• Journal of Advanced Marine Engineering and Technology
• /
• v.22 no.3
• /
• pp.353-361
• /
• 1998

The study on the vibration characteristics of annular sector plates is important for structural engineers. In this study the vibration modes and their natural frequencies of annular sector plates clamped along the inner circumferential edge are obtained by the time average holographic interferometer according to the varying sector angle. The experimental results agree well with those obtained by the numerical analysis. The vibration characteristics of annular sector plates shows great dependence on the sector angle. The radial nodal lines converge to the center of annular sector plate.

• Steel and Composite Structures
• /
• v.36 no.1
• /
• pp.87-101
• /
• 2020

A multi-scale epoxy/CNT/fiberglass annular sector plate is studied in this paper in the view of determining nonlinear forced vibration characteristics. A 3D Mori-Tanaka model is employed for evaluating multi-scale material properties. Thus, all of glass fibers are assumed to have uni-direction alignment and CNTs have random diffusion. The geometry of annular sector plate can be described based on the open angle and the value of inner/outer radius. In order to solve governing equations and derive exact forced vibration curves for the multi-scale annular sector, Jacobi elliptic functions are used. Obtained results demonstrate the significance of CNT distribution, geometric nonlinearity, applied force, fiberglass volume, open angle and fiber directions on forced vibration characteristics of multi-scale annular sector plates.

• Structural Engineering and Mechanics
• /
• v.51 no.6
• /
• pp.1067-1089
• /
• 2014

In this paper, three dimensional static and dynamic analyses of two dimensional functionally graded annular sector plates have been investigated. The material properties vary through both the radial and axial directions continuously. Graded finite element and Newmark direct integration methods have been used to solve the 3D-elasticity equations in time and space domains. The effects of power law exponents and different boundary conditions on the behavior of FGM annular sector plate have been investigated. Results show that using 2D-FGMs and graded elements have superiority over the homogenous elements and 1D-FGMs. The model has been compared with the result of a 1D-FGM annular sector plate and it shows good agreement.

• Computers and Concrete
• /
• v.26 no.1
• /
• pp.21-30
• /
• 2020

Buckling and post-buckling behaviors of geometrically imperfect annular sector plates made from nanoparticle reinforced composites have been investigated. Two types of nanoparticles are considered including graphene oxide powders (GOPs) and silicone oxide (SiO₂). Nanoparticles are considered to have uniform and functionally graded distributions within the matrix and the material properties are derived using Halpin-Tsai procedure. Annular sector plate is formulated based upon thin shell theory considering geometric nonlinearity and imperfectness. After solving the governing equations via Galerkin's technique, it is showed that the post-buckling curves of annular sector plates rely on the geometric imperfection, nanoparticle type, amount of nanoparticles, sector inner/outer radius and sector open angle.

• Structural Engineering and Mechanics
• /
• v.71 no.5
• /
• pp.525-544
• /
• 2019

In the present study, buckling and free vibration analyses of annular thin sector plate made of functionally graded materials (FGMs) resting on visco-elastic Pasternak foundation, subjected to external radial, circumferential and shear in-plane loads is investigated. Material properties are assumed to vary along the thickness according to an power law with Poisson's ratio held constant. First, based on the classical plate theory (CPT), the governing equation of motion is derived using Hamilton's principle and then is solved using the generalized differential quadrature method (GDQM). Numerical results are compared to those available in the literature to validate the convergence and accuracy of the present approach. Finally, the effects of power-law exponent, ratio of radii, thickness of the plate, sector angle, and coefficients of foundation on the fundamental and higher natural frequencies of transverse vibration and critical buckling loads are considered for various boundary conditions. Also, vibration and buckling mode shapes of functionally graded (FG) sector plate have been shown in this research. One of the important obtained results from this work show that ratio of the frequency of FG annular sector plate to the corresponding values of homogeneous plate are independent from boundary conditions and frequency number.

• Steel and Composite Structures
• /
• v.14 no.2
• /
• pp.121-132
• /
• 2013

This paper deals with multiobjective optimization of symmetrically laminated composite angle-ply annular sector plates subjected to axial uniform pressure load and thermal load. The design objective is the maximization of the weighted sum of the critical buckling load and fundamental frequency. The design variable is the fibre orientations in the layers. The performance index is formulated as the weighted sum of individual objectives in order to obtain the optimum solutions of the design problem. The first-order shear deformation theory is used for the mathematical formulation. Finally, the effects of different weighting factors, annularity, sector angle and boundary conditions on the optimal design are investigated and the results are compared.

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

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

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

• Structural Engineering and Mechanics
• /
• v.50 no.6
• /
• pp.773-796
• /
• 2014

This paper deals with free vibration analysis of continuous grading fiber reinforced (CGFR) and bi-directional FG annular sector plates on two-parameter elastic foundations under various boundary conditions, based on the three-dimensional theory of elasticity. The plates with simply supported radial edges and arbitrary boundary conditions on their circular edges are considered. A semi-analytical approach composed of differential quadrature method (DQM) and series solution is adopted to solve the equations of motion. Some new results for the natural frequencies of the plate are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. Results indicate that the non-dimensional natural frequency parameter of a functionally graded fiber volume fraction is larger than that of a discrete laminated and close to that of a 2-layer. It results that the CGFR plate attains natural frequency higher than those of traditional discretely laminated composite ones and this can be a benefit when higher stiffness of the plate is the goal and that is due to the reduction in spatial mismatch of material properties. Moreover, it is shown that a graded ceramic volume fraction in two directions has a higher capability to reduce the natural frequency than conventional one-dimensional functionally graded material. The multidirectional graded material can likely be designed according to the actual requirement and it is a potential alternative to the unidirectional functionally graded material. The new results can be used as benchmark solutions for future researches.