• Steel and Composite Structures
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• v.26 no.5
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• pp.649-662
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• 2018

In this study, based on the three-dimensional theory of elasticity, free vibration characteristics of sandwich sectorial plates with multiwalled carbon nanotube-(MWCNT)-reinforced composite core are considered. Modified Halpin-Tsai equation is used to evaluate the Young's modulus of the MWCNT/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 MWCNTs wt% range considered. In this paper, free vibration of thick functionally graded sandwich annular sectorial plates with simply supported radial edges and different circular edge conditions including simply supported-clamped, clamped-clamped, and free-clamped is investigated. A semi-analytical approach composed of two-dimensional differential quadrature method and series solution are adopted to solve the equations of motion. The material properties change continuously through the core thickness of the plate, which can vary according to a power-law, exponentially, or any other formulations in this direction. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of laminated sectorial plates.

• Journal of the Korea institute for structural maintenance and inspection
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• v.2 no.4
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• pp.209-216
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• 1998

본 논문에서는 부채꼴형 Mindlin 평판의 엄밀한 휨진동해를 제시하였다. 진동변위의 두 가지 적합 함수식, 즉 대수삼각다항식과 Mindlin 모서리함수를 Ritz방법에 적용하였다. 모서리함수는 부채꼴형 평판의 둔각 정점부에 존재하는 모멘트와 전단력의 특이도를 동시에 고려하고 있다. 이러한 모서리함수는 진동수의 수렴속도를 가속화한다. 본 연구에서는 부채꼴형 각도의 범위와 두께 비에 따른 엄밀한 진동수 및 수직진동 변위의 전형적인 등고선을 제시하였다.

• Structural Engineering and Mechanics
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• v.9 no.6
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• pp.519-540
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• 2000

In this study, a new functional based on the Reissner theory, for thick plates on a Winkler foundation is obtained. This functional has geometric and dynamic boundary conditions. In deriving the new functional, the $G{\hat{a}}teaux$ differential is used. This functional which is in polar coordinates is also transformable into the classical potential energy equation. Bending and torsional moments, transverse shear forces, rotations and displacements are the basic unknowns of the functional. Two different sectorial elements are developed with $3{\times}8$ degrees of freedom (SEC24) and $4{\times}8$ degrees of freedom (SEC32). The accuracy of the SEC24 and SEC32 elements together are verified by applying the method to some problems taken from literature.

• Journal of Korean Society of Steel Construction
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• v.10 no.4 s.37
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• pp.601-613
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• 1998

This paper reports the first-of-its-kind free vibration solutions for sectorial plates having re-entrant corners causing stress singularities when the circular edge is either clamped or simply supported. The Ritz method is employed with two sets of admissible functions assumed for the transverse vibratory displacements. Accurate frequencies and normalized contours of the transverse vibratory displacement are presented for the spectra of sector angles.

• Nuclear Engineering and Technology
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• v.31 no.2
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• pp.214-225
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• 1999

An accurate method is presented for flexural vibrations of sectorial plates having simply supported-free and free-free radial edges, when the circular edge is either clamped or simply supported. The classical Ritz method is employed with two sets of admissible functions assumed for the transverse vibratory displacements. These sets consist of : (1) mathematically complete algebraic-trigonometric polynomials which gurantee convergence to exact frequencies as sufficient terms are retained, and (2) comer functions which account for the bending moment singularities at re-entrant comer of the radial edges having arbitrary edge conditions. Accurate (at least four significant figures) frequencies and normalized contours of the transverse vibratory displacement are presented for the spectra of corner angles [90$^{\circ}$, 180$^{\circ}$(semi-circular), 270$^{\circ}$, 300$^{\circ}$, 330$^{\circ}$, 350$^{\circ}$, 355$^{\circ}$, 360$^{\circ}$ (complete circular)] causing a re-entrant comer of the radial edges. Future solutions drawn from alternative numerical procedures and finite element techniques may be compared with these accurate results.

• Journal of electromagnetic engineering and science
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• v.12 no.3
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• pp.216-222
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• 2012

This paper presents a single-pole eight-throw switch, based on an eight-way power divider, using substrate integrate waveguide(SIW) technology. Eight sectorial-lines are formed by inserting radial slot-lines on the top plate of SIW power divider. Each sectorial-line can be controlled independently with high level of isolation. The switching is accomplished by altering the capacitance of the varactor on the line, which causes different input impedances to be seen at a central probe to each sectorial line. The proposed structure works as a switching circuit and an eight-way power divider depending on the bias condition. The change in resonant frequency and input impedance are estimated by adapting a tapered transmission line model. The detailed design, fabrication, and measurement are discussed.

• Steel and Composite Structures
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• v.28 no.5
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• pp.541-557
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• 2018

This paper presents the influence of carbon nanotubes (CNTs) waviness and aspect ratio on the vibrational behavior of functionally graded nanocomposite sandwich annular sector plates resting on two-parameter elastic foundations. The carbon nanotube-reinforced (CNTR) sandwich plate has smooth variation of CNT fraction along the thickness direction. The distributions of CNTs are considered functionally graded (FG) or uniform along the thickness and their mechanical properties are estimated by an 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. Effects of CNT distribution, volume fraction, aspect ratio and waviness, and also effects of Pasternak's elastic foundation coefficients, sandwich plate thickness, face sheets thickness and plate aspect ratio are investigated on the free vibration of the sandwich plates with wavy CNT-reinforced face sheets. 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 sandwich 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.

• Steel and Composite Structures
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• v.48 no.1
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• pp.1-17
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• 2023

The main goal of this paper is to study vibration of damaged core laminated sectorial plates with Functionally graded (FG) face sheets based on 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. 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 sector 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 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. 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.

• Journal of the Korea institute for structural maintenance and inspection
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• v.2 no.4
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• pp.217-223
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• 1998

본 논문에서는 원형연단이 단순지지 되어 있을 때 단순과 자유의 방사연단 조건을 갖는 부채꼴형 평판의 휨진동에 대한 엄밀한 해석방법을 제시한다. Ritz방법을 이용하여 수직진동변위를 두가지 적합 함수식으로 가정하였다. 이러한 두가지의 적합 함수식은 (1) 수학적으로 완전한 대수삼각다항함수와, (2) 둔각 모서리에서의 휨모멘트 특이도를 고려하는 모서리함수로 구성되어있다. 본 연구에서는 방사연단의 둔각 모서리를 이루는 부채꼴형 각도의 범위에 따른 엄밀한 진동수 및 수직진동 변위의 전형적인 등고선을 제시하였다.

• Steel and Composite Structures
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• v.35 no.1
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• pp.111-127
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• 2020

The goal of this study is to fill this apparent gap in the area about investigating the effect of porosity distributions on vibrational behavior of FG sectorial plates resting on a two-parameter elastic foundation. The response of the elastic medium is formulated by the Winkler/Pasternak model. The internal pores and graphene platelets (GPLs) are distributed in the matrix either uniformly or non-uniformly according to three different patterns. The model is proposed with material parameters varying in the thickness of plate to achieve graded distributions in both porosity and nanofillers. The elastic modulus of the nanocomposite is obtained by using Halpin-Tsai micromechanics model. 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. The 2-D differential quadrature method as an efficient and accurate numerical approach is used to discretize the governing equations and to implement the boundary conditions. The convergence of the method is demonstrated and to validate the results, comparisons are made between the present results and those reported by well-known references for special cases treated before, have confirmed accuracy and efficiency of the present approach. It is observed that the maximum vibration frequency obtained in the case of symmetric porosity and GPL distribution, while the minimum vibration frequency is obtained using uniform porosity distribution. Results show that for better understanding of mechanical behavior of nanocomposite plates, it is crucial to consider porosities inside the material structure.