• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.2
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• pp.298-309
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• 1990

In this paper, a new method is suggested to analyze impulsive stresses at loading poing of concentrated impact load under certain impact conditions determined by impact velocity, stiffness of plate and mass of impact body, etc. The impulsive stresses are analyzed by using the three dimensional dynamic theory of elasticity so as to analytically clarify the generation phenomenon of cone crack at the impact fracture of fragile materials (to be discussed if the second paper). The Lagrange's plate theory and Hertz's law of contact theory are used for the analysis of impact load, and the approximate equation of impact load is suggested to analyze the impulsive stresses at the impact point to decide the ranage of impact load factor. When impact load factors are over and under 0.263, approximate equations are suggested to be F(t)=Aexp(-Bt)sinCt and F(t)=Aexp(-bt) {1-exp(Ct)} respectively. Also, the inverse Laplace transformation is done by using the F.F.T.(fast fourier transform) algorithm. And in order to clarity the validity of stress analysis method, experiments on strain fluctuation at impact point are performed on a supported square glass plate. Finally, these analytical results are shown to be in close agreement with experimental results.

• Nuclear Engineering and Technology
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• v.41 no.3
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• pp.335-346
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• 2009

This paper deals with a hydroelastic vibration analysis of two rectangular plates partially coupled with a liquid, which is bounded by two plates and two rigid side walls. The wet displacement of each plate is assumed to be a combination of the modal functions of a dry uniform beam with a clamped boundary condition. As the liquid is assumed to be an ideal liquid, the displacement potential satisfying the Laplace equation is determined so that the liquid boundary conditions can meet the requirements at the rigid surfaces and the free liquid surface. The wet dynamic modal functions of each plate are expanded by using the finite Fourier transform to obtain an appropriate form of the compatibility requirement along the contacting surfaces between the plates and the liquid. The liquid-coupled natural frequencies of the plates are derived by using the Rayleigh-Ritz method. Finite element analyses using commercial software are carried out to verify the proposed theory. It is observed that the theoretical method agrees excellently with the three-dimensional finite element analyses results. The effects of the liquid depth and the liquid thickness on the normalized natural frequencies are investigated to identify the dynamic characteristics of the liquid coupled system.

• Coupled systems mechanics
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• v.9 no.1
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• pp.77-89
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• 2020

This study is dedicated to the dynamic elasticity problem for a semi-strip. The semi-strip is loaded by the dynamic load at the center of its short edge. The conditions of fixing are given on the lateral sides of the semi-strip. The initial problem is reduced to one-dimensional problem with the help of Laplace's and Fourier's integral transforms. The one-dimensional boundary problem is formulated as the vector boundary problem in the transform's domain. Its solution is constructed as the superposition of the general solution for the homogeneous vector equation and the partial solution for the inhomogeneous vector equation. The matrix differential calculation is used for the deriving of the general solution. The partial solution is constructed with the help of Green's matrix-function, which is searched as the bilinear expansion. The case of steady-state oscillations is considered. The problem is reduced to the solving of the singular integral equation. The orthogonalization method is applied for the calculations. The stress state of the semi-strip is investigated for the different values of the frequency.

• Structural Engineering and Mechanics
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• v.40 no.5
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• pp.665-688
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• 2011

This paper presents a theoretical analysis for the free vibration of rectangular tanks partially filled with an ideal liquid. Wet dynamic displacements of the tanks are approximated by combining the orthogonal polynomials satisfying the boundary conditions, since the rectangular tanks are composed of four rectangular plates. The classical boundary conditions of the tanks at the top and bottom ends are considered, such as clamped, simply supported, and clamped-free boundary conditions. As the facing rectangular plates are assumed to be geometrically and structurally identical, the vibration modes of the facing plates of the tanks can be divided into two categories: symmetric and antisymmetric modes with respect to the planes passing through the center of the tanks and perpendicular to the free liquid surface. The liquid displacement potentials satisfying the Laplace equation and liquid boundary conditions are derived, and the wet dynamic modal functions of a quarter of the tanks can be expanded by the finite Fourier transform for compatibility requirements along the contacting surfaces between the tanks and liquid. An eigenvalue problem is derived using the Rayleigh-Ritz method. Consequently, the wet natural frequencies of the rectangular tanks can be extracted. The proposed analytical method is verified by observing an excellent agreement with three-dimensional finite element analysis results. The effects of the liquid level and boundary condition at the top and bottom edges are investigated.

• Geomechanics and Engineering
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• v.21 no.3
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• pp.279-288
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• 2020

The permeation grouting is a commonly used technique to improve the engineering geology condition of the soft ground. It is of great significance to predict the permeation range of the grout so as to ensure the effects of grouting. This paper conducts a theoretical analysis of jet-grouting effects in ground improvement and rotary grouting pile installation by utilizing deformation-permeation coupled poroelastic solutions based on Biot's theory and Laplace-Fourier integral transform technique. The exponential function and the intermittent trigonometric function are chosen to represent time-dependent grouting pressure usually encountered in ground improvement and rotary grouting pile installation process, respectively. The results, including the radial displacement, the hoop stress, the excess pore fluid pressure, the radial discharge, and the permeation radius of grout, are presented for different grouting time, radial positions and grouting lengths. Parametric study is conducted to explore the effects of variation of the exponent in the exponential grouting pressure-time relationship on grouting-induced responses. It is expected that the proposed solutions can be used to estimate the permeation range of grouting in ground improvement and rotary grouting pile installation.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2013.10a
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• pp.206-213
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• 2013

Transient response of a crack in a functionally graded piezoelectric material (FGPM) interface layer between two dissimilar homogeneous piezoelectric layers under anti-plane shear is analyzed using integral transform approaches. The properties of the FGPM layer vary continuously along the thickness. Laplace and Fourier transforms are used to reduce the problem to two sets of dual integral equations, which are then expressed to the Fredholm integral equations of the second kind. Numerical values on the dynamic energy release rate (DERR) are presented for the FGPM to show the effects on electric loading, gradient of the material properties, and thickness of the layers. Computed results yield following conclusions: (a) the DERR increases with the increase of the gradient of the material properties of the FGPM layer; (b) certain direction and magnitude of the electric impact loading impedes crack extension; (c) increase of the thickness of the FGPM layer and the homogeneous piezoelectric layer which has larger material properties than those of the crack plane are beneficial to increase of the resistance of transient fracture of the FGPM layer.