scholarly journals Three-Dimensional Exact Free Vibration Analysis of Spherical, Cylindrical, and Flat One-Layered Panels

2014 ◽  
Vol 2014 ◽  
pp. 1-29 ◽  
Author(s):  
Salvatore Brischetto
Keyword(s):  
Free Vibration ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Closed Shell ◽  
Free Vibrations ◽  
Curvilinear Coordinates ◽  
Shell Panel ◽  
Plates And Shells ◽  
Orthogonal Curvilinear Coordinates

The paper proposes a three-dimensional elastic analysis of the free vibration problem of one-layered spherical, cylindrical, and flat panels. The exact solution is developed for the differential equations of equilibrium written in orthogonal curvilinear coordinates for the free vibrations of simply supported structures. These equations consider an exact geometry for shells without simplifications. The main novelty is the possibility of a general formulation for different geometries. The equations written in general orthogonal curvilinear coordinates allow the analysis of spherical shell panels and they automatically degenerate into cylindrical shell panel, cylindrical closed shell, and plate cases. Results are proposed for isotropic and orthotropic structures. An exhaustive overview is given of the vibration modes for a number of thickness ratios, imposed wave numbers, geometries, embedded materials, and angles of orthotropy. These results can also be used as reference solutions to validate two-dimensional models for plates and shells in both analytical and numerical form (e.g., closed solutions, finite element method, differential quadrature method, and global collocation method).

scholarly journals AN EXACT 3D SOLUTION FOR FREE VIBRATIONS OF MULTILAYERED CROSS-PLY COMPOSITE AND SANDWICH PLATES AND SHELLS

2014 ◽  
Vol 06 (06) ◽  
pp. 1450076 ◽  
Author(s):  
SALVATORE BRISCHETTO
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Free Vibrations ◽  
Curvilinear Coordinates ◽  
Sandwich Plates ◽  
Multilayered Structures ◽  
Plate And Shell ◽  
Sandwich Plates And Shells ◽  
Plates And Shells

A 3D free vibration analysis of multilayered structures is proposed. An exact solution is developed for the differential equations of equilibrium written in general orthogonal curvilinear coordinates. The equations consider a geometry for shells without simplifications and allow the analysis of spherical shell panels, cylindrical shell panels, cylindrical closed shells and plates. The 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 structures. Results are given for multilayered composite and sandwich plates and shells. A free vibration analysis is proposed for a number of vibration modes, thickness ratios, imposed wave numbers, geometries and multilayer configurations embedding isotropic and orthotropic composite materials. These results can also be used as reference solutions for plate and shell 2D models developed for the analysis of multilayered structures.

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.

Three-Dimensional Static and Free Vibration Analysis of Carbon Nano Tube Reinforced Composite Cylindrical Shell Using Differential Quadrature Method

2016 ◽  
Vol 08 (03) ◽  
pp. 1650033 ◽  
Author(s):  
A. Alibeigloo ◽  
H. Jafarian
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Radial Coordinate ◽  
Axial Coordinate ◽  
Reinforced Composite ◽  
Space Technique

In this paper, bending and free vibration analysis of carbon nanotubes reinforced composite (CNTRC) cylindrical shell is carried out using the three-dimensional theory of elasticity. The single-walled carbon nanotubes (SWCNT) reinforcement is either uniformly distributed (UD) or functionally graded (FG) in the thickness direction which, are specified as the cases [Formula: see text], [Formula: see text], [Formula: see text] and FG-X. Effective material properties of CNTRC cylindrical shell are estimated according to the rule of mixture as well as considering the CNT efficiency parameters. An analytical solution is performed by using Fourier series along the axial coordinate together with state space technique along the radial coordinate for the simply supported CNTRC cylindrical shell. Moreover, for CNTRC cylindrical shell with other edges boundary conditions, a semi-analytical solution is accomplished by using differential quadrature method (DQM) along the axial coordinate and state space technique along the radial coordinate. Present approach is validated by comparing the numerical results with the available published results. Furthermore, effect of types of CNT distributions in the polymer matrix, volume fraction of CNT, edges boundary conditions and radial-to-thickness ratio on the bending and free vibration behavior of FG-CNTRC cylindrical are examined.

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.

On buckling and free vibration studies of sandwich plates and cylindrical shells: A review

2018 ◽  
Vol 33 (5) ◽  
pp. 673-724 ◽  
Author(s):  
Pavan Kumar ◽  
CV Srinivasa
Keyword(s):  
Free Vibration ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Future Research ◽  
Sandwich Plates ◽  
Composite Sandwich ◽  
Sandwich Plates And Shells ◽  
Graded Material ◽  
Plates And Shells

Many review articles were published on free vibration and buckling of laminated composites, sandwich plates, and shells. The present article reviews the literature on the buckling and free vibration analysis of shear deformable isotropic and laminated composite sandwich plates and shells using various methods available for plates in the past few decades. Various theories, finite element modeling, and experimentations have been reported for the analysis of sandwich plates and shells. Few papers on functionally graded material plates, plates with smart skin (electrorheological, magnetorheological, and piezoelectric), and also viscoelastic materials were also reviewed. The scope for future research on sandwich plates and shells was also accessed.

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