• Transactions of the Korean Society of Mechanical Engineers A
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• v.22 no.3
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• pp.635-643
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• 1998

A spectral element method(SEM) is introduced for the vibration analysis of a rectangular plate subject to dynamic concentrated loads. First, the spectral plate element is derived from the relations between the forces and displacements along the two opposite edges of plate element. The global spectral matrix equation is then formulated by assembling two spectral plate elements so that the dynamic concentrated load is located at the connection nodal line between two plate elements. the concentrated load is then spatially Fourier transformed in the direction of the connection nodal line to transform the two-dimensional plate problem into a simplified equivalent one-dimensional beam-like problem. We may benefit from these procedures in that the spectral results from the present SEM is compared with the exact analytical solutions to prove the remarkable accuracy of the present SEM, while this is not true for conventional finite element solutions, especially at high frequency.

• Journal of the Korean Society of Propulsion Engineers
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• v.20 no.2
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• pp.24-30
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• 2016

An experimental study for the characteristics of the thrust-vectoring of a sonic jet utilizing the coanda flap installed at a rectangular nozzle exit is performed. Two side plates are installed at both sides of the flap to decrease the three dimensional effects of the jet on the flap surface. Schlieren flow visualizations and quantitative measurements of the deflection angle of thrusting vector show that the side plates are able to delay the separation of the jet at the downstream of the flap surface. Substantial increase in the deflection angle of the jet as high as $72^{\circ}$ and small thrust loss as low as 7% are obtained by the present thrust-vectoring technique using the side plates.

• Structural Engineering and Mechanics
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• v.86 no.4
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• pp.443-459
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• 2023

This study investigates the theoretical thermal buckling analyses of thick porous rectangular functionally graded (FG) plates with different geometrical boundary conditions resting on a Winkler-Pasternak elastic foundation using a new higher-order shear deformation theory (HSDT). This new theory has only four unknowns and involves indeterminate integral variables in which no shear correction factor is required. The variation of material properties across the plate's thickness is considered continuous and varied following a simple power law as a function of volume fractions of the constituents. The effect of porosity with two different types of distribution is also included. The current formulation considers the Von Karman nonlinearity, and the stability equations are developed using the virtual works principle. The thermal gradients are involved and assumed to change across the FG plate's thickness according to nonlinear, linear, and uniform distributions. The accuracy of the newly proposed theory has been validated by comparing the present results with the results obtained from the previously published theories. The effects of porosity, boundary conditions, foundation parameters, power index, plate aspect ratio, and side-to-thickness ratio on the critical buckling temperature are studied and discussed in detail.

• Advances in aircraft and spacecraft science
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• v.5 no.5
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• pp.515-531
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• 2018

In this manuscript, buckling response of the functionally graded material (FGM) nanoplate is investigated. Two opposite edges of nanoplate is under linear and nonlinear varying normal stresses. The small-scale effect is considered by Eringen's nonlocal theory. Governing equation are derived by nonlocal theory and Hamilton's principle. Navier's method is used to solve governing equation in simply boundary conditions. The obtained results exactly match the available results in the literature. The results of this research show the important role of nonlocal effect in buckling and stability behavior of nanoplates. In order to study the FG-index effect and different loading condition effects on buckling of rectangular nanoplate, Navier's method is applied and results are presented in various figures and tables.

• Computers and Concrete
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• v.27 no.3
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• pp.269-282
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• 2021

A dynamic analytical solution for a simply supported, rectangular functionally graded plate with a porous middle layer under time-dependent load based on a refined third-order shear deformation theory with a cubic variation of in-plane displacements according to the thickness and linear/quadratic transverse displacement is presented. The solution achieved in the trigonometric series form and rests on the Green's function method. Two porosity types and their influence on material properties, and mechanical behavior are considered. The network of pores is assumed to be empty or filled with low-pressure air, and the material properties are calculated using the power-law distribution idealization. Numerical calculations have been carried out to demonstrate the accuracy of the kinematic model for the dynamic problem, the effect of porosity, thickness of porous layers, power-law index, and type of loading on the dynamic response of an imperfect functionally graded material plate.

• Journal of the Korean Society for Precision Engineering
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• v.21 no.3
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• pp.38-43
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• 2004

This paper describes the construction of a circular polariscope. Generally, a circular polariscope contains four optical elements and a light source. The first element following the light source is called the linear polarizer. It converts the ordinary light into plane-polarized light. The second element is a quarter wave plate which converts the plane-polarized light into circularly polarized light. Following the quarter wave plate, a specimen made of transparent photoelastic material is located in a loading device. The second quarter wave plate is set and the last element is the analyzer. These polarizing elements, two quarter wave plates and two linear polarizing filters, were purchased from the USA. Frames and other structures for holding polarizing filters were machined and assembled to be rotated. Light box, which includes four incandescent lamps and two sodium-vapor lamps, was made. In order to proof the function of the newly built polariscope, Tardy compensation test was applied to a rectangular shaped specimen made of poly-carbonate material (PSM 1). The error of the fringe constant, which was measured by the newly built polariscope, was within 4.4 percent compared to the standard value of this material. It is possible to make a good quality of polariscope if accurate polarizing filters will be used.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1994.10a
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• pp.35-39
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• 1994

One of the important characteristics of the response of nonlinear systems is the existence of subharmonic resonances. When some conditions in parameter space are satisfied. It is possible even in the presence of damping for a periodically excited nonlinear system to possess a response which is the combination of a contribution at the excitation frequency and a component at the system natural frequency. The system natural frequency being a submultiple of the excitation frequency implies that the resulting response is a subharmonic oscillation. In general, there also co-exists, for the system, a response at the excitation frequency, and initial conditions determine which of the steady-state responses is achieved in an experiment or a numerical simulation. In single-degree-of-freedom systems with harmonic excitation, depending on the type of the nonlinearity, e.g., cubic or quadratic the frequency of subharmonic response is respectively, one-third or one-half of that of the excitation frequency. Although subharmonic resonance is one of the principal characteristics of a nonlinear system the subharmonic responses of structures in the presence of internal resonances have been studied very rarely. In this work, we consider subharmonic responses in the two-mode approximation of the plate equations. It is assumed that the two modes are in one-to-one internal resonance. Constant and periodic steady-state solutions of the averaged equations are studied. Finally, the results of direct time integration of the original equations of motion are presented and compared with those obtained from the averaged equations.

• Journal of Energy Engineering
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• v.2 no.3
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• pp.251-257
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• 1993

The purpose of this study is to obtain an improved interpretation of heat transfer phenomena between blocks and fluids in the parallel conducting plates. Flow is two-dimensional, incompressible steady laminar flow over rectangular blocks, representing finite heat source on parallel plate. Heat transfer phenomena, temperature of blocks and heat transfer into the flow field are investigated for different spacings between blocks and Reynolds numbers. Results indicate that Nusselt number on the far upstream corner of the block was higher than that of any part of the block. As Reynolds number and spacings of blocks increased, Nusselt number increased. The distribution of local Nusselt number on the top surface of the conducting plate is similar to the case with insulated plate. Temperature of the block which has heat source in half cubage was approximately twice as high as temperature of the block which has heat source in whole cubage. As Reynolds number and spacings of blocks increased, overall temperature decreased. The peak value of block temperature occurred at position shifted to the right or upper right from center. The maximum temperature of block can be expressed as a function of Reynolds number, spacings between blocks, position of maximum temperature of each block and then it is possible to predict the maximum temperature of blocks.

• Structural Engineering and Mechanics
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• v.52 no.6
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• pp.1069-1084
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• 2014

The long-term performance of plates resting on viscoelastic foundations is a major concern in the analysis of soil-structure interaction. As a powerful mathematical tool, fractional calculus may address these plate-on-foundation problems. In this paper, a fractionalized Zener model is proposed to study the time-dependent behavior of a uniformly loaded rectangular thin foundation plate. By use of the viscoelastic-elastic correspondence principle and the Laplace transforms, the analytical solutions were obtained in terms of the Mittag-Leffler function. Through the analysis of a numerical example, the calculated plate deflection, bending moment and foundation reaction were compared to those from ideal elastic and standard viscoelastic models. It is found that the upper and lower bound solutions of the plate response estimated by the proposed model can be determined using the elastic model. Based on a parametric study, the impacts of model parameters on the long-term performance of a foundation plate were systematically investigated. The results show that the two spring stiffnesses govern the upper and lower bound solutions of the plate response. By varying the values of the fractional differential order and the coefficient of viscosity, the time-dependent behavior of a foundation plate can be accurately captured. The fractional differential order seems to be dependent on the mechanical properties of the ground soil. A sandy foundation will have a small fractional differential order while in order to simulate the creeping of clay foundation, a larger fractional differential order value is needed. The fractionalized Zener model is capable of accounting for the primary and secondary consolidation processes of the foundation soil and can be used to predict the plate performance over many decades of time.

• Geomechanics and Engineering
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• v.10 no.3
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• pp.357-386
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• 2016

In this research work, an exact analytical solution for thermal stability of solar functionally graded rectangular plates subjected to uniform, linear and non-linear temperature rises across the thickness direction is developed. It is assumed that the plate rests on two-parameter elastic foundation and its material properties vary through the thickness of the plate as a power function. The neutral surface position for such plate is determined, and the efficient hyperbolic plate theory based on exact neutral surface position is employed to derive the governing stability equations. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the quadratic distribution of transverse shear stress through the thickness in such a way that shear stresses vanish on the plate surfaces. Therefore, there is no need to use shear correction factor. Just four unknown displacement functions are used in the present theory against five unknown displacement functions used in the corresponding ones. The non-linear strain-displacement relations are also taken into consideration. The influences of many plate parameters on buckling temperature difference will be investigated. Numerical results are presented for the present theory, demonstrating its importance and accuracy in comparison to other theories.