• Steel and Composite Structures
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• v.20 no.4
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• pp.889-911
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• 2016

Using the hyperbolic shear deformation plate model and including plate-foundation interaction (Winkler and Pasternak model), an analytical method in order to determine the deflection and stress distributions in simply supported rectangular functionally graded plates (FGP) subjected to a sinusoidal load, a temperature and moisture fields. The present theory exactly satisfies stress boundary conditions on the top and the bottom of the plate. No transversal shear correction factors are needed because a correct representation of the transversal shearing strain is given. Materials properties of the plate (elastic, thermal and moisture expansion coefficients) are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. Numerical examples are presented and discussed for verifying the accuracy of the present theory in predicting the bending response of FGM plates under sinusoidal load and a temperature field as well as moisture concentration. The effects of material properties, temperature, moisture, plate aspect ratio, side-to-thickness ratio, ratio of elastic coefficients (ceramic-metal) and three distributions for both temperature and moisture on deflections and stresses are investigated.

• 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.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.9 s.114
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• pp.949-957
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• 2006

In this Paper, reduction of noise and vibration in ship cabins by using floating floor is studied. Two theoretical models are presented and predicted insertion losses of floating floor are compared to experimental results, where measurements have been done in mock-up built for simulating typical ship cabin structures. In ships, mineral wool is usually used as the impact absorbing materials. The first model (M-S-Plate Model) is that upper plate and mineral wool are assumed as a one-dimensional mass-spring system, which is in turn attached to the simply supported elastic floor. The second model (Wave-Plate Model) is that mineral wool is assumed as an elastic medium for wave propagation. The comparisons show that M-S-Plate model is in good agreement with experimental results when density of mineral wool is 140K, and fiber direction is horizontal. For higher density and vertical fiber direction, Wave-Plate model shows good agreements with measurements. It is found that including the elastic behavior of the floor is essential in improving accuracy of the prediction for low frequency ranges below $100{sim}200Hz$.

• Structural Engineering and Mechanics
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• v.90 no.6
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• pp.551-568
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• 2024

The present study deals with static and dynamic behaviors including forced vibrations of an elastic rectangular nano plate on the two-parameter foundation. Firstly, the rectangular plate is assumed to be subjected to uniformly distributed and eccentrically applied concentrated loads. The governing equations of the problem are derived by considering the dynamic response of the plate, employing a series of the Chebyshev polynomials for the displacement function and applying the Galerkin method. Then, effects of the non-essential boundary conditions of the plate, i.e., the boundary conditions related to the shearing forces, the bending moments and the corner forces, are included in the governing equation of motion to compensate for the non-satisfied boundary conditions and increase the accuracy of the Galerkin method. The approximate numerical solution is accomplished using an iterative process due to the non-linearity of the unilateral property of the two-parameter foundation. The plate under static concentrated load is investigated in detail numerically by considering a wide range of parameters of the plate and the foundation stiffnesses. Numerical treatment of the problem in the time domain is carried out by assuming a stepwise variation of the concentrated load and the linear acceleration procedure is employed in the solution of the system of governing differential equations derived from the equation of motion. Time variations of the contact region and those of the displacements of the plate are presented in the figures for various numbers of the two-parameter of the foundation, as well as the classical and nano parameters of the plate particularly focusing on the non-linearity of the problem due to the plate lift-off from the unilateral foundation. The effects of classical and nonlocal parameters and loading are investigated in detail. Definition of the separation between the plate and the two-parameter foundation is presented and applied to the given problem. The effect of the lift-off on the static and dynamic behavior of the rectangular plate is studied in detail by considering various loading conditions. The numerical study shows that the effect of nonlocal parameters on the behavior of the plate becomes significant, when nonlinearity becomes more profound, due to the lift-off of the plate. It is seen that the size effects are significant in static and dynamic analysis of nano-scaled rectangular plates and need to be included in the mechanical analyses. Furthermore, the corner displacement of the plate is affected more significantly from the lift-off, whereas it is less marked in the time variation of the middle displacement of the plate. Several numerical examples are presented to examine the sensibility of various parameters associated with nonlocal parameters of the plate and foundation. Both stiffening and softening nonlocal parameters behavior of the plate are identified in the numerical solutions which show that increasing the foundation stiffness decreases the extent of the contact region, whereas the stiffness of the shear layer increases the contact region and reduces the foundation settlement considerably.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.38 no.4
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• pp.347-355
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• 2014

Thermal problems that are directly related to the lifetime of an electronic device are becoming increasingly important owing to the miniaturization of electronic devices. To solve thermal problems, it is essential to study thermal stability through thermal diffusion and insulation. A honeycomb sandwich plate has anisotropic thermal conductivity. To analyze the thermal deformation and temperature distribution of a system that employs a honeycomb sandwich plate, the thermal and elastic properties need to be determined. In this study, the thermal and elastic properties of a honeycomb sandwich plate, such as thermal conductivity, coefficient of thermal expansion, elastic modulus, Poisson's ratio, and shear modulus, are predicted. The properties of a honeycomb sandwich plate vary according to the hexagon size, thickness, and material properties.

• Steel and Composite Structures
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• v.34 no.4
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• pp.511-524
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• 2020

In this research, a simple four-variable trigonometric integral shear deformation model is proposed for the static behavior of advanced functionally graded (AFG) ceramic-metal plates supported by a two-parameter elastic foundation and subjected to a nonlinear hygro-thermo-mechanical load. The elastic properties, including both the thermal expansion and moisture coefficients of the plate, are also supposed to be varied within thickness direction by following a power law distribution in terms of volume fractions of the components of the material. The interest of the current theory is seen in its kinematics that use only four independent unknowns, while first-order plate theory and other higher-order plate theories require at least five unknowns. The "in-plane displacement field" of the proposed theory utilizes cosine functions in terms of thickness coordinates to calculate out-of-plane shear deformations. The vertical displacement includes flexural and shear components. The elastic foundation is introduced in mathematical modeling as a two-parameter Winkler-Pasternak foundation. The virtual displacement principle is applied to obtain the basic equations and a Navier solution technique is used to determine an analytical solution. The numerical results predicted by the proposed formulation are compared with results already published in the literature to demonstrate the accuracy and efficiency of the proposed theory. The influences of "moisture concentration", temperature, stiffness of foundation, shear deformation, geometric ratios and volume fraction variation on the mechanical behavior of AFG plates are examined and discussed in detail.

• Journal of Korean Association for Spatial Structures
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• v.1 no.1 s.1
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• pp.95-108
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• 2001

A system of equations is developed for the theory of bending of thick orthotropic elastic plates which takes into account the transverse shear deformability of the plate. This system of equations is of such nature that three boundary conditions can and must be prescribed along the edge of the plate, i.e. ${\omega}=0,\;M_x=0,\;M_{xy}=0\;({\omega}=0,\;M_x=0,\;M_{xy}=0)$ at simple supported edges. It can be obtained general solution that is added complementary solution ${\omega}^e$ and paticular solution ${\omega}^p$ by an assumption of solution function. In the next paper, this analytical results will be obtained for perforated thick plates.

• Journal of Ocean Engineering and Technology
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• v.27 no.3
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• pp.61-66
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• 2013

This paper presents the results of finite element simulations of elastic wave propagation in an underwater steel plate and the verification of a proposed method utilizing elastic wave-based damage detection. For the simulation and verification, we carried out the following procedures. First, three-dimensional finite element models were constructed using a general purpose finite element program. Second, two types of damages (mechanical defects and deteriorations) were applied to the underwater steel plate and three parameters (defect location, defect width, and depth) were considered to adjust the severity of the applied damages. Third, elastic waves were generated using the oblique incident method with a Gaussian tone burst, and the response signals were obtained at the receiving point for each defect or deterioration case. In addition, the received time domain signals were analyzed, particularly by measuring the magnitudes of the maximum amplitudes. Finally, the presence and severity of each type of damage were identified by the decreasing ratios of the maximum amplitudes. The results showed that the received signals for the models had the same global pattern with minor changes in the amplitudes and phases, and the decreasing ratio generally increased as the damage area increased. In addition, we found that the defect depth was more critical than the width in the decrease of the amplitude. This mainly occurred because the layout of the depth interfered with the elastic wave propagation in a more severe manner than the layout of the width. An inverse analysis showed that the proposed method is applicable for detecting mechanical defects and quantifying their severity.

• Steel and Composite Structures
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• v.46 no.5
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• pp.709-718
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• 2023

The absence of an important portion of the web plate in steel beams with multiple circular perforations, cellular beams, causes the web plate to undergo distortions prior to and during lateral torsional buckling (LTB). The conventional LTB equations in the codes and literature underestimate the buckling moments of cellular beams due to web distortions. The present study is an attempt to develop analytical methods for estimating the elastic buckling moments of cellular beams. The proposed methods rely on the reductions in the torsional and warping rigidities of the beams due to web distortions and the reductions in the weak-axis bending and torsional rigidities due to the presence of web openings. To test the accuracy of the analytical estimates from proposed solutions, a total of 114 finite element analyses were conducted for six different standard IPEO sections and varying unbraced lengths within the elastic limits. These analyses clearly indicated that the LTB solutions in the AISC 360-16 and AS4100:2020 codes overestimate the buckling loads of cellular beams within elastic limits, particularly at shorter span lengths. The LDB solutions in the literature and the Eurocode 3 LTB solution, on the other hand, provided conservative buckling moment estimates along the entire range of elastic buckling.

• Journal of the Korean Society for Nondestructive Testing
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• v.36 no.6
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• pp.474-482
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• 2016

A Kelvin foam plate - widely used in the energy and transport industries as a lightweight structural material - was examined to estimate its Young's modulus using ultrasound. An isotropic tetrakaidecahedron foam structure was designed in SolidWorks and printed using 3D printer with an ABS plastic material. The 3D printed foam structure was used to build a foam plate with a 14 mm thickness ($50mm{\times}100mm$ in size) for the ultrasonic test. The Kelvin foam plate, a significantly porous medium, was completely filled with paraffin wax to enable the ultrasound to penetrate through the porous medium. The acoustic wave velocity of the wax-filled Kelvin foam was measured using the time of flight (TOF) method. Furthermore, the elastic modulus of the Kelvin foam was estimated based on an elastic structural model developed in this study. The Young's modulus of the produced Kelvin foam was observed to be approximately 3.4% of the bulk value of the constituent material (ABS plastic). This finding is consistent with experimental and theoretical results reported by previous studies.