Large Amplitude Free Vibration Analysis of Thin Annular Sector Plates Using Differential Quadrature Method

2010 ◽  
Author(s):  
S. H. Mirtalaie ◽  
M. A. Hajabasi
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Large Amplitude ◽  
Plate Theory ◽  
Nonlinear Eigenvalue Problem ◽  
Differential Quadrature Method ◽  
Free Vibration Analysis ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Annular Sector

In this paper, the Differential Quadrature Method (DQM) is used to study the large amplitude free vibration of thin annular sector plates. The geometrical nonlinear governing equations of motion are derived based on the classical plate theory and using the von Karman nonlinear strain-displacement relationships. Following the DQ-procedure and employing the concept of new degrees of freedom a nonlinear eigenvalue problem is obtained which is solved iteratively and nonlinear natural frequencies of the plate are obtained. The results show a very good convergence and they are compared with the available literature for the clamped boundary conditions to demonstrate the validity of the work. The effects of boundary conditions, inner to outer radius ratio and sector angle on the large amplitude free vibration of thin plate are studied.

Free Vibration Analysis of Functionally Graded Moderately Thick Annular Sector Plates Using Differential Quadrature Method

2011 ◽  
Vol 110-116 ◽  
pp. 2990-2998 ◽  
Author(s):  
S.H. Mirtalaie ◽  
M.A. Hajabasi ◽  
F. Hejripour
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Volume Fraction ◽  
Differential Quadrature Method ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Differential Quadrature ◽  
Radius Ratio ◽  
Quadrature Method ◽  
Annular Sector

In this paper, the free vibration of moderately thick annular sector plates made of functionally graded materials is studied using the Differential Quadrature Method (DQM). The material properties of the functionally graded plate are assumed to vary continuously through the thickness, according to a power-law distribution. The governing differential equations of motion are derived based on the First order Shear Deformation plate Theory (FSDT) and then solved numerically using DQM under different boundary conditions. The results for the isotropic plates which are derivable with this approach are presented and compared with the literature and they are in good agreement. The natural frequencies of the functionally graded moderately thick annular sector plates under various combinations of clamped, simple supported and free boundary conditions are presented for the first time. The effects of boundary conditions, sector angle, radius ratio, thickness to outer radius ratio, volume fraction exponent and variation of the Poisson’s ratio on the free vibration behavior of the plate are studied

Free vibration analysis of functionally graded thin annular sector plates using the differential quadrature method

2010 ◽  
Vol 225 (3) ◽  
pp. 568-583 ◽  
Author(s):  
S H Mirtalaie ◽  
M A Hajabasi
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Differential Quadrature Method ◽  
Functionally Graded ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Fg Plates ◽  
Annular Sector

In this article, the differential quadrature method (DQM) is used to study the free vibration of functionally graded (FG) thin annular sector plates. The material properties of the FG-plate are assumed to vary continuously through the thickness, according to the power-law distribution. The governing differential equations of motion are derived based on the classical plate theory and solved numerically using DQM. The natural frequencies of thin FG annular sector plates under various combinations of clamped, free, and simply supported boundary conditions are presented for the first time. To ensure the accuracy of the method, the natural frequencies of a pure metallic plate are calculated and compared with those existing in the literature for the homogeneous plate. In this case, the result shows very good agreement. For the FG-plates, the effects of boundary conditions, volume fraction exponent, and variation of Poisson's ratio on the free vibrational behaviour of the plate are studied.

A modified state space differential quadrature method for free vibration analysis of soft-core sandwich panels

2017 ◽  
Vol 21 (6) ◽  
pp. 1843-1879 ◽  
Author(s):  
Balavishnu Udayakumar ◽  
KV Nagendra Gopal
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
State Space ◽  
Vibration Analysis ◽  
Differential Quadrature Method ◽  
Sandwich Panels ◽  
Free Vibration Analysis ◽  
Differential Quadrature ◽  
Soft Core ◽  
Quadrature Method

Modifications and improvements to conventional state space differential quadrature method are proposed for free vibration analysis of thick, soft-core sandwich panels with arbitrary edge boundary conditions, using an exact two-dimensional elasticity model. The modifications are based on a systematic procedure to implement all possible combinations of edge boundary conditions including simply supported, clamped, free and guided edges. Natural frequencies and mode shapes are obtained and compared with exact elasticity solutions from state space method and approximate solution from finite element simulations; demonstrating the high numerical accuracy and rapid convergence of the modified method. Further, the proposed framework is compared to the conventional implementation of the state space differential quadrature method for thick cantilever sandwich panels and is shown to give results with better accuracy and faster convergence.

Differential Quadrature Free Vibration Analysis of Functionally Graded Thin Annular Sector Plates in Thermal Environments

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
S. H. Mirtalaie
Keyword(s):  
Free Vibration ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Plate Theory ◽  
Differential Quadrature Method ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Differential Quadrature ◽  
Annular Sector

In this paper, the free vibration behavior of functionally graded (FG) thin annular sector plates in thermal environment is studied using the differential quadrature method (DQM). The material properties of the FG plate are assumed to be temperature dependent and vary continuously through the thickness, according to the power-law distribution of the volume fraction of the constituents. The nonlinear temperature distribution along the thickness direction of the plate is considered. Based on the classical plate theory, the governing differential equations of motion of the plate are derived and solved numerically using DQM. The natural frequencies of thin FG annular sector plates in thermal environment under various combinations of clamped, free, and simply supported boundary conditions (BCs) are presented for the first time. To ensure the accuracy of the method, the natural frequencies of a pure metallic plate are calculated and compared with those existing in the literature for the homogeneous plate where the results are in good agreement. The effects of temperature field, BCs, volume fraction exponent, radius ratio, and the sector angle on the free vibrations of the FG-plate are examined.

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