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.

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.

scholarly journals Free Vibration of Sandwich Plates and Shells by Using Zig-Zag Function

2009 ◽  
Vol 16 (5) ◽  
pp. 495-503 ◽  
Author(s):  
S. Brischetto ◽  
E. Carrera ◽  
L. Demasi
Keyword(s):  
Free Vibration ◽  
Free Vibration Analysis ◽  
Sandwich Plates ◽  
Vibration Modes ◽  
Fundamental Vibration ◽  
First Derivative ◽  
The Core ◽  
Sandwich Plates And Shells ◽  
Plates And Shells ◽  
Free Vibration Response

This paper analyses the free vibration response of sandwich curved and flat panels by introducing the zig-zag function (—1)kζk(ZZF) in the displacement models of classical and higher order two-dimensional shell theories. The main advantage of ZZF is the introduction of a discontinuity in the first derivative, zig-zag effect, of the displacements distribution with correspondence to the core/faces interfaces. Results including and discarding ZZF are compared. Several values of face-to-core stiffness ratio (FCSR) and geometrical plate/shell parameters have been analyzed. Both fundamental vibration modes and those corresponding to high wave numbers are considered in the analysis. It is concluded that: (1) ZZF is highly recommended in the free vibration analysis of sandwich plates and shells; (2) the use of ZZF makes the error almost independent by FCSR parameter; (3) ZZF is easy to implement and its use should be preferred with respect to other `more cumbersome' refined theories.

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).

Computational Models for Sandwich Panels and Shells

1996 ◽  
Vol 49 (3) ◽  
pp. 155-199 ◽  
Author(s):  
Ahmed K. Noor ◽  
W. Scott Burton ◽  
Charles W. Bert
Keyword(s):  
Computational Models ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Local Buckling ◽  
Sandwich Panels ◽  
Free Vibrations ◽  
Sandwich Plates ◽  
Material Parameters ◽  
Sandwich Plates And Shells ◽  
Plates And Shells

The focus of this review is on the hierarchy of computational models for sandwich plates and shells, predictor-corrector procedures, and the sensitivity of the sandwich response to variations in the different geometric and material parameters. The literature reviewed is devoted to the following application areas: heat transfer problems; thermal and mechanical stresses (including boundary layer and edge stresses); free vibrations and damping; transient dynamic response; bifurcation buckling, local buckling, face-sheet wrinkling and core crimping; large deflection and postbuckling problems; effects of discontinuities (eg, cutouts and stiffeners), and geometric changes (eg, tapered thickness); damage and failure of sandwich structures; experimental studies; optimization and design studies. Over 800 relevant references are cited in this review, and another 559 references are included in a supplemental bibliography for completeness. Extensive numerical results are presented for thermally stressed sandwich panels with composite face sheets showing the effects of variation in their geometric and material parameters on the accuracy of the free vibration response, and the sensitivity coefficients predicted by eight different modeling approaches (based on two-dimensional theories). The standard of comparison is taken to be the analytic three-dimensional thermoelasticity solutions. Some future directions for research on the modeling of sandwich plates and shells are outlined.

Curvature Approximation Effects in the Free Vibration Analysis of Functionally Graded Shells

2016 ◽  
Vol 08 (06) ◽  
pp. 1650079 ◽  
Author(s):  
Salvatore Brischetto
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Curvilinear Coordinates ◽  
Equilibrium Equations ◽  
Partial Differential ◽  
Exact Geometry

The present work investigates the effects of the curvature terms in the three-dimensional (3D) equilibrium equations used for the free vibration analysis of functionally graded material (FGM) structures. The 3D equilibrium equations have been written in general orthogonal curvilinear coordinates which are valid for spherical shells. They automatically degenerate in those for cylindrical shells and plates considering one of the two radii of curvature and both radii of curvature equal to infinite, respectively. The approximation of curvature terms in the 3D equilibrium equations has been evaluated by means of frequency analyses. Results obtained via 3D equilibrium equations with exact geometry have been compared with those calculated via 3D equilibrium equations written with the approximation of the curvature terms. The effects of the curvature approximations depend on the thickness and curvature of the structures, on the materials, lamination sequences and FGM laws, on the frequency orders and vibration modes. The resulting system of second order partial differential equations has been reduced into a system of first order partial differential equations redoubling the variables. Therefore, the exponential matrix method has been employed using a layer wise approach. The final 3D equations have been solved in exact form considering harmonic displacement components and simply supported structures. The approximation of the curvature terms has been introduced in the 3D equilibrium shell equations. For numerical reasons, interlaminar continuity conditions and the top and bottom boundary and loading conditions have been written including the exact geometry. The introduction of curvature approximations only in the equilibrium equations is sufficient to obtain an exhaustive qualitative analysis of the importance of curvature terms in the free vibration problems for FGM structures.

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