• Structural Engineering and Mechanics
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• v.33 no.6
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• pp.697-708
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• 2009

Stresses are solved for two parallel cracks in an infinite orthotropic plate during passage of incoming shock stress waves normal to their surfaces. Fourier transformations were used to reduce the boundary conditions with respect to the cracks to two pairs of dual integral equations in the Laplace domain. To solve these equations, the differences in the crack surface displacements were expanded to a series of functions that are zero outside the cracks. The unknown coefficients in the series were solved using the Schmidt method so as to satisfy the conditions inside the cracks. The stress intensity factors were defined in the Laplace domain and were inverted numerically to physical space. Dynamic stress intensity factors were calculated numerically for selected crack configurations.

• Structural Engineering and Mechanics
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• v.35 no.4
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• pp.409-430
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• 2010

The present paper will be concerned to the investigation of the stress-strain field around the cavity that is loaded or partially loaded at the inner surface by the rotationally symmetric loading. The cavity of the spherical, cylindrical or elliptical shape is situated in a stressed elastic continuum, subjected to the gravitation field. As the contribution to the similar investigations, the paper introduces the new function of loading in the form of the infinite sine series. Besides, in this paper the solution of stresses around an oblong ellipsoid cavity, has been obtained using appropriate curvilinear elliptical coordinates. This analytical approach avoids the solutions of the same problem that lead to expressions that contain rather complex integrations. Thus the presented solutions provide the applicable and explicit expressions for stresses and strains developed in infinite series with easily determinable coefficients by the use of contemporary mathematical packages. The numerical examples are also included to confirm the convergence of the obtained solutions.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.671-697
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• 2024

In this paper, we formally introduce the notion of a general parametric digamma function Ψ(−s; A, a) and we find the Laurent expansion of Ψ(−s; A, a) at the integers and poles. Considering the contour integrations involving Ψ(−s; A, a), we present some new identities for infinite series involving Dirichlet type parametric harmonic numbers by using the method of residue computation. Then applying these formulas obtained, we establish some explicit relations of parametric linear Euler sums and some special functions (e.g. trigonometric functions, digamma functions, Hurwitz zeta functions etc.). Moreover, some illustrative special cases as well as immediate consequences of the main results are also considered.

• Wind and Structures
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• v.30 no.5
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• pp.485-497
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• 2020

A study, using potential water wave theory, is conducted on the oblique water wave motion over two fixed submerged rectangular blocks (breakwaters) placed over a finite step bottom. We have considered infinite and semi-infinite fluid domains. In both domains, the Fourier expansion method is employed to obtain the velocity potentials explicitly in terms of the infinite Fourier series. The unknown coefficients appearing in the velocity potentials are determined by the eigenfunction expansion matching method at the interfaces. The derived velocity potentials are used to compute the hydrodynamic horizontal and vertical forces acting on the submerged blocks for different values of block thickness, gap spacing between the two blocks, and submergence depth of the upper block from the mean free surface. In addition, the wave load on the vertical wall is computed in the case of the semi-infinite fluid domain for different values of blocks width and the incident wave angle. It is observed that the amplitudes of hydrodynamic forces are negligible for larger values of the wavenumber. Furthermore, the upper block experiences a higher hydrodynamic force than the lower block, regardless of the gap spacing, submergence depth, and block thickness.

• International Journal of Naval Architecture and Ocean Engineering
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• v.13 no.1
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• pp.50-56
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• 2021

An accurate evaluation of three-dimensional (3D) Time-Domain Green Function (TDGF) in infinite water depth is essential for ship's hydrodynamic analysis. Various numerical algorithms based on the TDGF properties are considered, including the ascending series expansion at small time parameter, the asymptotic expansion at large time parameter and the Taylor series expansion combines with ordinary differential equation for the time domain analysis. An efficient method (referred as "Present Method") for a better accuracy evaluation of TDGF has been proposed. The numerical results generated from precise integration method and analytical solution of Shan et al. (2019) revealed that the "Present method" provides a better solution in the computational domain. The comparison of the heave hydrodynamic coefficients in solving the radiation problem of a hemisphere at zero speed between the "Present method" and the analytical solutions proposed by Hulme (1982) showed that the difference of result is small, less than 3%.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.3 no.2
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• pp.39-45
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• 2010

In this paper, an equally spaced $3{\times}2$ microstrip patch array antenna based on the fundamental infinite wavelength supported by the composite right/left-handed (CRLH) transmission line (TL) is proposed. The proposed CRLH TL unit cell consists of an inter-digit capacitor to realize left-handed (LH) series capacitance and non-symmetric shunt meander line with a shorted via to realize LH shunt inductance. At the infinite wavelength frequency of 2.09 GHz a 6-port series power divider consisting of a 19 unit cells shows a maximum magnitude difference of 0.73 dB and a $0.52^{\circ}$ maximum phase difference between output ports. The measured resonant frequency and maximum gain of the fabricated array antenna is 2.09 GHz and 10.98 dBi, respectively.

• Korean Journal of Logic
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• v.11 no.2
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• pp.127-170
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• 2008

This paper aims to present solutions to three intriguing puzzles on causation that Benardete presents by considering the results of infinite series of telescoping events. The main conceptual tool used in the solutions is the notion of collective causation, what many events cause collectively. It is straightforward to apply the notion to resolve two of the three puzzles. It does not seem as straightforward to apply it to the other puzzle. After some preliminary clarifications of the situation that Benardete describes to present the puzzle, however, we can apply the notion to resolve it as well.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.52 no.12
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• pp.641-648
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• 2003

This paper proposes a novel UPFE based on H-bridge modules, isolated through single-phase multi-winding transformers. The dynamic performance of proposed system was analyzed by simulation with EMTDC, assuming that the UPFC is connected with the 138-kV transmission line of one-machine-infinite-bus power system. The proposed system can be directly connected to the transmission line without series injection transformers. It has flexibility in expanding the operation voltage by increasing the number of H-bridge modules.

• Proceedings of the KIEE Conference
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• 1996.07b
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• pp.655-657
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• 1996

The objective of this paper is to compare the series and shunt approaches of controlled reactive power compensation to improve power system transient stabilities. Including main circuit considerations of series and shunt compensators, application aspects are thought to have major impacts on efficiency and economy of the installation of the compensators. The concept is studied by means of EMTP simulations on one machine-Infinite Bus Test System which consists of a 612MVA steam turbin generator and transformer and double circuit 345KV transmission line. Idealized dynamic models of Thyristor Controlled Series Compensation and Shunt Compensation are used for the comparative study of the series and shunt compensation approach to damp power system oscillations.

• Honam Mathematical Journal
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• v.38 no.4
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• pp.849-856
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• 2016

General summation formula for sums involving ${\sigma}(n)/n$ is expressed with infinite series containing a Bessel function.