽  
pp. 141-159
Author(s):  
Vu Tan Van ◽  
Nguyen Huynh Tan Tai ◽  
Nguyen Ngoc Hung
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Meshless Method ◽  
Vibration Analysis ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Kriging Interpolation ◽  
Moving Kriging Interpolation

This paper presents a numerical approach for static bending and free vibration analysis of the functionally graded porous plates (FGPP) resting on the elastic foundation using the refined quasi-3D sinusoidal shear deformation theory (RQSSDT) combined with the Moving Kriging–interpolation meshfree method. The plate theory considers both shear deformation and thickness-stretching effects by the sinusoidal distribution of the in-plane displacements, satisfies the stress-free boundary conditions on the top and bottom surfaces of the plate without shear correction coefficient. The advantage of the plate theory is that the displacement field of plate is approximated by only four variables leading to reduce computational efforts. Comparison studies are performed for the square FGPP with simply supported all edges to verify the accuracy of the present approach. The effect of the aspect ratio, volume fraction exponent, and elastic foundation parameters on the static deflections and natural frequency of FGPP are also investigated and discussed. Keywords: meshless method; Moving Kriging interpolation; refined quasi-3D theory; porous functionally\break graded plate; Pasternak foundation.

Free Vibration Analysis of FGM Beams With Different Boundary Conditions Using RKPM Meshless Method

2011 ◽  
Author(s):  
R. Saljooghi ◽  
M. T. Ahmadian
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Meshless Method ◽  
Vibration Analysis ◽  
Reproducing Kernel ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Different Boundary Conditions ◽  
Special Cases

This paper presents free vibration analysis of functionally graded material (FGM) beams with different boundary conditions, using RKPM (Reproducing Kernel Particle Method), which is a meshless method. System of equations of motion is derived by using Lagrange’s method under the assumption of Euler-Bernoulli beam theory. Boundary conditions of beam are taken into account by using Lagrange multipliers. It is assumed that material properties of the beam vary continuously in the thickness direction according to the power-law form. RKPM is applied to obtain eigenvalue equation of vibration and natural frequencies are obtained. It should be noted that for special cases where the beam is uniform, natural frequencies match nicely with theoretical prediction.

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