Natural frequencies of sandwich plate with functionally graded face and homogeneous core

2013 ◽  
Vol 96 ◽  
pp. 226-231 ◽  
Author(s):  
Song Xiang ◽  
Gui-wen Kang ◽  
Ming-sui Yang ◽  
Yan Zhao
Keyword(s):  
Sandwich Plate ◽  
Natural Frequencies ◽  
Functionally Graded ◽  
Homogeneous Core

scholarly journals Three-Dimensional Vibration Analysis of a Functionally Graded Sandwich Rectangular Plate Resting on an Elastic Foundation Using a Semi-Analytical Method

Materials ◽  
2019 ◽  
Vol 12 (20) ◽  
pp. 3401 ◽  
Author(s):  
Cui ◽  
Zhou ◽  
Ye ◽  
Gaidai ◽  
Li ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Elastic Foundation ◽  
Power Law ◽  
Analytical Method ◽  
Sandwich Plate ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Sandwich Plates

The three-dimensional vibration of a functionally graded sandwich rectangular plate on an elastic foundation with normal boundary conditions was analyzed using a semi-analytical method based on three-dimensional elasticity theory. The material properties of the sandwich plate varied with thickness according to the power law distribution. Two types of functionally graded material (FGM) sandwich plates were investigated in this paper: one with a homogeneous core and FGM facesheets, and another with homogeneous panels and an FGM core. Various displacements of the plates were created using an improved Fourier series consisting of a standard Fourier cosine series along with a certain number of closed-form auxiliary functions satisfying the essential boundary conditions. The vibration behavior of the FGM sandwich plate, including the natural frequencies and mode shapes, was obtained using the Ritz method. The effectiveness and accuracy of the suggested technique were fully verified by comparing the natural frequencies of sandwich plates with results from investigations of other functionally graded sandwich rectangular plates in the literature. A parametric study, including elastic parameters, foundation parameters, power law exponents, and layer thickness ratios, was performed, and some new results are presented.

scholarly journals Free Vibrations and Impact Resistance of a Functionally Graded Honeycomb Sandwich Plate

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Jun-hua Zhang ◽  
Bao-juan Dong ◽  
Bince He ◽  
Ying Sun
Keyword(s):  
Sandwich Plate ◽  
Natural Frequencies ◽  
Impact Resistance ◽  
Shear Deformation Theory ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Dynamic Responses ◽  
Inhomogeneous Materials ◽  
Honeycomb Sandwich ◽  
Honeycomb Sandwich Plate

The functionally graded honeycomb has the characteristic of light weight, low density, high impact resistance, noise reduction, and energy absorption as a kind of new composite inhomogeneous materials. It has the advantages of both functionally graded materials and honeycombs. In this paper, a functionally graded honeycomb sandwich plate with functionally graded distributed along the thickness of the plate is constructed. The equivalent elastic parameters of the functionally graded honeycomb core are given. Based on Reddy’s higher-order shear deformation theory (HSDT) and Hamilton’s principle, the governing partial differential equation of motion is derived under four simply supported boundary conditions. The natural frequencies of the graded honeycomb sandwich plate are obtained by both the Navier method from the governing equation and the finite element model. The results obtained by the two methods are consistent. Based on this, the effects of parameters and graded on the natural frequencies of the functionally graded honeycomb sandwich plate are studied. Finally, the dynamic responses of the functionally graded honeycomb sandwich plate under low-speed impacts are studied. The results obtained in this paper will provide a theoretical basis for further study of the complex dynamics of functionally graded honeycomb structures.

Natural vibration of imperfect sandwich plates considering the effects of transverse stretching

2021 ◽  
pp. 107754632110131
Author(s):  
YX Hao ◽  
MX Wang ◽  
W Zhang ◽  
LT Liu ◽  
SW Yang
Keyword(s):  
Functionally Graded Material ◽  
Natural Vibration ◽  
Sandwich Plate ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Three Dimensional ◽  
Core Layer ◽  
Functionally Graded ◽  
Three Dimensional Model ◽  
Graded Material

In this article, the natural vibration investigation of a functionally graded material sandwich plate with initial geometrical imperfection of the exponential function is conducted. Two face sheets of the sandwich plate are composited by functionally graded material. Their material coefficients are affected by temperature and vary in the direction of thickness following the power law. The core layer is only the metal. With the aid of Reddy’s displacement fields, a quasi-three-dimensional model is used, in which the effects of transverse stretching on natural vibration are considered. The natural frequencies and model shapes of the system are calculated on the basis of Rayleigh–Ritz method and Chebyshev polynomials. A comparison of these results with those of the existing three-dimensional theory results shows the validity and computability of present method. The influences of various parameters on the natural frequencies are researched in detail.

Elastic Foundation Analysis of Uniformly Loaded Functionally Graded Viscoelastic Sandwich Plates

2012 ◽  
Vol 28 (3) ◽  
pp. 439-452 ◽  
Author(s):  
A. M. Zenkour ◽  
M. Sobhy
Keyword(s):  
Power Law ◽  
Sandwich Plate ◽  
Plate Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Equilibrium Equations ◽  
Graded Material ◽  
Plate Aspect Ratio ◽  
Type V ◽  
Power Law Index

AbstractThis paper deals with the static response of simply supported functionally graded material (FGM) viscoelastic sandwich plates subjected to transverse uniform loads. The FG sandwich plates are considered to be resting on Pasternak's elastic foundations. The sandwich plate is assumed to consist of a fully elastic core sandwiched by elastic-viscoelastic FGM layers. Material properties are graded according to a power-law variation from the interfaces to the faces of the plate. The equilibrium equations of the FG sandwich plate are given based on a trigonometric shear deformation plate theory. Using Illyushin's method, the governing equations of the viscoelastic sandwich plate can be solved. Parametric study on the bending analysis of FG sandwich plates is being investigated. These parameters include (i) power-law index, (ii) plate aspect ratio, (iii) side-to-thickness ratio, (iv) loading type, (v) foundation stiffnesses, and (vi) time parameter.

Analysis of vibration in rotating pretwisted functionally graded graphene platelets reinforced nanocomposite laminated blades with an attached point mass

2021 ◽  
pp. 095440622110084
Author(s):  
Amin Ghorbani Shenas ◽  
Parviz Malekzadeh ◽  
Sima Ziaee
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Polymer Matrix ◽  
Natural Frequencies ◽  
Weight Fraction ◽  
Functionally Graded ◽  
Point Mass ◽  
Attached Mass ◽  
Graphene Platelets ◽  
Twisted Beam

This work presents an investigation on the free vibration behavior of rotating pre-twisted functionally graded graphene platelets reinforced composite (FG-GPLRC) laminated blades/beams with an attached point mass. The considered beams are constituted of [Formula: see text] layers which are bonded perfectly and made of a mixture of isotropic polymer matrix and graphene platelets (GPLs). The weight fraction of GPLs changes in a layer-wise manner. The effective material properties of FG-GPLRC layers are computed by using the modified Halpin-Tsai model together with rule of mixture. The free vibration eigenvalue equations are developed based on the Reddy’s third-order shear deformation theory (TSDT) using the Chebyshev–Ritz method under different boundary conditions. After validating the approach, the influences of the GPLs distribution pattern, GPLs weight fraction, angular velocity, the variation of the angle of twist along the beam axis, the ratio of attached mass to the beam mass, boundary conditions, position of attached mass, and geometry on the vibration behavior are investigated. The findings demonstrate that the natural frequencies of the rotating pre-twisted FG-GPLRC laminated beams significantly increases by adding a very small amount of GPLs into polymer matrix. It is shown that placing more GPLs near the top and bottom surfaces of the pre-twisted beam is an effective way to strengthen the pre-twisted beam stiffness and increase the natural frequencies.

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.

Free Vibration and Instability Analysis of Sandwich Plates with Carbon Nanotubes-Reinforced Composite Faces and Honeycomb Core

2021 ◽  
Author(s):  
Sushila Chowdhary ◽  
Mesfin Kebede Kassa ◽  
Yitbarek Gashaw Tadesse ◽  
Ananda Babu Arumugam ◽  
Rajeshkumar Selvaraj
Keyword(s):  
Finite Element ◽  
Glass Fiber ◽  
Sandwich Plate ◽  
Natural Frequencies ◽  
Element Formulation ◽  
The Core ◽  
Glass Fiber Reinforced ◽  
End Conditions ◽  
Honeycomb Sandwich ◽  
Instability Regions

In this study, the instability regions of a honeycomb sandwich plate are investigated for different end conditions under periodic in-plane loading. The core layer of the sandwich plate is made of carbon nanotube (CNT)/glass fiber-reinforced honeycomb and the face layers of CNT/glass fiber- reinforced laminated composite. The governing equations are derived using classical laminated plate theory (CLPT) and solved numerically by using finite element formulation. The effectiveness of the developed finite element formulation is demonstrated by comparing the results in terms of natural frequencies with those available in the literature. The effects of CNT wt.% on the core material, CNT wt.% on the skin material, ply orientation and various end conditions on the variation of natural frequencies, loss factors and instability regions are studied. Finally, some inferences for the effects of CNT reinforcement on the honeycomb sandwich plate subjected to the periodic in-plane loads are discussed.

Nonlinear Vibration Analysis of Viscoelastic Smart Sandwich Plates Through the use of Fractional Derivative Zener Model

2021 ◽  
pp. 2150061
Author(s):  
Hamid Reza Talebi Amanieh ◽  
Seyed Alireza Seyed Roknizadeh ◽  
Arash Reza
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Nonlinear Vibration ◽  
Fractional Order ◽  
Sandwich Plate ◽  
Functionally Graded ◽  
Viscoelastic Layer ◽  
Sandwich Plates ◽  
Multiple Time ◽  
Nonlinear Frequency

In this paper, the nonlinear vibrational behavior of a sandwich plate with embedded viscoelastic material is studied through the use of constitutive equations with fractional derivatives. The studied sandwich structure is consisted of a viscoelastic core that is located between the faces of functionally graded magneto-electro-elastic (FG-MEE). In order to determine the frequency-dependent feature of the viscoelastic layer, four-parameter fractional derivative model is utilized. The material properties of FG-MEE face sheets have been distributed considering the power law scheme along the thickness. In addition, for derivation of the governing equations on the sandwich plate, first-order shear deformation plate theory along with von Karman-type of kinematic nonlinearity are implemented. The derived partial differential equations (PDEs) have been transformed to the ordinary differential equations (ODEs) through the Galerkin method. After that, the nonlinear vibration equations for the sandwich plate have been solved by multiple time scale perturbation technique. Moreover, for evaluating the effect of different parameters such as electric and magnetic fields, fractional order, the ratio of the core-to-face thickness and the power low index on the nonlinear vibration characteristics of sandwich plates with FG-MEE face sheets, the parametric analysis has been performed. The obtained results revealed the enhanced nonlinear natural frequency through an increment in the fractional order. Furthermore, the prominent influence of fractional order on the nonlinear frequency of sandwich plate was declared at the negative electric potential and positive magnetic potential.

scholarly journals UNCOUPLED VIBRATIONS IN FUNCTIONALLY GRADED TIMOSHENKO BEAM

2016 ◽  
Vol 54 (6) ◽  
pp. 785 ◽  
Author(s):  
Nguyen Tien Khiem ◽  
Nguyen Ngoc Huyen
Keyword(s):  
Free Vibration ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Flexural Vibration ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Power Law Distribution ◽  
Material Parameters ◽  
Flexural Vibrations ◽  
Fgm Beam

Free vibration of FGM Timoshenko beam is investigated on the base of the power law distribution of FGM. Taking into account the actual position of neutral plane enables to obtain general condition for uncoupling of axial and flexural vibrations in FGM beam. This condition defines a class of functionally graded beams for which axial and flexural vibrations are completely uncoupled likely to the homogeneous beams. Natural frequencies and mode shapes of uncoupled flexural vibration of beams from the class are examined in dependence on material parameters and slendernes

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