Free vibration analysis of a composite elliptical plate made of a porous core and two piezoelectric layers

2020 ◽  
pp. 146442072097323
Author(s):  
Morteza Balak ◽  
Saeed Jafari Mehrabadi ◽  
Hamid Mohseni Monfared ◽  
Hassan Feizabadi
Keyword(s):  
Free Vibration ◽  
Porous Materials ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Industrial Applications ◽  
Geometrical Parameters ◽  
Classical Plate Theory ◽  
Porous Core ◽  
Piezoelectric Layers ◽  
Plates And Shells

Porous materials are used extensively to manufacture beams, plates, and shells, and have been studies from different perspectives. Composite porous plates in various shapes and dimensions have numerous industrial applications. The vibration behaviors of rectangular and circular plates have been previously studied; however, less attention has been paid to the analysis of complex configuration, such as elliptical plates. We analyzed the free vibration of composite elliptical plates, consisting of a porous core and two piezoelectric layers. The governing equations were based on the classical plate theory and Rayleigh–Ritz’s energy method. The properties of porous materials with varying thickness of the core and porosity distributions continuously undergo changes due to the intended applications and functions. The proposed theoretical functions satisfy the boundary conditions in simple and clamped forms, and with a high degree of accuracy in the frequencies. Finally, we investigated the effects of important variables, such as geometric parameters and material specifications on the natural frequencies. The results of our analyses were consistent with the findings of previous studies. Based on our vibration analyses, the most crucial factors in composite elliptical plates are geometrical parameters, material specifications, and their effects on the vibration frequencies of the proposed model.

An Exact Levy Solution for Free Vibration Analysis of FGM Plates With Integrated Piezoelectric Layers

2011 ◽  
Author(s):  
M. A. Askari-Farsangi ◽  
A. R. Saidi
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Open Circuit ◽  
Classical Plate Theory ◽  
Arbitrary Boundary ◽  
Piezoelectric Layers ◽  
Coupled Plates

In the present research, an exact Levy solution for the free vibration analysis of FGM plates with integrated piezoelectric layers is established. The electrical boundary conditions and the Maxwell’s equation are satisfied by assuming the transverse distribution of electric potential to be a combination of a parabolic and a linear function. On the basis of classical plate theory, the coupled governing equations for both closed and open circuit piezoelectric coupled structures are reformulated into two new decoupled equations. The numerical results for the Levy type of boundary conditions, two opposite edges simply supported and arbitrary boundary conditions at the other edges, and both closed and open circuit piezoelectric coupled plates have been presented. The effects of piezoelectric layer thickness on the natural frequency for different power law indices, thickness-length ratios, modes, boundary conditions, and material properties are investigated.

Free vibration analysis of imperfect functionally graded sandwich plates: analytical and experimental investigation

2021 ◽  
Vol 111 (2) ◽  
pp. 49-65
Author(s):  
E.K. Njim ◽  
S.H. Bakhy ◽  
M. Al-Waily
Keyword(s):  
Free Vibration ◽  
Power Law ◽  
Vibration Analysis ◽  
Sandwich Plate ◽  
Plate Theory ◽  
Slenderness Ratio ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Classical Plate Theory

Purpose: This paper develops a new analytical solution to conduct the free vibration analysis of porous functionally graded (FG) sandwich plates based on classical plate theory (CPT). The sandwich plate made of the FGM core consists of one porous metal that had not previously been taken into account in vibration analysis and two homogenous skins. Design/methodology/approach: The analytical formulations were generated based on the classical plate theory (CPT). According to the power law, the material properties of FG plates are expected to vary along the thickness direction of the constituents. Findings: The results show that the porosity parameter and the power gradient parameter significantly influence vibration characteristics. It is found that there is an acceptable error between the analytical and numerical solutions with a maximum discrepancy of 0.576 % at a slenderness ratio (a/h =100), while the maximum error percentage between the analytical and experimental results was found not exceeding 15%. Research limitations/implications: The accuracy of analytical solutions is verified by the adaptive finite elements method (FEM) with commercial ANSYS 2020 R2 software. Practical implications: Free vibration experiments on 3D-printed FGM plates bonded with two thin solid face sheets at the top and bottom surfaces were conducted. Originality/value: The novel sandwich plate consists of one porous polymer core and two homogenous skins which can be widely applied in various fields of aircraft structures, biomedical engineering, and defense technology. This paper presents an analytical and experimental study to investigate the free vibration problem of a functionally graded simply supported rectangular sandwich plate with porosities. The objective of the current work is to examine the effects of some key parameters, such as porous ratio, power-law index, and slenderness ratio, on the natural frequencies and damping characteristics.

scholarly journals Thermoelectrically induced nonlinear free vibration analysis of piezo laminated composite conical shell panel with random fiber orientation

2017 ◽  
Vol 4 (1) ◽  
pp. 237-254 ◽  
Author(s):  
Achchhe Lal ◽  
Niranjan L. Shegokar
Keyword(s):  
Free Vibration ◽  
Electric Field ◽  
Conical Shell ◽  
Plate Theory ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Transverse Component ◽  
Piezoelectric Layers ◽  
Parametric Studies ◽  
Shell Panel

Abstract This paper presents the free vibration response of piezo laminated composite geometrically nonlinear conical shell panel subjected to a thermo-electrical loading. The temperature field is assumed to be a uniform distribution over the shell surface and through the shell thickness and the electric field is assumed to be the transverse component E2 only. The material properties are assumed to be independent of the temperature and the electric field. The basic formulation is based on higher order shear deformation plate theory (HSDT) with von-Karman nonlinearity. A C0 nonlinear finite element method based on direct iterative approach is outlined and applied to solve nonlinear generalized eigenvalue problem. Parametric studies are carried out to examine the effect of amplitude ratios, stacking sequences, cone angles, piezoelectric layers, applied voltages, circumferential length to thickness ratios, change in temperatures and support boundary conditions on the nonlinear natural frequency of laminated conical shell panels. The present outlined approach has been validated with those available results in the literature.

On the Application of Mindlin’s Plate Theory to Free Vibration Analysis of Piezoelectric Coupled Circular FGM Plate

2008 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Abbas Rastgoo
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mindlin Plate ◽  
Piezoelectric Layers ◽  
Mindlin Plate Theory ◽  
Clamped Edge

In this paper, a free vibration analysis of moderately thick circular functionally graded (FG) plate integrated with two thin piezoelectric (PZT4) layers is presented based on Mindlin plate theory. The material properties of the FG core plate are assumed to be graded in the thickness direction while the distribution of electric potential field along the thickness of piezoelectric layers is simulated by sinusoidal function. The differential equations of motion are solved analytically for two boundary conditions of the plate: clamped edge and simply supported edge. The analytical solution is validated by comparing the obtained resonant frequencies with those of an isotropic host plate. The emphasis is placed on investigating the effect of varying the gradient index of FG plate on the free vibration characteristics of the structure. Good agreement between the results of this paper and those of the finite element analyses validated the presented approach.

An analytical study on the free vibration of moderately thick fluid-infiltrated porous annular sector plates

2017 ◽  
Vol 24 (18) ◽  
pp. 4130-4144 ◽  
Author(s):  
AS Rezaei ◽  
AR Saidi
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Mindlin Plate ◽  
Geometrical Parameters ◽  
Inviscid Fluid ◽  
Interconnected Network ◽  
Various Boundary Conditions ◽  
Annular Sector

An exact analytical approach based on Mindlin plate theory is considered for free vibration analysis of fluid-saturated porous annular sector plates. The interconnected network of pores is saturated by inviscid fluid and the fluid is trapped in the network. The plate’s radial edges are considered to be simply supported and four auxiliary functions are used to evaluate the natural frequencies of porous plates under undrained condition. The mechanical properties of the material are considered to vary through the thickness by expressing shear modulus and density in terms of a simple cosine rule in case of plates with pores free of fluid. The present method is validated by comparing it with the results of other accurate solutions found in the literature. The influence of the coefficient of plate porosity, geometrical parameters as well as the effect of fluid on natural frequency response of porous annular sector plates under various boundary conditions are comprehensively investigated. It is found that the presence of fluid in the interconnected network of pores causes the fundamental natural frequency to increase. The method proposed in this paper may provide useful information for the future assessments of the dynamic response of porous structures when fluid–solid interaction effects are fully taken into account.

Length scale-dependent natural frequencies of piezoelectric microplates

2017 ◽  
Vol 24 (13) ◽  
pp. 2749-2759 ◽  
Author(s):  
M Jafari ◽  
E Jomehzadeh ◽  
M Rezaeizadeh
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Couple Stress Theory ◽  
Free Vibration Analysis ◽  
Length Scale ◽  
Governing Equations ◽  
Classical Plate Theory ◽  
Wide Range ◽  
Piezoelectric Layers

The length-scale free vibration analysis of a rectangular microplate coupled with piezoelectric layers is presented. The modified couple stress theory is used to describe the size effect of the system. The governing equations of motion are obtained using Hamilton’s principle based on the classical plate theory. The transverse part of the electric potential for the piezoelectric layers is considered to satisfy the Maxwell’s equation and the electrical boundary conditions. A new procedure is introduced to decouple the governing equations and then an analytical Levy-type solution is obtained. The exact natural frequencies are established for a wide range of length scales, various plate dimensions, several piezoelectric layer thicknesses, and different boundary conditions. The results show that the effect of length scale parameter is decreased by the piezoelectric electrical field.

Dynamical Behaviors of Sinusoidal Nanocomposite Plates Subjected to Thermomechanical Loads

2021 ◽  
Author(s):  
Vu Ngoc Viet Hoang ◽  
Dinh Gia Ninh
Keyword(s):  
Thermal Environment ◽  
Plate Theory ◽  
Micromechanical Model ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Rectangular Plates ◽  
Sine Function ◽  
Classical Plate Theory ◽  
Wolfram Mathematica ◽  
Number Of Cycles

In this paper, a new plate structure has been found with the change of profile according to the sine function which we temporarily call as the sinusoidal plate. The classical plate theory and Galerkin’s technique have been utilized in estimating the nonlinear vibration behavior of the new non-rectangular plates reinforced by functionally graded (FG) graphene nanoplatelets (GNPs) resting on the Kerr foundation. The FG-GNP plates were assumed to have two horizontal variable edges according to the sine function. Four different configurations of the FG-GNP plates based on the number of cycles of sine function were analyzed. The material characteristics of the GNPs were evaluated in terms of two models called the Halpin–Tsai micromechanical model and the rule of mixtures. First, to verify this method, the natural frequencies of new non-rectangular plates made of metal were compared with those obtained by the Finite Element Method (FEM). Then, the numerical outcomes are validated by comparing with the previous papers for rectangular FGM/GNP plates — a special case of this structure. Furthermore, the impacts of the thermal environment, geometrical parameters, and the elastic foundation on the dynamical responses are scrutinized by the 2D/3D graphical results and coded in Wolfram-Mathematica. The results of this work proved that the introduced approach has the advantages of being fast, having high accuracy, and involving uncomplicated calculation.

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.

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