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.

Free vibration analysis of functionally graded beams using an exact plane elasticity approach

2014 ◽  
Vol 228 (14) ◽  
pp. 2488-2494 ◽  
Author(s):  
K Celebi ◽  
N Tutuncu
Keyword(s):  
Free Vibration ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Future Research ◽  
Graded Material ◽  
Beam Thickness ◽  
Plane Elasticity Theory

Exact natural frequencies of functionally graded beams are determined using plane elasticity theory. The analysis yields infinitely many frequencies. For verification purposes, a comparison with the existing beam theory results is performed and a close agreement is observed for slender members. The elasticity solutions are general in the sense that they are valid for slender members as well as short and thick structural elements. Both flexural and axial free vibration mode shapes are presented for top and bottom surfaces and the effect of the beam thickness is discussed. The exact results presented herein can be used as benchmarks for future research of free vibration behavior of short and thick functionally graded material beams.

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.

Computational Development of a 4-Unknowns Trigonometric Quasi-3D Shear Deformation Theory to Study Advanced Sandwich Plates and Shells

2016 ◽  
Vol 08 (04) ◽  
pp. 1650049 ◽  
Author(s):  
J. L. Mantari
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Sandwich Plates And Shells ◽  
Plates And Shells ◽  
First Time ◽  
Stretching Effect

In this paper, a simple and accurate sinusoidal trigonometric theory (STT) for the bending analysis of functionally graded single-layer and sandwich plates and shells is presented for the first time. The principal feature of this theory is that models the thickness stretching effect with only 4-unknowns, even less than the first order shear deformation theory (FSDT) which as it is well-known has 5-unknowns. The governing equations and boundary conditions are derived by employing the principle of virtual work. Then, a Navier-type closed-form solution is obtained for functionally graded plates and shells subjected to bi-sinusoidal load for simply supported boundary conditions. Consequently, numerical results of the present STT are compared with other refined theories, FSDT, and 3D solutions. Finally, it can be concluded that: (a) An accurate but simple 4-unknown STT with thickness stretching effect is developed for the first time. (b) Optimization procedure (described in the paper) appear to be of paramount importance for 4-unknown higher order shear deformation theories (HSDTs) of this gender, so deserves a lot of further research. (c) Transverse shear stresses results are sensitive to the theory and need carefully attention.

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