• Coupled systems mechanics
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• 제9권1호
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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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• 제31권2호
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• pp.211-223
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• 2009

Transient response analysis can be conducted either in the time domain, or via the frequency domain. Sometimes a frequency domain method (FDM) has advantages over a time domain method. A practical issue in the FDM is to find out an appropriate extended period, which may be affected by several factors, such as the excitation duration, the system damping, the artificial damping, the period of interest, etc. In this report, the extended period of the FDM based on the Duhamel's integral is investigated. This Duhamel's integral based FDM does not involve the unit impulse response function (UIRF) beyond the period of interest. Due to this fact, the ever-lasting UIRF can be simply set as zero beyond the period of interest to shorten the extended period. As a result, the preferred extended period is the summation of the period of interest and the excitation duration. This conclusion is validated by numerical examples. If the extended period is too short, then the front portion of the period of interest is more prone to errors than the rear portion, but the free vibration segment is free of the wraparound error.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2013년도 추계학술대회 논문집
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• pp.206-213
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• 2013

본 논문에서는 적분변환법을 이용하여 면외전단 충격하중이 작용하는 두 개의 서로 다른 압전재료층 사이의 기능경사압전재료 접합층 내부 균열에 대한 과도응답 해석 을 수행한다. 기능경사압전재료의 물성치는 두께 방향을 따라 연속적으로 변하는 것으로 가정한다. 라플라스 변환과 푸리에 변환을 이용하여 문제를 복합적분방정식으로 구성하고, 수치해석을 위해 복합적 분방정식을 제 2 종 프레드홀름 적분방정식으로 표현한다. 전기적 하중, 재료물성 치의 변화율, 각 접합층의 두께가 균열의 과도응답에 미치는 영향을 보기 위해 동에너지 해방률에 대한 수치해석 결과를 제시한다.

• 한국항공운항학회지
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• 제19권1호
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• pp.15-23
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• 2011

The purpose of this paper is to investigate the time behavior of a multiple crack problems. It is assumed that the medium contains cracks perpendicular to the crack surfaces, that the thermo-mechanical properties are continuous functions of the thickness coordinate. we use the laminated composite plate model to simulate the material non-homogeneity. By utilizing the Laplace transform and Fourier transform techniques, the multiple crack problems in the non-homogeneous medium is formulated. Singular integral equations are derived and solved to investigate the multiple crack problems. As a numerical illustration, transient thermal stress intensity factors(TSIFs) for a functionally graded material plate subjected to sudden heating on its boundary are provided. The variation in the TSIFs due to the change in material gradient and the crack position is studied.

• 대한수학회지
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• 제53권4호
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• pp.929-967
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• 2016

Let p(t, x) be the fundamental solution to the problem $${\partial}^{\alpha}_tu=-(-{\Delta})^{\beta}u,\;{\alpha}{\in}(0,2),\;{\beta}{\in}(0,{\infty})$$. If ${\alpha},{\beta}{\in}(0,1)$, then the kernel p(t, x) becomes the transition density of a Levy process delayed by an inverse subordinator. In this paper we provide the asymptotic behaviors and sharp upper bounds of p(t, x) and its space and time fractional derivatives $$D^n_x(-{\Delta}_x)^{\gamma}D^{\sigma}_tI^{\delta}_tp(t,x),\;{\forall}n{\in}{\mathbb{Z}}_+,\;{\gamma}{\in}[0,{\beta}],\;{\sigma},{\delta}{\in}[0,{\infty})$$, where $D^n_x$ x is a partial derivative of order n with respect to x, $(-{\Delta}_x)^{\gamma}$ is a fractional Laplace operator and $D^{\sigma}_t$ and $I^{\delta}_t$ are Riemann-Liouville fractional derivative and integral respectively.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 춘계학술대회논문집
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• pp.85-89
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• 2001

The problem of the transient interaction of a plane acoustic shock wave which has an infinitely steep wave front with a cylindrical or spherical elastic shell has been studied analytically from early fifties based on the integral transform and series solution techniques. Huang adopted an inverse Laplace transform, and used a finite number of terms of the infinite series expansion of the equations for the shells. In the 1990s, the results have been used by many authors for validation of computer codes. The object of this paper is to discuss the interaction between a moving source and submerged spherical shells. Since the center of source is moving the first contact location between the waves and shell changes depending on the source velocity and distance. These are considered in the analysis. Furthermore, constant source strength and decreasing strength are considered in the analysis. Radial velocities at several locations on the structure are obtained and the results are discussed.

• Interaction and multiscale mechanics
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• 제2권4호
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• pp.431-454
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• 2009

This paper presents a simple model for studying the dynamic response of multi-span bridges resting on piers with different heights and subjected to earthquake forces acting transversely to the bridge, but varying spatially along its length. The analysis is carried out using the modal superposition technique, while the solution of the resulting integral-differential equations is obtained via the Laplace transformation. It has been found that the piers' height and the quality of the foundation soil can affect significantly the dynamic behavior of such bridges. Typical examples showing the effectiveness of the method are presented with useful results listed.

• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.193-212
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• 2004

A new model of generalized thermoelasticity equations for isotropic media with temperature-dependent mechanical properties is established. The modulus of elasticity is taken as a linear function of reference temperature. The present model is described both generalizations, Lord Shulman (L-S) theory with one relaxation time and Green-Lindsay (G-L) with two relaxation times, as well as the coupled theory, instantaneously. The method of the matrix exponential, which constitutes the basis of the state space approach of modern control theory, applied to two-dimensional equations. Laplace and Fourier integral transforms are used. The resulting formulation is applied to a problem of a thick plate subject to heating on parts of the upper and lower surfaces of the plate that varies exponentially with time. Numerical results are given and illustrated graphically for the problem considered. A comparison was made with the results obtained in case of temperature-independent modulus of elasticity in each theory.

• Journal of Mechanical Science and Technology
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• 제18권3호
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• pp.419-431
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• 2004

The dynamic response of a cracked functionally graded piezoelectric material (FGPM) under transient anti-plane shear mechanical and in-plane electrical loads is investigated in the present paper. It is assumed that the electroelastic material properties of the FGPM vary smoothly in the form of an exponential function along the thickness of the strip. The analysis is conducted on the basis of the unified (or natural) crack boundary condition which is related to the ellipsoidal crack parameters. By using the Laplace and Fourier transforms, the problem is reduced to the solutions of Fredholm integral equations of the second kind. Numerical results for the stress intensity factor and crack sliding displacement are presented to show the influences of the elliptic crack parameters, the electric field, FGPM gradation, crack length, and electromechanical coupling coefficient.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 춘계학술대회논문집B
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• pp.540-545
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• 2001

In this paper dynamic responses of an engine, which is supported by hydraulic mount, to throttle tip-in/tip out are analyzed. Because the hydraulic mounts have non-linearity which the characteristics of stiffness and damping vary with frequencies, it is difficult to analyze the dynamic behavior of an engine using general integral algorithms. Convolution integrals and relationships between unit impulse response functions and frequency response functions are therefore used to simulate the transient behavior of an engine indirectly. In time domain, impulse response functions are calculated by two-side discrete inverse Fourier transform of frequency response function achieved by Laplace transform of equations of motion. Considering the fact that the shapes of behavior of an engine simulated by the proposed method are in good agreement with test results, it is confirmed that the proposed method is very effective for the analysis of transient response to throttle tip-in/out of an engine with hydraulic mounts.