• Title/Summary/Keyword: Integral Transform

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Elastodynamic Response of a Crack Perpendicular to the Graded Interfacial Zone in Bonded Dissimilar Materials Under Antiplane Shear Impact

  • Kim, Sung-Ho;Choi, Hyung-Jip
    • Journal of Mechanical Science and Technology
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    • v.18 no.8
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    • pp.1375-1387
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    • 2004
  • A solution is given for the elastodynamic problem of a crack perpendicular to the graded interfacial zone in bonded materials under the action of anti plane shear impact. The interfacial zone is modeled as a nonhomogeneous interlayer with the power-law variations of its shear modulus and mass density between the two dissimilar, homogeneous half-planes. Laplace and Fourier integral transforms are employed to reduce the transient problem to the solution of a Cauchy-type singular integral equation in the Laplace transform domain. Via the numerical inversion of the Laplace transforms, the values of the dynamic stress intensity factors are obtained as a function of time. As a result, the influences of material and geometric parameters of the bonded media on the overshoot characteristics of the dynamic stress intensities are discussed. A comparison is also made with the corresponding elastostatic solutions, addressing the inertia effect on the dynamic load transfer to the crack tips for various combinations of the physical properties.

Influence of various sources in micropolar thermoelastic medium with voids

  • Kumar, Rajneesh;Ailawalia, Praveen
    • Structural Engineering and Mechanics
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    • v.31 no.6
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    • pp.717-735
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    • 2009
  • The present problem is concerned with the study of deformation of micropolar thermoelastic medium with voids under the influence of various sources acting on the plane surface. The analytic expressions of displacement components, force stress, couple stress, change in volume fraction field and temperature distribution are obtained in the transformed domain for Lord-Shulman (L-S) theory of thermoelasticity after applying the integral transforms. A numerical inversion technique has been applied to obtain the solution in the physical domain. The numerical results are presented graphically. Some useful particular cases have also been deduced.

Time-domain hydroelastic analysis with efficient load estimation for random waves

  • Kang, H.Y.;Kim, M.H.
    • International Journal of Naval Architecture and Ocean Engineering
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    • v.9 no.3
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    • pp.266-281
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    • 2017
  • Hydroelastic interactions of a deformable floating body with random waves are investigated in time domain. Both hydroelastic motion and structural dynamics are solved by expansion of elastic modes and Fourier transform for the random waves. A direct and efficient structural analysis in time domain is developed. In particular, an efficient way of obtaining distributive loads for the hydrodynamic integral terms including convolution integral by using Fubini theory is explained. After confirming correctness of respective loading components, calculations of full distributions of loads in random waves are expedited by reformulating all the body loading terms into distributed forms. The method is validated by extensive convergence tests and comparisons against the counterparts of the frequency-domain analysis. Characteristics of motion/deformation responses and stress resultants are investigated through a parametric study with varying bending rigidity and types of random waves. Relative contributions of componential loads are identified. The consequence of elastic-mode resonance is underscored.

Calculation of Impact Forces of an Arbitrary Force Applied Vibro-Impact system (임의 하중이 작용하는 진동-충격시스템에서의 충격력계산)

  • 이창희
    • Journal of KSNVE
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    • v.10 no.4
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    • pp.679-685
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    • 2000
  • A procedure is presented for calculating the magnitude and shape of impact pulses in a vibro-impact system when an arbitrary input force is applied to a point in the system. The procedure utilizes the condition that the displacements of two contacting point in the primary and secondary system are the same during a contacting period. The displacements of those points are calculated numerically through the convolution integral which involve the impulse response functions and applied forces. The validity of the calculation procedure is demonstrated by using it to calculated the impact forces of a simple system where a theoretical solution is known and also of systems for which other researchers have published results. The agreement between the results derived by the numerical method and the theoretical and also some published results is good.

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Response of temperature dependence of an elastic modulus in microstretch generalized thermoelasticity

  • Kumar, Rajneesh;Gupta, Rajani Rani
    • Structural Engineering and Mechanics
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    • v.30 no.5
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    • pp.577-592
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    • 2008
  • Laplace-Fourier transform techniques are used to investigate the interaction caused by mechanical, thermal and microstress sources in a generalized thermomicrostretch elastic medium with temperature-dependent mechanical properties. The modulus of elasticity is taken as a linear function of reference temperature. The integral transforms are inverted using a numerical technique to obtain the normal stress, tangential stress, tangential couple stress, microstress and temperature distribution. Effect of temperature dependent modulus of elasticity and thermal relaxation times have been depicted graphically on the resulting quantities. Comparisons are made with the results predicted by the theories of generalized thermoelasticity. Some particular cases are also deduced from the present investigation.

ERTAIN k-FRACTIONAL CALCULUS OPERATORS AND IMAGE FORMULAS OF GENERALIZED k-BESSEL FUNCTION

  • Agarwal, P.;Suthar, D.L.;Tadesse, Hagos;Habenom, Haile
    • Honam Mathematical Journal
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    • v.43 no.2
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    • pp.167-181
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    • 2021
  • In this paper, the Saigo's k-fractional integral and derivative operators involving k-hypergeometric function in the kernel are applied to the generalized k-Bessel function; results are expressed in term of k-Wright function, which are used to present image formulas of integral transforms including beta transform. Also special cases related to fractional calculus operators and Bessel functions are considered.

The dynamic response of the FGM coated half-plane with hysteretic damping under time harmonic loading

  • Xiao-Min Wang;Liao-Liang Ke;Yue-Sheng Wang
    • Structural Engineering and Mechanics
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    • v.87 no.1
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    • pp.95-106
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    • 2023
  • This paper investigates the dynamic response of a functionally graded material (FGM) coated half-plane excited by distributed time harmonic loading. Three types of typical distributed surface loads, including uniform load, Hertz load, and square-root singular load, are considered. The mass density and elastic modulus of the FGM coating are supposed to be described by the exponential function. The material damping is modelled by a linearly hysteretic damping which is expressed by a complex modulus in the time harmonic motion. Using Fourier integral transform technique and numerical integral method, the effects of the excitation frequency, gradient index, damping, and load type on the dynamic stresses and displacements are discussed.

Synthesis method of elemental images from Kinect images for space 3D image (공간 3D 영상디스플레이를 위한 Kinect 영상의 요소 영상 변환방법)

  • Ryu, Tae-Kyung;Hong, Seok-Min;Kim, Kyoung-Won;Lee, Byung-Gook
    • Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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    • 2012.05a
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    • pp.162-163
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    • 2012
  • In this paper, we propose a synthesis method of elemental images from Kinect images for 3D integral imaging display. Since RGB images and depth image obtained from Kinect are not able to display 3D images in integral imaging system, we need transform the elemental images in integral imaging display. To do so, we synthesize the elemental images based on the geometric optics mapping from the depth plane images obtained from RGB image and depth image. To show the usefulness of the proposed system, we carry out the preliminary experiments using the two person object and present the experimental results.

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A Representation of Green Function Using Discrete Wavelet Concept for Fast Field Analysis (고속 전자파 해석을 위한 그린 함수의 이산 웨이블릿 표현법)

  • Kim Hyung-Hoon;Park Jong-Il;Kim Hyeong-Dong
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.17 no.9 s.112
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    • pp.895-899
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    • 2006
  • A compact representation of Green function is proposed by applying the discrete wavelet concept in the k-domain, which can be used for the acceleration of scattered field calculations in integral equation methods. Since the representation of Green function is very compact in the joint spatio-spectral domain, it can be effectively utilized in the fast computation of radiation integral of electromagnetic problems. A mathematical expression of Green function based on the discrete wavelet concept is derived and its characteristics are discussed.

Analytical and finite element solution of a receding contact problem

  • Adiyaman, Gokhan;Yaylaci, Murat;Birinci, Ahmet
    • Structural Engineering and Mechanics
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    • v.54 no.1
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    • pp.69-85
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    • 2015
  • In this paper, a receding contact problem for an elastic layer resting on two quarter planes is considered. The layer is pressed by a stamp and distributed loads. It is assumed that the contact surfaces are frictionless and only compressive traction can be transmitted through the contact surfaces. In addition the effect of body forces are neglected. Firstly, the problem is solved analytically based on theory of elasticity. In this solution, the problem is reduced into a system of singular integral equations in which contact areas and contact stresses are unknowns using boundary conditions and integral transform techniques. This system is solved numerically using Gauss-Jacobi integral formulation. Secondly, two dimensional finite element analysis of the problem is carried out using ANSYS. The dimensionless quantities for the contact areas and the contact pressures are calculated under various distributed load conditions using both solutions. It is concluded that the position and the magnitude of the distributed load have an important role on the contact area and contact pressure distribution between layer and quarter plane contact surface. The analytic results are verified by comparison with finite element results.