• Progress in Medical Physics
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• v.4 no.2
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• pp.37-47
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• 1993

The quality of radiation for a high energy x-ray beam can be specified by its attenuation curve in a selected material. The inverse Laplace transform of the attenuation curve can be used as an approximate indication of the energy spectrum of the beam. We have made a comparative investigation of the estimated spectrum obtained by the Laplace transform analysis of the transmitted exposure data measured in an absorption study of a 6MV x-ray beam. Two of existing transform pair models have been investicated and discussed.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.381-392
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• 2021

During the last several decades, a great variety of fractional kinetic equations involving diverse special functions have been broadly and usefully employed in describing and solving several important problems of physics and astrophysics. In this paper, we aim to find solutions of a type of fractional kinetic equations associated with the (p, q)-extended 𝜏 -hypergeometric function and the (p, q)-extended 𝜏 -confluent hypergeometric function, by mainly using the Laplace transform. It is noted that the main employed techniques for this chosen type of fractional kinetic equations are Laplace transform, Sumudu transform, Laplace and Sumudu transforms, Laplace and Fourier transforms, P_𝛘-transform, and an alternative method.

• Proceedings of the KIEE Conference
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• 1997.07a
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• pp.309-311
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• 1997

In this paper, it is proposed that a algorithm which is applicable to the transient analysis by combined use of the Laplace transform and the finite element method. The proposed method removes the time terms using the Laplace transform and then solves the associated equation with the finite element method. The solution which is solved at frequency domain is transformed into time domain by use of the Laplace inversion. To verify proposed algorithm, heat conduction problem is analysed and found a good agreement with analytic solution.

• Steel and Composite Structures
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• v.18 no.4
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• pp.889-907
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• 2015

This paper aims to present an alternative analytical method for transient vibration analysis of doubly-curved laminated shells subjected to dynamic loads. In the method proposed, the governing differential equations of laminated shell are derived using the dynamic version of the principle of virtual displacements. The governing equations of first order shear deformation laminated shell are obtained by Navier solution procedure. Time-dependent equations are transformed to the Laplace domain and then Laplace parameter dependent equations are solved numerically. The results obtained in the Laplace domain are transformed to the time domain with the help of modified Durbin's numerical inverse Laplace transform method. Verification of the presented method is carried out by comparing the results with those obtained by Newmark method and ANSYS finite element software. Also effects of number of laminates, different material properties and shell geometries are discussed. The numerical results have proved that the presented procedure is a highly accurate and efficient solution method.

• Journal of KSNVE
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• v.7 no.1
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• pp.135-142
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• 1997

This paper presents a digital modeling technique of the distributed system. The basic idea of the proposed technique is to discretize a continuous system with respect to the spatial coordinates using bilinear method. The response of the discretized system is analyzed by Laplace transform and z-transform. The computational results in torsional shaft and Timoshenko beam using the proposed technique are compared with the exact solutions and the results of finite element method.

• Journal of the Korean Magnetics Society
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• v.8 no.3
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• pp.161-168
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• 1998

In this paper, a algorithm is proposed, which is applicable to the transient analysis of diffusion equations by combined use of the Laplace transform and the finite element method. The proposed method removes the time terms using the Laplace transform and then solves the associated equation with the finite element method. The solution which is solved at frequency domain is transformed into time domain by use of the Laplace inversion. To verify the proposed algorithm, a heat conduction problem is analysed. And the solution showed a good agreement with analytic solution. Because the time-step method is not needed, the proposed method is very useful in solving various kinds of diffusion equations.

• Interaction and multiscale mechanics
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• v.6 no.1
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• pp.15-29
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• 2013

Phononic system composed of periodical elastic structures exhibit band gap phenomenon, and all elastic wave cannot propagate within the band gap. In this article, we consider one-dimensional binary materials which are periodically arranged as a 20-layered medium instead of infinite layered system for phononic system. The layered medium with finite dimension is subjected to a uniformly distributed sinusoidal loading at the upper surface, and the bottom surface is assumed to be traction free. The transient wave propagation in the 20-layered medium is analyzed by Laplace transform technique. The analytical solutions are presented in the transform domain and the numerical Laplace inversion (Durbin's formula) is performed to obtain the transient response in time domain. The numerical results show that when a sinusoidal loading with a specific frequency within band gap is applied, stress response will be significantly decayed if the receiver is away from the source. However, when a sinusoidal force with frequency is out of band gap, the attenuation of the stress response is not obvious as that in the band gap.

• Proceedings of the Korean Statistical Society Conference
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• 2002.11a
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• pp.115-117
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• 2002

In this paper, we obtain an explicit formula of the Laplace transform of the forward recurrence time at finite time t > 0 in an alternating renewal process, by adopting a Markovian approach. As a consequence, we obtain the first two moments of the forward recurrence time.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1659-1671
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• 2013

In this paper, we are concerned with the analysis of the waiting time distribution in the M/M/m retrial queue. We give expressions for the Laplace-Stieltjes transform (LST) of the waiting time distribution and then provide a numerical algorithm for calculating the LST of the waiting time distribution. Numerical inversion of the LSTs is used to calculate the waiting time distribution. Numerical results are presented to illustrate our results.

• Structural Engineering and Mechanics
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• v.15 no.6
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• pp.735-752
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• 2003

The quasi-static and dynamic responses of a linear viscoelastic circular beam on Winkler foundation are studied numerically by using the mixed finite element method in transformed Laplace-Carson space. This element VCR12 has 12 independent variables. The solution is obtained in transformed space and Schapery, Dubner, Durbin and Maximum Degree of Precision (MDOP) transform techniques are employed for numerical inversion. The performance of the method is presented by several quasi-static and dynamic example problems.