Three-Dimensional Vibrations of Cross-ply Laminated Hollow Cylinders With Clamped Edge Boundaries

1997 ◽  
Vol 119 (3) ◽  
pp. 317-323 ◽  
Author(s):  
J. Q. Ye ◽  
K. P. Soldatos
Keyword(s):  
Vibration Analysis ◽  
Three Dimensional ◽  
Normal Modes ◽  
Free Vibration Analysis ◽  
Dimensional Solution ◽  
Simply Supported ◽  
Recursive Solution ◽  
Modes Of Vibration ◽  
Hollow Cylinders ◽  
Clamped Edge

Using fully three-dimensional elasticity considerations, this paper presents a free vibration analysis of cross-ply laminated hollow cylinders having clamped edge boundaries. The analysis is based on a recursive solution that has been published elsewhere and is suitable for three-dimensional vibration analysis of corresponding simply supported cylinders. Clamped boundary conditions are initially imposed by means of a number of fixed circles located at the edge(s) of the cylinder considered. Using certain dynamic considerations together with the Lagrange multipliers method, this is achieved by suitably coupling a certain number of different normal modes of vibration of the corresponding simply supported cylinder. Hence, an approximate solution, which however is practically very close to the exact three-dimensional solution, is finally obtained by appropriately increasing either the number of the coupled vibration modes or the number of fixed circles on a clamped edge.

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.

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.

Three Dimensional Vibration Analysis of Rectangular Plates With Undamaged and Damaged Boundaries by the Spectral Collocation Method

2011 ◽  
Author(s):  
Ma’en S. Sari ◽  
Eric A. Butcher
Keyword(s):  
Boundary Conditions ◽  
Collocation Method ◽  
Vibration Analysis ◽  
Numerical Technique ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Simply Supported ◽  
Grid Points

This paper presents a new numerical technique for the free vibration analysis of isotropic three dimensional elastic plates with damaged boundaries. In the study, it is assumed that the plates have free lateral surfaces, and two opposite simply supported edges, while the other edges could be clamped, simply supported or free. For this purpose, the Chebyshev collocation method is applied to obtain the natural frequencies of three dimensional plates with damaged clamped boundary conditions, where the governing equations and boundary conditions are discretized by the presented method and put into matrix vector form. The damaged boundaries are represented by distributed translational springs. In the present study the boundary conditions are coupled with the governing equation to obtain the eigenvalue problem. Convergence studies are carried out to determine the sufficient number of grid points used. First, the results obtained for the undamaged plates are verified with previous results in the literature. Subsequently, the results obtained for the damaged three dimensional plates indicate the behavior of the natural vibration frequencies with respect to the severity of the damaged boundary. This analysis can lead to an efficient technique for damage detection of structures in which joint or boundary damage plays a significant role in the dynamic characteristics. The results obtained from the Chebychev collocation solutions are seen to be in excellent agreement with those presented in the literature.

scholarly journals Exact 3D solutions and finite element 2D models for free vibration analysis of plates and cylinders

2014 ◽  
Vol 1 (1) ◽  
Author(s):  
Salvatore Brischetto ◽  
Roberto Torre
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Curvilinear Coordinates ◽  
The Finite Element Method ◽  
Dimensional Solution ◽  
Isotropic Composite ◽  
Orthogonal Curvilinear Coordinates

AbstractThe paper proposes a comparison between classical two-dimensional (2D) finite elements (FEs) and an exact three-dimensional (3D) solution for the free vibration analysis of one-layered and multilayered isotropic, composite and sandwich plates and cylinders. Low and high order frequencies are analyzed for thick and thin simply supported structures. Vibration modes are investigated to make a comparison between results obtained via the finite element method and those obtained by means of the exact three-dimensional solution. The 3D exact solution is based on the differential equations of equilibrium written in general orthogonal curvilinear coordinates. This exact method is based on a layer-wise approach, the continuity of displacements and transverse shear/normal stresses is imposed at the interfaces between the layers of the structure. The geometry for shells is considered without any simplifications. The 2D finite element results are obtained by means of a well-known commercial FE code. The differences between 2D FE solutions and 3D exact solutions depend on the considered mode, the order of frequency, the thickness ratio of the structure, the geometry, the embedded material and the lamination sequence.

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