• Coupled systems mechanics
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• v.13 no.3
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• pp.231-245
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• 2024

In the present work, a microelogated thermoelastic model based on Lord-Shulman (1967) and Green-Lindsay (1972) theories of thermoelasticity has been constructed. The governing equations for the simulated model are converted into two-dimensional case and made dimensionless for further simplification. Laplace and Hankel transforms followed by eigen value approach has been employed to solve the problem. The use of eigen value approach hasthe advantage of finding the solution of governing equationsin matrix form notations. This approach is straight forward and convenient for numerical computation and avoids the complicate nature of the problem. The components of displacement,stress and temperature distribution are obtained in the transformed domain. Numerical inversion techniques have been used to invert the resulting quantities in the physical domain. Graphical representation of the resulting quantities for describing the effect of microelongation are presented. A special case is also deduced from the present investigation. The problem find application in many engineering problems like thick-walled pressure vesselsuch as a nuclear containment vessel, a cylindricalroller etc.

• Communications of the Korean Mathematical Society
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• v.4 no.2
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• pp.251-263
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• 1989

• Economic and Environmental Geology
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• v.27 no.1
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• pp.41-47
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• 1994

A fast Hankel transform (FHT) algorithm (Anderson, 1982) is applied to numerical evaluation of many Green's tensor integrals encountered in three-dimensional electromagnetic modeling using integral equations. Efficient computation of Hankel transforms is obtained by a combination of related and lagged convolutions which are available in the FHT. We express Green's tensor integrals for a layered half-space, and rewrite those to a form of related functions so that the FHT can be applied in an efficient manner. By use of the FHT, a complete or full matrix of the related Hankel transform can be rapidly and accurately calculated for about the same computation time as would be required for a single direct convolution. Computing time for a five-layer half-space shows that the FHT is about 117 and 4 times faster than conventional direct and multiple lagged convolution methods, respectively.

• Advances in Computational Design
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• v.5 no.4
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• pp.363-380
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• 2020

In this paper, a cylindrical shell is immersed in a non-viscous fluid using first order shell theory of Sander. These equations are partial differential equations which are solved by approximate technique. Robust and efficient techniques are favored to get precise results. Employment of the Rayleigh-Ritz procedure gives birth to the shell frequency equation. Use of acoustic wave equation is done to incorporate the sound pressure produced in a fluid. Hankel's functions of second kind designate the fluid influence. Mathematically the integral form of the Lagrange energy functional is converted into a set of three partial differential equations. Throughout the computation, simply supported edge condition is used. Expressions for modal displacement functions, the three unknown functions are supposed in such way that the axial, circumferential and time variables are separated by the product method. Comparison is made for empty and fluid-filled cylindrical shell with circumferential wave number, length- and height-radius ratios, it is found that the fluid-filled frequencies are lower than that of without fluid. To generate the fundamental natural frequencies and for better accuracy and effectiveness, the computer software MATLAB is used.

• Structural Engineering and Mechanics
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• v.57 no.2
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• pp.327-355
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• 2016

A new analytical derivation of the elastodynamic point load solutions for an isotropic multi-layered half-space is presented by means of the precise integration method (PIM) and the approach of dual vector. The time-harmonic external load is prescribed either on the external boundary or in the interior of the solid medium. Starting with the axisymmetric governing motion equations in a cylindrical coordinate system, a second order ordinary differential matrix equation can be gained by making use of the Hankel integral transform. Employing the technique of dual vector, the second order ordinary differential matrix equation can be simplified into a first-order one. The approach of PIM is implemented to obtain the solutions of the ordinary differential matrix equation in the Hankel integral transform domain. The PIM is a highly accurate algorithm to solve sets of first-order ordinary differential equations and any desired accuracy of the dynamic point load solutions can be achieved. The numerical simulation is based on algebraic matrix operation. As a result, the computational effort is reduced to a great extent and the computation is unconditionally stable. Selected numerical trials are given to validate the accuracy and applicability of the proposed approach. More examples are discussed to portray the dependence of the load-displacement response on the isotropic parameters of the multi-layered media, the depth of external load and the frequency of excitation.

• Geophysics and Geophysical Exploration
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• v.25 no.1
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• pp.38-43
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• 2022

In case axial symmetrical bodies with varying cross sections such as volcanic conduits and unexploded ordnance (UXO), it is efficient to approximate them by adding the response of thin disks perpendicular to the axis of symmetry. To compute the vector magnetic and magnetic gradient tensor respones by such bodies, it is necessary to derive an analytical expression of the circular disk. Therefore, in this study, we drive closed-form expressions of the vector magnetic and magnetic gradient tensor due to a circular disk. First, the vector magnetic field is obtained from the existing gravity gradient tensor using Poisson's relation where the gravity gradient tensor due to the same disk with a constant density can be transformed into a magnetic field. Then, the magnetic gradient tensor is derived by differentiating the vector magnetic field with respect to the cylindrical coordinates converted from the Cartesian coordinate system. Finally, both the vector magnetic and magnetic gradient tensors are derived using Lipschitz-Hankel type integrals based on the axial symmetry of the circular disk.

• Honam Mathematical Journal
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• v.32 no.4
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• pp.763-767
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• 2010

In this note, we give a solution of a $H^{\infty}$-optimization problem.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10a
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• pp.1018-1023
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• 1992

In this paper we proposed the systematic method of reducing the order of controller with robustness. State space formulae for all controllers is found by solving two coupled J-lossless coprime factorizations and model reduction problem. To reduce the order of controller, balanced truncation and Hankel approximation are used.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.197-205
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• 2018

In this note we give a relationship between the degree and coprime-ness of matrix-valued rational functions.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.161-170
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• 2023

We consider dual Toeplitz operators acting on the orthogonal complement of the Dirichlet space on the unit disk. We give a characterization of when a finite sum of products of two dual Toeplitz operators is equal to 0. Our result extends several known results by using a unified way.