• Title/Summary/Keyword: a linear theory

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MULTIPLE SOLUTIONS FOR THE NONLINEAR HAMILTONIAN SYSTEM

  • Jung, Tacksun;Choi, Q-Heung
    • Korean Journal of Mathematics
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    • v.17 no.4
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    • pp.507-519
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    • 2009
  • We give a theorem of the existence of the multiple solutions of the Hamiltonian system with the square growth nonlinearity. We show the existence of m solutions of the Hamiltonian system when the square growth nonlinearity satisfies some given conditions. We use critical point theory induced from the invariant function and invariant linear subspace.

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ASYMPTOTICALLY LINEAR BEAM EQUATION AND REDUCTION METHOD

  • Choi, Q-Heung;Jung, Tacksun
    • Korean Journal of Mathematics
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    • v.19 no.4
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    • pp.481-493
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    • 2011
  • We prove a theorem which shows the existence of at least three ${\pi}$-periodic solutions of the wave equation with asymptotical linearity. We obtain this result by the finite dimensional reduction method which reduces the critical point results of the infinite dimensional space to those of the finite dimensional subspace. We also use the critical point theory and the variational method.

Linear Stability of Compositional Convection in a Mushy Layer during Solidification of Ammonium Chloride Solution (염화암모늄 수용액 응고시에 Mush 층에서 성분적 대류의 선형안정성)

  • Hwang, In Gook
    • Korean Chemical Engineering Research
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    • v.50 no.1
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    • pp.61-65
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    • 2012
  • The onset of convection in a mushy layer is analyzed by using linear stability theory in time-dependent solidification of a binary melt. A simplified model of a near-eutectic mush, in which the mush is assumed to be a porous block, is used and the propagation theory is applied to determine the critical conditions for the onset of convection. The present critical Rayleigh number is higher than the existing experimental result and also theoretical results obtained by considering the mushy layer with an overlying liquid layer. The constant pressure (permeable) condition applied on the mush-liquid interface produces a lower critical Rayleigh number, which is closer to the experimental results of aqueous ammonium chloride solution, compared with the impermeable condition.

Thermal buckling of FGM nanoplates subjected to linear and nonlinear varying loads on Pasternak foundation

  • Ebrahimi, Farzad;Ehyaei, Javad;Babaei, Ramin
    • Advances in materials Research
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    • v.5 no.4
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    • pp.245-261
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    • 2016
  • Thermo-mechanical buckling problem of functionally graded (FG) nanoplates supported by Pasternak elastic foundation subjected to linearly/non-linearly varying loadings is analyzed via the nonlocal elasticity theory. Two opposite edges of the nanoplate are subjected to the linear and nonlinear varying normal stresses. Elastic properties of nanoplate change in spatial coordinate based on a power-law form. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of nanoplate. The equations of motion for an embedded FG nanoplate are derived by using Hamilton principle and Eringen's nonlocal elasticity theory. Navier's method is presented to explore the influences of elastic foundation parameters, various thermal environments, small scale parameter, material composition and the plate geometrical parameters on buckling characteristics of the FG nanoplate. According to the numerical results, it is revealed that the proposed modeling can provide accurate results of the FG nanoplates as compared some cases in the literature. Numerical examples show that the buckling characteristics of the FG nanoplate are related to the material composition, temperature distribution, elastic foundation parameters, nonlocality effects and the different loading conditions.

HIGHER ORDER ZIG-ZAG SHELL THEORY FOR SMART COMPOSITE STRUCTURES UNDER THERMO-ELECTRIC-MECHANICAL LOADING (고차 지그재그 이론을 이용한 열_전기_기계 하중하의 스마트 복합재 쉘 구조물의 해석)

  • Oh, Jin-Ho;Cho, Maeng-Hyo
    • Proceedings of the Korean Society For Composite Materials Conference
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    • 2005.04a
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    • pp.1-4
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    • 2005
  • A higher order zig-zag shell theory is developed to refine accurately predict deformation and stress of smart shell structures under the mechanical, thermal, and electric loading. The displacement fields through the thickness are constructed by superimposing linear zig-zag field to the smooth globally cubic varying field. Smooth parabolic distribution through the thickness is assumed in the transverse deflection in order to consider transverse normal deformation. The mechanical, thermal, and electric loading is applied in the sinusoidal distribution function in the in-surface direction. Thermal and electric loading is given in the linear variation through the thickness. Especially, in electric loading case, voltage is only applied in piezo-layer. The layer-dependent degrees of freedom of displacement fields are expressed in terms of reference primary degrees of freedom by applying interface continuity conditions as well as bounding surface conditions of transverse shear stresses. In order to obtain accurate transverse shear and normal stresses, integration of equilibrium equation approach is used. The numerical examples of present theory demonstrate the accuracy and efficiency of the proposed theory. The present theory is suitable for the predictions of behaviors of thick smart composite shell under mechanical, thermal, and electric loadings combined.

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OPTIMAL CONTROL OF THE HEAT EQUATION IN AN INHOMOGENEOUS BODY

  • Borzabadi, A.H.;Kamyad, A.V.;farahi, M.H.
    • Journal of applied mathematics & informatics
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    • v.15 no.1_2
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    • pp.127-146
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    • 2004
  • In this paper we consider a heat flow in an inhomogeneous. body without internal source. There exists special initial and boundary conditions in this system and we intend to find a convenient coefficient of heat conduction for this body so that body cool off as much as possible after definite time. We consider this problem in a general form as an optimal control problem which coefficient of heat conduction is optimal function. Then we replace this problem by another in which we seek to minimize a linear form over a subset of the product of two measures space defined by linear equalities. Then we construct an approximately optimal control.

Duality in non-linear programming for limit analysis of not resisting tension bodies

  • Baratta, A.;Corbi, O.
    • Structural Engineering and Mechanics
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    • v.26 no.1
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    • pp.15-30
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    • 2007
  • In the paper, one focuses on the problem of duality in non-linear programming, applied to the solution of no-tension problems by means of Limit Analysis (LA) theorems for Not Resisting Tension (NRT) models. In details, one demonstrates that, starting from the application of the duality theory to the non-linear program defined by the static theorem approach for a discrete NRT model, this procedure results in the definition of a dual problem that has a significant physical meaning: the formulation of the kinematic theorem.

GENERALIZED INTERTWINING LINEAR OPERATORS WITH ISOMETRIES

  • Hyuk Han
    • Journal of the Chungcheong Mathematical Society
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    • v.36 no.1
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    • pp.13-23
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    • 2023
  • In this paper, we show that for an isometry on a Banach space the analytic spectral subspace coincides with the algebraic spectral subspace. Using this result, we have the following result. Let T be a bounded linear operator with property (δ) on a Banach space X. And let S be an isometry on a Banach space Y . Then every generalized intertwining linear operator θ : X → Y for (S, T) is continuous if and only if the pair (S, T) has no critical eigenvalue.

WAVE-CURRENT INTERACTIONS IN MARINE CURRENT TURBINES

  • Barltrop, N.;Grant, A.;Varyani, K.S.;Clelland, D.;Pham, X.P.
    • Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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    • 2006.11a
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    • pp.80-90
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    • 2006
  • The influence of waves on the dynamic properties of bending moments at the root of blades of tidal stream vertical axis rotors is reported. Blade theory for wind turbine is combined with linear wave theory and used to analyse this influence. Experiments were carried out to validate the simulation and the comparison shows the usefulness of the theory in predicting the bending moments. The mathematical model is then used to study the importance of waves for the fatigue design of the blade-hub connection.

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Dynamic Modeling and Analysis of the Composite Beams with a PZT Layer (PZT층을 갖는 복합재 보의 동역학 모델링 및 해석)

  • Kim, Dae-Hwan;Lee, U-Sik
    • Proceedings of the KSR Conference
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    • 2011.05a
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    • pp.314-316
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    • 2011
  • This paper develops a spectral element model for the composite beams with a surface-bonded piezoelectric layer from the governing equations of motion. The governing equations of motion are derived from Hamilton's principle by applying the Bernoulli-Euler beam theory for the bending vibration and the elementary rod theory for the longitudinal vibration of the composite beams. For the PZT layer, the Bernoulli-Euler beam theory and linear piezoelectricity theory are applied. The high accuracy of the present spectral element model is evaluated through the numerical examples by comparing with the finite element analysis results.

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