• Steel and Composite Structures
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• v.45 no.5
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• pp.767-774
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• 2022

A geometrically nonlinear stability analysis of sandwich annular plates with cellular core and particle-reinforced composite layers has been performed in the present research. The particles are powders of graphene oxide (GOP) which act as nanoscale filler of epoxy matrix. To this regard, Halpin-Tsai micromechanical scheme has been used to define the material properties of the layers. A square shaped core has been considered for which the material properties have been defined based on the relative density concept. Large deflection theory of thin shells has been selected to develop the complete formulation of sandwich plate. The geometrically nonlinear stability analysis of sandwich annular plates has been carried out by indicating that the buckling load is dependent on particle amount, thickness of layer and core relative density.

• Structural Engineering and Mechanics
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• v.29 no.4
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• pp.411-422
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• 2008

In the present study, free vibration analysis of thick annular plates is analyzed by discrete singular convolution method. The Mindlin plate theory is employed. The material is isotropic, homogeneous and obeys Hook's law. In this paper, discrete singular convolution method is used for discretization of equations of motion. Axisymmetric frequency values are presented illustrating the effect of radius ratio and thickness to radius ratio of the annular plate. The influence of boundary conditions on the frequency characteristics is also discussed. Comparing results with those in the literature validates the present analysis. It is shown that the obtained results are very accurate by this approach.

• Structural Engineering and Mechanics
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• v.34 no.4
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• pp.491-505
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• 2010

A computational analysis of the nonlinear free vibration of corrugated annular plates with shallow sinusoidal corrugations under uniformly static ambient temperature is examined. The governing equations based on Hamilton's principle and nonlinear bending theory of thin shallow shell are established for a corrugated plate with a concentric rigid mass at the center and rotational springs at the outer edges. A simple harmonic function in time is assumed and the time variable is eliminated from partial differential governing equations using the Kantorovich averaging procedure. The resulting ordinary equations, which form a nonlinear two-point boundary value problem in spatial variable, are then solved numerically by shooting method, and the temperature-dependent characteristic relations of frequency vs. amplitude for nonlinear vibration of heated corrugated annular plates are obtained. Several numerical results are presented in both tabular and graphical forms, which demonstrate the accuracy of present method and illustrate the amplitude frequency dependence for the plate under such parameters as ambient temperature, plate geometry, rigid mass and elastic constrain.

• Steel and Composite Structures
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• v.44 no.1
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• pp.65-79
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• 2022

The main goal of this paper is to study the vibration of damaged core laminated annular plates with FG face sheets based on a three-dimensional theory of elasticity. The structures are made of a damaged isotropic core and two external face sheets. These skins are strengthened at the nanoscale level by randomly oriented Carbon nanotubes (CNTs) and are reinforced at the microscale stage by oriented straight fibers. These reinforcing phases are included in a polymer matrix and a three-phase approach based on the Eshelby-Mori-Tanaka scheme and on the Halpin-Tsai approach, which is developed to compute the overall mechanical properties of the composite material. In this study the effect of microcracks on the vibrational characteristic of the sandwich plate is considered. In particular, the structures are made by an isotropic core that undergoes a progressive uniform damage, which is modeled as a decay of the mechanical properties expressed in terms of engineering constants. These defects are uniformly distributed and affect the central layer of the plates independently from the direction, this phenomenon is known as "isotropic damage" and it is fully described by a scalar parameter. Three complicated equations of motion for the sectorial plates under consideration are semi-analytically solved by using 2-D differential quadrature method. Using the 2-D differential quadrature method in the r- and z-directions, allows one to deal with sandwich annular plate with arbitrary thickness distribution of material properties and also to implement the effects of different boundary conditions of the structure efficiently and in an exact manner. The fast rate of convergence and accuracy of the method are investigated through the different solved examples. The sandwich annular plate is assumed to have any arbitrary boundary conditions at the circular edges including simply supported, clamped and, free. Several parametric analyses are carried out to investigate the mechanical behavior of these multi-layered structures depending on the damage features, through-the-thickness distribution, and boundary conditions.

• Steel and Composite Structures
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• v.25 no.6
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• pp.649-661
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• 2017

This paper is motivated by the lack of studies in the technical literature concerning to the influence of carbon nanotubes (CNTs) waviness and aspect ratio on the vibrational behavior of functionally graded nanocomposite annular sector plates resting on two-parameter elastic foundations. The carbon nanotube-reinforced (CNTR) plate has smooth variation of CNT fraction based on the power-law distribution in the thickness direction, and the material properties are also estimated by the extended rule of mixture. In this study, the classical theory concerning the mechanical efficiency of a matrix embedding finite length fibers has been modified by introducing the tube-to-tube random contact, which explicitly accounts for the progressive reduction of the tubes' effective aspect ratio as the filler content increases. Parametric studies are carried out to highlight the influence of CNTs volume fraction, waviness and aspect ratio, boundary conditions and elastic foundation on vibrational behavior of FG-CNT thick sectorial plates. The study is carried out based on three-dimensional theory of elasticity and in contrary to two-dimensional theories, such as classical, the first- and the higher-order shear deformation plate theories, this approach does not neglect transverse normal deformations. The annular sector plate is assumed to be simply supported in the radial edges while any arbitrary boundary conditions are applied to the other two circular edges including simply supported, clamped and free. For an overall comprehension on 3-D vibration of annular sector plates, some mode shape contour plots are reported in this research work.

• Steel and Composite Structures
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• v.27 no.6
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• pp.789-801
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• 2018

A weak-form formulation of finite annular prism methods (FAPM) based on Reissner's mixed variational theorem (RMVT), is developed for the quasi three-dimensional (3D) static analysis of two-directional functionally graded (FG) circular plates with various boundary conditions and under mechanical loads. The material properties of the circular plate are assumed to obey either a two-directional power-law distribution of the volume fractions of the constituents through the radial-thickness surface or an exponential function distribution varying doubly exponentially through it. These FAPM solutions of the loaded FG circular plates with both simply-supported and clamped edges are in excellent agreement with the solutions obtained using the 3D analytical approach and two-dimensional advanced plate theories available in the literature.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1996.10a
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• pp.414-421
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• 1996

The study of the vibration characteristics of annular sector plates which are clamped along their inner circumferential edge is important for structural engineers. The present analysis consists of experimental method and numerical method. The experimental method using time-average holographic interferometry is obtained vibration modes and frequencies. The experimental results are verified by a numerical method using F.E.M. The important aspects of the present paper is the dependence of the natural frequencies and the mode shape on the annular area changing sector angle. The radial nodal lines converge to the center of the plate. As increasing sector angle, the radial modes are predominant.

• Smart Structures and Systems
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• v.15 no.5
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• pp.1345-1362
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• 2015

The present paper deals with the free vibration analysis of the functionally graded solid and annular circular plates with two functionally graded piezoelectric layers at top and bottom subjected to an electric field. Classical plate theory (CPT) is used for description of the all deformation components based on a symmetric distribution. All the mechanical and electrical properties except Poisson's ratio can vary continuously along the thickness direction of the plate. The properties of plate core can vary from metal at bottom to ceramic at top. The effect of non homogeneous index of functionally graded and functionally graded piezoelectric sections can be considered on the results of the system. $1^{st}$ and $2^{nd}$ modes of natural frequencies of the system have been evaluated for both solid and annular circular plates, individually.

• Steel and Composite Structures
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• v.23 no.6
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• pp.657-668
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• 2017

In the most of previous studies, researchers have restricted their own studies to consider the effect of single walled carbon nanotubes as a reinforcement on the vibrational behavior of structures. In the present work, free vibration characteristics of functionally graded annular plates reinforced by multi-walled carbon nanotubes resting on Pasternak foundation are presented. The response of the elastic medium is formulated by the Winkler/Pasternak model. Modified Halpin-Tsai equation was used to evaluate the Young's modulus of the multi-walled carbon nanotube/epoxy composite samples by the incorporation of an orientation as well as an exponential shape factor in the equation. The exponential shape factor modifies the Halpin-Tsai equation from expressing a straight line to a nonlinear one in the multi-walled carbon nanotubes wt% range considered. The 2-D generalized differential quadrature method as an efficient and accurate numerical tool is used to discretize the equations of motion and to implement the various boundary conditions. The effects of two-parameter elastic foundation modulus, geometrical and material parameters together with the boundary conditions on the frequency parameters of the plates are investigated. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of annular plates.

• Journal of Korean Society of Steel Construction
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• v.22 no.3
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• pp.241-251
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• 2010

This paper presents the development of a new analytical solution to the governing differential equation for isotropic annular sector plates subjected to uniform loading in a three-dimensional polar coordinate system. The 4th order governing partial differential equation (PDE) was converted to an ordinary differential equation (ODE) by assuming the Levy-type series solution form and the subsequent mathematical operations. Finally, a series-type solution was assembled with homogeneous and nonhomogeneous solution parts after operating real values and complex conjugates derived from the characteristic equation. To demonstrate the convergence rate and the accuracy of the featured method, several examples with various sector angles were selected and solved. The deflections and internal moments in the example annular sector plates that were obtained from the proposed solution were compared with those obtained from other analytical studies and numerical analyses using the finite element analysis package program, ABAQUS. Very good agreement with the results of other analytical and numerical methodologies was shown.