• Structural Engineering and Mechanics
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• v.40 no.1
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• pp.49-64
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• 2011

An analytical method is presented to investigate electromagnetothermoelastic behaviors of a hollow sphere composed of functionally graded piezoelectric material (FGPM), placed in a uniform magnetic field, subjected to electric, thermal and mechanical loads. For the case that material properties obey an identical power law in the radial direction of the FGPM hollow sphere, exact solutions for electric displacement, stresses, electric potential and perturbation of magnetic field vector in the FGPM hollow sphere are determined by using the infinitesimal theory of electromagnetothermoelasticity. Some useful discussion and numerical examples are presented to show the significant influence of material inhomogeneity. The aim of this research is to understand the effect of composition on electromagnetothermoelastic stresses and to design optimum FGPM hollow spheres.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.9 no.5
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• pp.83-89
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• 2010

In this paper, the dynamic response of a CNC 5 Axles machining center was analyzed and then controlled passively by using the dynamic absorber. For the simplification of the theoretical approach, the CNC 5 Axles machining center was modeled as a flexible beam(Bed) having a point mass(Column), two discrete systems(a Table-set and a dynamic absorber). Specifically by using the dynamic absorber, the dynamic response of a Table-set which be caused by the vibration of a flexible beam, was reduced down to the infinitesimal level. The optimal design factors of the dynamic absorber were obtained from the minimization of the cost function. It was found that the natural frequencies of a UT-380 machining center be varied due to the movement of the Table-set. In view of the dynamic response of a Table-set, the larger spring stiffness and mass of the dynamic absorber were found to give the greater reduction.

• Journal of the Korea Computer Graphics Society
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• v.10 no.1
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• pp.15-21
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• 2004

This paper proposes a real-time technique for simulating large rotational deformations. Modal analysis based on a linear strain tensor has been shown to be suitable for real-time simulation, but is accurate only for moderately small deformations. In the present work, we identify the rotational component of an infinitesimal deformation, and extend linear modal analysis to track that component. We then develop a procedure to integrate the small rotations occurring al the nodal points. An interesting feature of our formulation is that it can implement both position and orientation constraints in a straightforward manner. These constraints can be used to interactively manipulate the shape of a deformable solid by dragging/twisting a set of nodes, Experiments show that the proposed technique runs in real-time even for a complex model, and that it can simulate large bending and/or twisting deformations with acceptable realism.

• Transactions of the Korean Society of Automotive Engineers
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• v.6 no.6
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• pp.88-97
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• 1998

Compliance elements such as bushings of a suspension system play a crucial role in determining the ride and handling characteristics of the vehicle. In this paper, a general procedure is proposed for the optimum design of compliance elements to meet various design targets. Based on the assumption that the displacements of elastokinematic behavior of a suspension system under external forces are very small, linearized elastokinematic equations in terms of infinitesimal displacements and joint reaction forces are derived. Directly differentiating the linear elastokinematic equations with respect to design variables associated with bushing stiffness, sensitivity equations are obtained. The design process for determining the bushing stiffness using sensitivity analysis and optimization technique is demonstrated.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.1
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• pp.150-155
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• 1994

An Approximate solution for plane two-dimensional incompressible laminar jet issuing from a finite opening with arbitrary initial profile into the same ambient fluid is proposed. For an arbitrary initial velocity profile, the problem is generated from the well known similarity solution for the jet of infinitesimal opening and provides good approximations in the region where the similarity solution cannot be used as an approximation. The asymptotic behavior of this solution is investigated and it is shown that, as goes downstream, the present solution approachs the similarity solution.

• Journal of the Korean Society for Nondestructive Testing
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• v.12 no.2
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• pp.7-13
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• 1992

In this study, we examine the characteristics of beam and the effect of these characteristics on the flaw detection by using different type of two transducers, which are PZT and PVDF film transducer. Consequently, the detection of infinitesimal flaw is more possible than PZT, since it has beam width at focus of $60%{\sim}65%$ in contrast with PZT's. Moreover we can know PVDF transducer has superiority in detecting ability for sub-surface flaw detection in view of its acoustic impedance is near to water's and its focusing range is narrower than PZT's as $65{\sim}85%$ because it has spherical surface.

• Computers and Concrete
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• v.23 no.5
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• pp.303-309
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• 2019

This study investigates axisymmetric fractional vibration of an isotropic hyperelastic semi-linear thin disc with a view to examine effects of finite deformation associated with the material of the disc and effects of fractional vibration associated with the motion of the disc. The generalized three-dimensional equation of motion is reduced to an equivalent time fraction one-dimensional vibration equation. Using the method of variable separable, the resulting equation is further decomposed into second-order ordinary differential equation in spatial variable and fractional differential equation in temporal variable. The obtained solution of the fractional vibration problem under consideration is described by product of one-parameter Mittag-Leffler and Bessel functions in temporal and spatial variables respectively. The obtained solution reduces to the solution of the free vibration problem in literature. Finally, and amongst other things, the Cauchy's stress distribution in thin disc under finite deformation exhibits nonlinearity with respect to the displacement fields whereas in infinitesimal deformation hypothesis, these stresses exhibit linear relation with the displacement field.

• Structural Engineering and Mechanics
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• v.82 no.4
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• pp.459-467
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• 2022

We investigated the influence of variable thermal conductivity on waves propagating through the elastic medium. Infinitesimal deformation results in generation of thermal signal, and is analyzed by using dual phase lag heat (DPL) conduction model. The medium considered is homogenous, isotropic and bounded by thermal shock. The elastic waves propagating through the medium are considered to be harmonic in nature, and expressions for the physical variables are obtained accordingly. Analytically, we obtained the expressions for displacement components, temperature, micro-temperature component and stresses. The theoretical results obtained are computed graphically for the particular medium by using MATLAB.

• Bulletin of the Korean Mathematical Society
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• v.23 no.2
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• pp.167-170
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• 1986

Let M be a von Neumann algebra and .alpha., .betha. be *-automorphisms of M satisfying the operator equation .alpha.+.alpha.$^{-1}$ =.betha.+.betha.$^{-1}$ This operator equation has been extensively studied and many important decomposition theorems have been obtained by several authors (for instance see [4], [5], [2], [1]). Originally, this operator equation arose in the paper of Van Daele on the new approach of the Tomita-Takesaki theory in the case of modular operators ([7]). In the case of one-parameter automorphism groups, this equation has produced a bounded and completely positive map which can play a role similar to the infinitesimal generator (for details see [6] and [1]). A recent and one of the most important applications of this equation has been in developing an anglogue of the Tomita-Takesaki theory for Jordan algebras by Haagerup [3]. One general result of this theory is the following.

• Journal for History of Mathematics
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• v.21 no.2
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• pp.19-38
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• 2008

This study aims to investigate the evolution of calculating the volume of a sphere in eastern and western mathematical history. In western case, Archimedes', Cavalieri's and Kepler's approaches, and in eastern case, Nine Chapters';, Liu Hui's and Zus' approaches are worthy of noting. The common idea of most of these approaches is the infinitesimal concept corresponding to Cavalieri's or Liu-Zu's principle which would developed to the basic idea of Calculus. So this study proposes an alternative to organization of math-textbooks or instructional procedures for teaching the volume of a sphere based on the principle.