Static and free vibration analyses of carbon nanotube-reinforced composite plate using differential quadrature method

Meccanica ◽  
2014 ◽  
Vol 50 (1) ◽  
pp. 61-76 ◽  
Author(s):  
Akbar Alibeigloo ◽  
Ali Emtehani
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Composite Plate ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Reinforced Composite

Elasticity Solution of Free Vibration and Bending Behavior of Functionally Graded Carbon Nanotube-Reinforced Composite Beam with Thin Piezoelectric Layers Using Differential Quadrature Method

2015 ◽  
Vol 07 (01) ◽  
pp. 1550002 ◽  
Author(s):  
A. Alibeigloo ◽  
K. M. Liew
Keyword(s):  
Carbon Nanotube ◽  
Boundary Conditions ◽  
Mechanical Behavior ◽  
State Space ◽  
Differential Quadrature Method ◽  
Functionally Graded ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Reinforced Composite ◽  
Piezoelectric Layers

Based on the theory of elasticity, bending and free vibrational analyses of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beam embedded in piezoelectric layers are carried out, using the state-space differential quadrature method (DQM). Applying the DQM to the governing differential equations and boundary conditions along the longitudinal directions, new state equations about state variables at discrete points are derived. By using the state-space technique across the thickness direction, semi- analytical closed form solutions are derived. The method is validated by comparing numerical results for beams without piezoelectric layers. Both the direct and the inverse piezoelectric effects are investigated and the influence of piezoelectric layers on the mechanical behavior of beam is studied. Furthermore, the effects of CNT volume fraction, kind of CNT distribution, length to thickness ratio and edge boundary conditions on the mechanical behavior of the beams are examined.

Analysis of free vibration of an isotropic plate with surface or internal long crack using generalized differential quadrature method

2019 ◽  
Vol 55 (1-2) ◽  
pp. 42-52
Author(s):  
Milad Ranjbaran ◽  
Rahman Seifi
Keyword(s):  
Differential Equations ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Isotropic Plate ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Generalized Differential Quadrature Method ◽  
Generalized Differential

This article proposes a new method for the analysis of free vibration of a cracked isotropic plate with various boundary conditions based on Kirchhoff’s theory. The isotropic plate is assumed to have a part-through surface or internal crack. The crack is considered parallel to one of the plate edges. Existence of the crack modified the governing differential equations which were formulated based on the line-spring model. Generalized differential quadrature method discretizes the obtained governing differential equations and converts them into an algebraic system of equations. Then, an eigenvalue analysis was used to determine the natural frequencies of the cracked plates. Some numerical results are given to demonstrate the accuracy and convergence of the obtained results. To demonstrate the efficiency of the method, the results were compared with finite element solutions and available literature. Also, effects of the crack depth, its location along the thickness, the length of the crack and different boundary conditions on the natural frequencies were investigated.

Sign in / Sign up

Export Citation Format

Share Document