• Title/Summary/Keyword: parabolic

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Effects of photostrictive actuator and active control of flexible membrane structure

  • Gajbhiye, S.C.;Upadhyay, S.H.;Harsha, S.P.
    • Smart Structures and Systems
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    • v.14 no.2
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    • pp.71-83
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    • 2014
  • The purpose of this paper is to investigate the flexible structure of parabolic shell using photostrictive actuators. The analysis is made to know its dynamic behavior and light-induced control forces for coupled parabolic shell. The effects of an actuator location as well as membrane and bending components under the control action have been analyzed considering the approximate spherical model. The parabolic membrane shell accuracy is being mathematically approximated and validated comparing the light induced control forces using approximate equivalent spherical shell model. The parabolic shell with kapton smart material and photostrictive actuators has been used to formulate the governing equation in the transverse direction. The Kirchhoff-Love assumptions are used to obtain the governing equation of shell with actuator. The mechanical membrane forces and bending moments for parabolic thin shell with actuator is used to analyze the dynamic effect. The results show that membrane control action is much more significant than bending control action. Photostrictive actuators oriented along circumferential direction (actuator-2) can give better control effect than actuators placed along longitudinal direction (actuator-1). The slight difference is observed between spherical and parabolic shell for a surface with focal length to the diameter ratio of 1.00 or more than unity. Space applications often have the shape of parabolical shells or shell of revolution, due to their required focusing, aiming, or reflecting performance. The present approach is focused that photostrictive actuators can effectively control the vibration of parabolical membrane shell. Also, the actuator's location plays an important role in defining the control force.

NONHOMOGENEOUS DIRICHLET PROBLEM FOR ANISOTROPIC DEGENERATE PARABOLIC-HYPERBOLIC EQUATIONS WITH SPATIALLY DEPENDENT SECOND ORDER OPERATOR

  • Wang, Qin
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.6
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    • pp.1597-1612
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    • 2016
  • There are fruitful results on degenerate parabolic-hyperbolic equations recently following the idea of $Kru{\check{z}}kov^{\prime}s$ doubling variables device. This paper is devoted to the well-posedness of nonhomogeneous boundary problem for degenerate parabolic-hyperbolic equations with spatially dependent second order operator, which has not caused much attention. The novelty is that we use the boundary flux triple instead of boundary layer to treat this problem.

CONNECTIONS ON REAL PARABOLIC BUNDLES OVER A REAL CURVE

  • Amrutiya, Sanjay
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.4
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    • pp.1101-1113
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    • 2014
  • We give analogous criterion to admit a real parabolic connection on real parabolic bundles over a real curve. As an application of this criterion, if real curve has a real point, then we proved that a real vector bundle E of rank r and degree d with gcd(r, d) = 1 is real indecomposable if and only if it admits a real logarithmic connection singular exactly over one point with residue given as multiplication by $-\frac{d}{r}$. We also give an equivalent condition for real indecomposable vector bundle in the case when real curve has no real points.

The Tool Path Determination for Machining the Plane Curve by an Adaptive Mesh Generation Technique - Comparision among the Adaptive Linear Interpolation, Parabolic Interpolation & Linear-Parabolic Interpolation Method - (적응요소분할법에 의한 평면곡선가공의 공구경로 결정 - 적응요소직선보간과 적응요소포물선보간 및 혼합보간법의 비교 -)

  • Hyun, Chang-Heon
    • Journal of Industrial Technology
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    • v.12
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    • pp.69-76
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    • 1992
  • An attempt has been made to determination the NC milling machine's tool-path through the adaptive parabolic interpolation method & the adaptive linear-parabolic interpolation method in consideration of the economical machining time. The algorithms for the above-mentioned interpolation methods have been designed and the numerical experiments for these methods have been conducted with the existing adaptive linear interpolation methods for comparision.

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MULTIPLE SOLUTIONS FOR THE NONLINEAR PARABOLIC PROBLEM

  • Jung, Tacksun;Choi, Q-Heung
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.2
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    • pp.251-259
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    • 2009
  • We investigate the multiple solutions for the nonlinear parabolic boundary value problem with jumping nonlinearity crossing two eigenvalues. We show the existence of at least four nontrivial periodic solutions for the parabolic boundary value problem. We restrict ourselves to the real Hilbert space and obtain this result by the geometry of the mapping.

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SOLVABILITY FOR THE PARABOLIC PROBLEM WITH JUMPING NONLINEARITY CROSSING NO EIGENVALUES

  • Jung, Tacksun;Choi, Q-Heung
    • Korean Journal of Mathematics
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    • v.16 no.4
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    • pp.545-551
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    • 2008
  • We investigate the multiple solutions for a parabolic boundary value problem with jumping nonlinearity crossing no eigenvalues. We show the existence of the unique solution of the parabolic problem with Dirichlet boundary condition and periodic condition when jumping nonlinearity does not cross eigenvalues of the Laplace operator $-{\Delta}$. We prove this result by investigating the Lipschitz constant of the inverse compact operator of $D_t-{\Delta}$ and applying the contraction mapping principle.

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OSCILLATIONS OF CERTAIN NONLINEAR DELAY PARABOLIC BOUNDARY VALUE PROBLEMS

  • Zhang, Liqin;Fu, Xilin
    • Journal of applied mathematics & informatics
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    • v.8 no.1
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    • pp.137-149
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    • 2001
  • In this paper we consider some nonlinear parabolic partial differential equations with distributed deviating arguments and establish sufficient conditions for the oscillation of some boundary value problems.

EXISTENCE OF MULTIPLE PERIODIC SOLUTIONS FOR SEMILINEAR PARABOLIC EQUATIONS WITH SUBLINEAR GROWTH NONLINEARITIES

  • Kim, Wan-Se
    • Journal of the Korean Mathematical Society
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    • v.46 no.4
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    • pp.691-699
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    • 2009
  • In this paper, we establish a multiple existence result of T-periodic solutions for the semilinear parabolic boundary value problem with sublinear growth nonlinearities. We adapt sub-supersolution scheme and topological argument based on variational structure of functionals.