• Structural Engineering and Mechanics
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• v.83 no.4
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• pp.451-463
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• 2022

The present study deals with forced vibrations of an elastic circular plate supported along its circular edge by unilateral elastic springs. The plate is assumed to be subjected to a uniformly distributed and a concentrated load. Under the combination of these loads, equations of motion are explicitly derived for static and dynamic response analyses by assuming a series of the displacement functions of time and other unknown parameters which are to be determined by employing Lagrangian functional. The approximate solution is sought by applying the Lagrange equations of motions by using the potential energy of the external forces that includes the contributions of the edge forces and the external moments, i.e., those of the effects of the boundary condition to the analysis. For the numerical treatment of the problem in the time domain, the linear acceleration procedure is adopted. The tensionless character of the support is taken into account by using an iterative process and, the coordinate functions for the displacement field are selected to partially fulfill the boundary conditions so that an acceptable approximation can be achieved faster. Numerical results are presented in the figures focusing on the nonlinearity of the problem due to the plate lift-off from the unilateral springs at the edge support.

• Advances in concrete construction
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• v.15 no.2
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• pp.115-126
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• 2023

This paper investigates creep analysis of a plate made of Al-SiC functionally graded material using Mendelson's method of successive elastic solution. All mechanical and thermal material properties, except Poisson's ratio, are assumed to be variable along the thickness direction based on the volume fraction of reinforcement and thickness. First, the basic relations of the plate are derived using the Love-Kirchhoff plate theory. The solution of governing equations yields an elastic solution to start creep analysis. The creep behavior is demonstrated through Norton's equation based on Pandey's experimental results extracted for Al-SiC functionally graded material. A linear variation is assumed for temperature distribution along the thickness direction. The creep strain, as well as the thermal strain, are included in the governing equations derived from classical plate theory for mechanical strain. A successive elastic solution based on Mendelson's method is employed to derive the history of stresses, strains, and displacements over a long time. History of stresses and deformations are obtained over a long time to predict damage to the plate because of various loadings, and material composition along the thickness and planar directions.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.7
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• pp.1244-1254
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• 1992

This paper investigates the vibrational damping characteristics of laminated plates composed of elastic, viscoelastic and elastic layers by theoretical and experimental methods. Laminated plates are in cylindrical bending and visco-elastic adhesive layer is assumed as the visco-elastic spring which takes damping effect through both shear and normal deformations. Governing equations oof laminated plates are derived in the form of simultaneous first order differential equations, which account for the longitudinal displacements, rotary inertia and shear deformations of elastic base plate and elastic constraining plate. The numerical calculations of the equations are illustrated by the applications to the cantilever beam in transverse vibration. The results of the solutions agree well with the experimental measurements in general. The damping effects due to the shear and thickness deformations in the adhesives are analyzed and it is shown that for thicker adhesives, the damping effect due to thickness deformation becomes significant and for thinner adhesives, due to shear deformation.

• Smart Structures and Systems
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• v.21 no.4
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• pp.493-519
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• 2018

This article presents a finite element (FE) model to assess the free vibration and static response of a functionally graded skew magneto-electro-elastic (FGSMEE) plate. Through the thickness material grading of FGSMEE plate is achieved using power law distribution. The coupled constitutive equations along with the total potential energy approach are used to develop the FE model of FGSMEE plate. The transformation matrix is utilized in bringing out the element matrix corresponding to the global axis to a local axis along the skew edges to specify proper boundary conditions. The effect of skew angle on the natural frequency of an FGSMEE plate is analysed. Further, the study includes the evaluation of the static behavior of FGSMEE plate for various skew angles. The influence of skew angle on the primary quantities such as displacements, electric potential, and magnetic potential, and secondary quantities such as stresses, electric displacement and magnetic induction is studied in detail. In addition, the effect of power-law gradient, thickness ratio, boundary conditions and aspect ratio on the free vibration and static response characteristics of FGSMEE plate has been investigated.

• Steel and Composite Structures
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• v.20 no.3
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• pp.513-543
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• 2016

Third order shear deformation theory is used to evaluate electro-elastic solution of a sandwich plate with considering functionally graded (FG) core and composite face sheets made of piezoelectric layers. The plate is resting on the Pasternak foundation and subjected to normal pressure. Short circuited condition is applied on the top and bottom of piezoelectric layers. The governing differential equations of the system can be derived using Hamilton's principle and Maxwell's equation. The Navier's type solution for a sandwich rectangular thick plate with all edges simply supported is used. The numerical results are presented in terms of varying the parameters of the problem such as two elastic foundation parameters, thickness ratio ($h_p/2h$), and power law index on the dimensionless deflection, critical buckling load, electric potential function, and the natural frequency of sandwich rectangular thick plate. The results show that the dimensionless natural frequency and critical buckling load diminish with an increase in the power law index, and vice versa for dimensionless deflection and electrical potential function, because of the sandwich thick plate with considering FG core becomes more flexible; while these results are reverse for thickness ratio.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.6 s.111
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• pp.609-618
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• 2006

This study is undertaken for the vibration analysis of tapered thick plate with concentrated mass on elastic foundation. The boundary condition of the plate is analyzed with the 4-sides simply supported and 4-fixed basis. This study find out the frequency following the change in size for each foundational variable on Pasternak foundation, one of the two-parameter elastic foundation parameter that considered the shear layer to the Winkler foundation parameter. The concentrated mass is applied with the consideration of mass of the entire plate, and the change of frequency is studies on each location with the consideration of reacting for the three locations for concentrated mass. And, in order to find out the change of frequency on the thickness of the plate, it considered tapered ratio that linearly changes depending on the length of the plate with the thickness of the plate in x-direction, and the tapered ratio has changes with 4 types ($\alpha$=0.25, 0, 5, 0.75, and 1.0). For the interpretation, the program using finite element method (F.E.M.) is used and the element coordination is used the 8-node serendipity element. Therefore, the purpose of this study is to find out the characteristics of plate vibration under the mechanica vibration or external vibration factor to facilitate as the basic data of the design to secure the stability.

• Advances in materials Research
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• v.5 no.1
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• pp.35-53
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• 2016

Flexural bending analysis of perfect and imperfect functionally graded materials plates under hygro-thermo-mechanical loading are investigated in this present paper. Due to technical problems during FGM fabrication, porosities and micro-voids can be created inside FGM samples which may lead to the reduction in density and strength of materials. In this investigation, the FGM plates are assumed to have even and uneven distributions of porosities over the plate cross-section. The modified rule of mixture is used to approximate material properties of the FGM plates including the porosity volume fraction. In order the elastic coefficients, thermal coefficient and moisture expansion coefficient of the plate are assumed to be graded in the thickness direction. The elastic foundation is modeled as two-parameter Pasternak foundation. The equilibrium equations are given and a number of examples are solved to illustrate bending response of Metal-Ceramic plates subjected to hygro-thermo-mechanical effects and resting on elastic foundations. The influences played by many parameters are investigated.

• Smart Structures and Systems
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• v.15 no.6
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• pp.1569-1582
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• 2015

Two hyperbolic displacement models are used for the bending response of simply-supported orthotropic laminated composite plates resting on two-parameter elastic foundations under mechanical loading. The models contain hyperbolic expressions to account for the parabolic distributions of transverse shear stresses and to satisfy the zero shear-stress conditions at the top and bottom surfaces of the plates. The present theory takes into account not only the transverse shear strains, but also their parabolic variation across the plate thickness and requires no shear correction coefficients in computing the shear stresses. The governing equations are derived and their closed-form solutions are obtained. The accuracy of the models presented is demonstrated by comparing the results obtained with solutions of other theories models given in the literature. It is found that the theories proposed can predict the bending analysis of cross-ply laminated composite plates resting on elastic foundations rather accurately. The effects of Winkler and Pasternak foundation parameters, transverse shear deformations, plate aspect ratio, and side-to-thickness ratio on deflections and stresses are investigated.

• Advances in nano research
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• v.7 no.1
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• pp.63-75
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• 2019

This article represents a quasi-3D theory for the buckling investigation of magneto-electro-elastic functionally graded (MEE-FG) nanoplates. All the effects of shear deformation and thickness stretching are considered within the presented theory. Magneto-electro-elastic material properties are considered to be graded in thickness direction employing power-law distribution. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of such nanoplates. Using Hamilton's principle, the nonlocal governing equations based on quasi-3D plate theory are obtained for the buckling analysis of MEE-FG nanoplates including size effect and they are solved applying analytical solution. It is found that magnetic potential, electric voltage, boundary conditions, nonlocal parameter, power-law index and plate geometrical parameters have significant effects on critical buckling loads of MEE-FG nanoscale plates.

• Structural Engineering and Mechanics
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• v.27 no.2
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• pp.199-222
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• 2007

Composite laminated structures supported on elastic foundations are being increasingly used in a great variety of engineering applications. Composites exhibit larger dispersion in their material properties compared to the conventional materials due to large number of parameters associated with their manufacturing and fabrication processes. And also the dispersion in elastic foundation stiffness parameter is inherent due to inaccurate modeling and determination of elastic foundation properties in practice. For a better modeling of the material properties and foundation, these are treated as random variables. This paper deals with effects of randomness in material properties and foundation stiffness parameters on the free vibration response of laminated composite plate resting on an elastic foundation. A $C^0$ finite element method has been used for arriving at an eigen value problem. Higher order shear deformation theory has been used to model the displacement field. A mean centered first order perturbation technique has been employed to handle randomness in system properties for obtaining the stochastic characteristic of frequency response. It is observed that small amount of variations in random material properties and foundation stiffness parameters significantly affect the free vibration response of the laminated composite plate. The results have been compared with those available in the literature and an independent Monte Carlo simulation.