Three-Dimensional Free Vibration Analysis of Thick Laminated Composite Circular Plates with Simply-Supported Boundary Conditions

2017 ◽  
Vol 4 (9) ◽  
pp. 10054-10061
Author(s):  
Sumit Khare ◽  
N.D. Mittal
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Circular Plates ◽  
Simply Supported

Free vibration analysis of symmetrically laminated composite circular plates with curvilinear fibers

2017 ◽  
Vol 24 (1) ◽  
pp. 111-121 ◽  
Author(s):  
Ahmed Guenanou ◽  
Abderrahim Houmat
Keyword(s):  
Free Vibration ◽  
Fiber Orientation ◽  
Vibration Analysis ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Published Data ◽  
Circular Plates ◽  
Simply Supported ◽  
Curvilinear Fibers

AbstractThe free vibration analysis of symmetrically laminated composite circular plates with curvilinear fibers is performed using the first-order shear deformation theory along with a curved hierarchical square finite element. The blending function method is used to describe accurately the geometry of the circular plate. The hierarchical shape functions are constructed from Legendre orthogonal polynomials. The element stiffness and mass matrices are integrated numerically by means of the Gauss-Legendre quadrature. The equations of motion are derived using Lagrange’s method. Results for the fundamental frequency are obtained for clamped and soft simply supported laminated composite circular plates with E-glass, graphite, and boron curvilinear fibers in epoxy matrices. The element is validated by means of the convergence test and comparison with published data for isotropic and laminated composite circular plates with rectilinear fibers. Contour plots of frequency as a function of fiber orientation angles for laminated composite circular plates with curvilinear fibers are presented. The fiber material and boundary conditions are shown to influence the distribution of frequency throughout the design space. Frequency curves as a function of fiber orientation angles for the first five modes of laminated composite circular plates with curvilinear fibers are also presented. They reveal that none of the first five modes of clamped and soft simply supported laminates is affected by crossing but modes 3 and 4 of clamped graphite/epoxy and boron/epoxy laminates are affected by veering.

A semi-analytical three-dimensional free vibration analysis of functionally graded curved panels integrated with piezoelectric layers

2014 ◽  
Vol 21 (4) ◽  
pp. 571-587 ◽  
Author(s):  
Hamid Reza Saeidi Marzangoo ◽  
Mostafa Jalal
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Piezoelectric Layers ◽  
Curved Panels

AbstractFree vibration analysis of functionally graded (FG) curved panels integrated with piezoelectric layers under various boundary conditions is studied. A panel with two opposite edges is simply supported, and arbitrary boundary conditions at the other edges are considered. Two different models of material property variations based on the power law distribution in terms of the volume fractions of the constituents and the exponential law distribution of the material properties through the thickness are considered. Based on the three-dimensional theory of elasticity, an approach combining the state space method and the differential quadrature method (DQM) is used. For the simply supported boundary conditions, closed-form solution is given by making use of the Fourier series expansion, and applying the differential quadrature method to the state space formulations along the axial direction, new state equations about state variables at discrete points are obtained for the other cases such as clamped or free-end conditions. Natural frequencies of the hybrid curved panels are presented by solving the eigenfrequency equation, which can be obtained by using edges boundary conditions in this state equation. The results obtained for only FGM shell is verified by comparing the natural frequencies with the results obtained in the literature.

3-D Free Vibration Analysis of Functionally Graded Thick Circular and Annular Plates on Elastic Foundation

2010 ◽  
Author(s):  
Vahid Tajeddini ◽  
Abdolreza Ohadi ◽  
Mojtaba Sadighi
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Small Strain ◽  
Functionally Graded ◽  
Different Boundary Conditions ◽  
Fg Plates

This paper describes a study of three-dimensional free vibration analysis of thick circular and annular functionally graded (FG) plates resting on Pasternak foundation. The formulation is based on the linear, small strain and exact elasticity theory. Plates with different boundary conditions are considered and the material properties of the FG plate are assumed to vary continuously through the thickness according to power law. The kinematic and the potential energy of the plate-foundation system are formulated and the polynomial-Ritz method is used to solve the eigenvalue problem. Convergence and comparison studies are done to demonstrate the correctness and accuracy of the present method. With respect to geometric parameters, elastic coefficients of foundation and different boundary conditions some new results are reported which maybe used as a benchmark solution for future researches.

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