• Structural Engineering and Mechanics
• /
• v.31 no.5
• /
• pp.587-603
• /
• 2009

We performed a free vibration analysis of skew composite laminates with or without cutout based on the high-order shear deformation plate theory (HSDT). The effects of skew angles and ply orientations on the natural frequencies for various boundary conditions are studied using a nonlinear high-order finite element program developed for this study. The numerical results are in good agreement with those reported by other investigators for simple test cases, and the new results reported in this paper show the interactions between the skew angle, layup sequence and cutout size on the free vibration of the laminate. The findings highlight the importance of skew angles when analyzing laminated composite skew plates with cutout or without cutout.

• Geomechanics and Engineering
• /
• v.16 no.1
• /
• pp.1-9
• /
• 2018

In this paper an efficient and simple refined shear deformation theory is presented for the free vibration of Functionally Graded Plates Under Various Boundary Conditions. The theory accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The number of independent unknowns of present theory is four, as against five in other shear deformation theories. The plates are considered of the type having two opposite sides simply-supported, and the two other sides having combinations of simply-supported, clamped, and free boundary conditions. The mechanical properties of functionally graded material are assumed to vary according to power law distribution of the volume fraction of the constituents. Equations of motion are derived using Hamilton's principle. The results of this theory are compared with those of other shear deformation theories. Various numerical results including the effect of boundary conditions, power-law index, plate aspect ratio, and side-to-thickness ratio on the free vibration of FGM plates are presented.

• Steel and Composite Structures
• /
• v.22 no.6
• /
• pp.1281-1299
• /
• 2016

This paper deals with the analysis of vibration of antisymmetric angle-ply plates using spline method for higher order shear theory. Free vibration of laminated plates is addressed to show the capability of the present method in the vicinity of higher order shear deformation theory and simply supported edges of plates. The coupled differential equations are obtained in terms displacement and rotational functions. These displacement and rotational functions are approximated using cubic and quantic spline. A generalized eigenvalue problem is obtained and solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. The antisymmetric angle-ply fiber orientation are taken as design variables. Numerical results enable us to examine the frequencies for various geometric and material parameters and accuracy and effectiveness of the proposed method is also verified by comparative study.

• Structural Engineering and Mechanics
• /
• v.89 no.6
• /
• pp.601-615
• /
• 2024

Effect of ring and straight stiffeners in the buckling as well as vibration characteristics of metal-ceramic functionally graded plates with cutout subjected to various uniaxial and localized in-plane compressive edge loadings was explored in the present work. In the current work, the distinguishing characteristics of metal and ceramic are merged in a single volume, and power law was used for estimating the material composition throughout thickness. Buckling and free vibration characteristics were studied initially for unstiffened Al/SiC functionally graded plates with cutout. Subsequently, the influence of cutout ratio on buckling load as well as natural frequency for different power law indices was discussed. The functionally graded plate was stiffened by three different stiffener patterns, namely; ring stiffener, straight stiffener, as well as a combination of the ring and the straight stiffener, to enhance the buckling as well as vibration characteristics. The effect of stiffener depth ratio for different stiffener patterns was also presented for functionally graded plates having different cutout sizes under various loading conditions. Such studies on functionally graded material have potential applications in a variety of technological fields including the aerospace and defense sectors.

• Structural Engineering and Mechanics
• /
• v.56 no.2
• /
• pp.223-240
• /
• 2015

In this work, a nonlocal quasi-3D trigonometric plate theory for micro/nanoscale plates is proposed. In order to introduce the size influences, the Eringen's nonlocal elasticity theory is utilized. In addition, the theory considers both shear deformation and thickness stretching effects by a trigonometric variation of all displacements within the thickness, and respects the stress-free boundary conditions on the top and bottom surfaces of the plate without considering the shear correction factor. The advantage of this theory is that, in addition to considering the small scale and thickness stretching effects (${\varepsilon}_z{\neq}0$), the displacement field is modelled with only 5 unknowns as the first order shear deformation theory (FSDT). Analytical solutions for vibration of simply supported micro/nanoscale plates are illustrated, and the computed results are compared with the available solutions in the literature and finite element model using ABAQUS software package. The influences of the nonlocal parameter, shear deformation and thickness stretching on the vibration behaviors of the micro/nanoscale plates are examined.

• Structural Engineering and Mechanics
• /
• v.9 no.3
• /
• pp.269-288
• /
• 2000

The governing differential equations for free vibration of multi-step orthotropic shear plates with variably distributed mass, stiffness and viscous damping are established. It is shown that a shear plate can be divided into two independent shear bars to determine the natural frequencies and mode shapes of the plate. The jk-th natural frequency of a shear plate is equal to the square root of the square sum of the j-th natural frequency of a shear bar and the k-th natural frequency of another shear bar. The jk-th mode shape of the shear plate is the product of the j-th mode shape of a shear bar and the k-th mode shape of another shear bar. The general solutions of the governing equations of the orthotropic shear plates with various boundary conditions are derived by selecting suitable expressions, such as power functions and exponential functions, for the distributions of stiffness and mass along the height of the plates. A numerical example demonstrates that the present methods are easy to implement and efficient. It is also shown through the numerical example that the selected expressions are suitable for describing the distributions of stiffness and mass of typical multi-storey buildings.

• Journal of Magnetics
• /
• v.17 no.1
• /
• pp.61-67
• /
• 2012

The miniaturization of an electrostatic precipitator has become a key element in successfully constructing an efficient electrostatic precipitator because of the limited space allowed for installation in a subway tunnel. Therefore, the miniaturization of the rapping system of the electrostatic precipitator has also become important. This research proposes a resonant-type electromagnetic vibration exciter as a vibrating rapper for an electrostatic precipitator. The compact vibrating rapper removes collected dust from the collecting plates without direct impact on those collecting plates. To characterize the dynamic performance of the electromagnetic vibration exciter, finite element analysis was performed using a commercial electromagnetic analysis program, MAXEWLL. Moreover, we analyzed the resonant frequency of an electrostatic precipitator, to which the electromagnetic vibration exciter was applied, by ANSYS. Also, to measure the acceleration generated by the electromagnetic vibration exciter, we manufactured a prototype of the ESP and electromagnetic vibration exciter and measured its acceleration at the resonant frequency.

• 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.

• Journal of Korean Society of Steel Construction
• /
• v.13 no.5
• /
• pp.443-455
• /
• 2001

An energy method has been used for an elastic formulation of bending vibration and buckling analysis of laminated composite plates on two-parameter elastic foundations. A quasi-elastic method is used for the solution of viscoelastic analysis of the laminated composite plates. The third-order shear deformation theory is applied by using the double-fourier series. To validate the derived equations the obtained displacements for simply supported orthotropic plates on elastic foundations are compared with those of LUSAS program Numerical results of the viscoelastic bending vibration and buckling analysis are presented to show the effects of layup sequence number of layers material anisotropy and shear modulus of foundations.

• Proceedings of the KSME Conference
• /
• 2003.04a
• /
• pp.839-844
• /
• 2003

The effect of water level on the free vibration of a partially water-filled two rectangular plates structure was investigated by experimental modal analysis and finite element analysis using ANSYS computer program. Modal parameters of two rectangular plates coupled with water were obtained by means of experiment and the FEM solutions were compared with the experimental solutions to verify the finite element model. As a result, the comparison between the experiment and FEM results showed excellent agreement. The transverse vibration modes, in-phase and out-of-phase, were observed alternately in the fluid-coupled system. The effect of water level and water gap size on the fluid-coupled natural frequency were investigated. It was found that the natural frequency of the partially water-filled two rectangular plates are not proportional to the water level, but depend on mode number of plates.