• Title, Summary, Keyword: free and bound variable

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Frequency analysis of eccentric hemispherical shells with variable thickness

  • Kang, Jae-Hoon
    • Structural Engineering and Mechanics
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    • v.55 no.2
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    • pp.245-261
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    • 2015
  • A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies of eccentric hemi-spherical shells of revolution with variable thickness. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components $u_r$, $u_{\Theta}$, and $u_z$ in the radial, circumferential, and axial directions, respectively, are taken to be periodic in ${\theta}$ and in time, and algebraic polynomials in the r and z directions. Potential and kinetic energies of eccentric hemi-spherical shells with variable thickness are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to three or four-digit exactitude is demonstrated for the first five frequencies of the shells. Numerical results are presented for a variety of eccentric hemi-spherical shells with variable thickness.

Vibrations of truncated shallow and deep conical shells with non-uniform thickness

  • Kang, Jae-Hoon
    • Structural Engineering and Mechanics
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    • v.55 no.1
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    • pp.29-46
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    • 2015
  • A three-dimensional (3-D) method of analysis is presented for determining the natural frequencies of a truncated shallow and deep conical shell with linearly varying thickness along the meridional direction free at its top edge and clamped at its bottom edge. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components $u_r$, $u_{\theta}$, and $u_z$ in the radial, circumferential, and axial directions, respectively, are taken to be periodic in ${\theta}$ and in time, and algebraic polynomials in the r and z directions. Strain and kinetic energies of the truncated conical shell with variable thickness are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated. The frequencies from the present 3-D method are compared with those from other 3-D finite element method and 2-D shell theories.

FINITE-DIFFERENCE BISECTION ALGORITHMS FOR FREE BOUNDARIES OF AMERICAN OPTIONS

  • Kang, Sunbu;Kim, Taekkeun;Kwon, Yonghoon
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.19 no.1
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    • pp.1-21
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    • 2015
  • This paper presents two algorithms based on the Jamshidian equation which is from the Black-Scholes partial differential equation. The first algorithm is for American call options and the second one is for American put options. They compute numerically free boundary and then option price, iteratively, because the free boundary and the option price are coupled implicitly. By the upwind finite-difference scheme, we discretize the Jamshidian equation with respect to asset variable s and set up a linear system whose solution is an approximation to the option value. Using the property that the coefficient matrix of this linear system is an M-matrix, we prove several theorems in order to formulate a bisection method, which generates a sequence of intervals converging to the fixed interval containing the free boundary value with error bound h. These algorithms have the accuracy of O(k + h), where k and h are step sizes of variables t and s, respectively. We prove that they are unconditionally stable. We applied our algorithms for a series of numerical experiments and compared them with other algorithms. Our algorithms are efficient and applicable to options with such constraints as r > d, $r{\leq}d$, long-time or short-time maturity T.

Vibrations of Complete Paraboloidal Shells with Variable Thickness form a Three-Dimensional Theory

  • Chang, Kyong-Ho;Shim, Hyun-Ju;Kang, Jae-Hoon
    • Journal of the Korean Association for Spatial Structures
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    • v.4 no.4
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    • pp.113-128
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    • 2004
  • A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of solid paraboloidal and complete (that is, without a top opening) paraboloidal shells of revolution with variable wall thickness. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. The ends of the shell may be free or may be subjected to any degree of constraint. Displacement components $u_r,\;u_{\theta},\;and\;u_z$ in the radial, circumferential, and axial directions, respectively, are taken to be sinusoidal in time, periodic in ${\theta}$, and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the paraboloidal shells of revolution are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four digit exactitude is demonstrated for the first five frequencies of the complete, shallow and deep paraboloidal shells of revolution with variable thickness. Numerical results are presented for a variety of paraboloidal shells having uniform or variable thickness, and being either shallow or deep. Frequencies for five solid paraboloids of different depth are also given. Comparisons are made between the frequencies from the present 3-D Ritz method and a 2-D thin shell theory.

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Frequencies and Mode Shapes of Annular Plates tilth Variable Thickness by the Ritz Method in Three-Dimensional Analysis (변두께를 갖는 두꺼운 환형판의 삼차원적 리츠방법에 의한 진동수와 모드형상)

  • 양근혁;강재훈
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.11 no.5
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    • pp.89-100
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    • 2001
  • The Ritz method Is applied In a three-dimensional (3-D) analysis to obtain accurate frequencies for thick. linearly tapered. annular plates. The method is formulated for annular plates haying any combination of free or fixed boundaries at both Inner and outer edges. Admissible functions for the three displacement components are chosen as trigonometric functions in the circumferential co-ordinate. and a1gebraic polynomials in the radial and thickness co-ordinates. Upper bound convergence of the non-dimensional frequencies to the exact values within at least four significant figures is demonstrated. Comparisons of results for annular plates with linearly varying thickness are made with ones obtained by others using 2-D classical thin place theory. Extensive and accurate ( four significant figures ) frequencies are presented 7or completely free. thick, linearly tapered annular plates haying ratios of average place thickness to difference between outer radius (a) and inner radius (b) radios (h$_{m}$/L) of 0.1 and 0.2 for b/L=0.2 and 0.5. All 3-D modes are included in the analyses : e.g., flexural, thickness-shear. In-plane stretching, and torsional. Because frequency data liven is exact 7o a\ulcorner least four digits. It is benchmark data against which the results from other methods (e.g.. 2-D 7hick plate theory, finite element methods. finite difference methods) and may be compared. Throughout this work, Poisson\`s ratio $\upsilon$ is fixed at 0.3 for numerical calculations.s.

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Localized Surface Plasmon Resonance (LSPR) Biosensors on Metal Nanoparticles with the Design of Bioreceptors

  • Kim, Min-Gon;Park, Jin-Ho;Byun, Ju-Young;Shin, Yong-Beom
    • Proceedings of the Korean Vacuum Society Conference
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    • pp.126-126
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    • 2014
  • Label-free biomolecular assay based localized surface plasmon resonance (LSPR) of noble metal nanoparticles enables simple and rapid detection with the use of simple equipment. Nanosized metal nanoparticles exhibit a strong absorption band when the incident light frequency is resonant with the collective oscillation of the electrons, which is known as the LSPR. Here we demonstrate localized surface plasmon resonance (LSPR) substrates such as plasmonic Au nanodisks fabricated by a nanoimprinting process and gold nanorod-immobilized surfaces and their applications to highly sensitive and/or label-free biosensing. To increase detection sensitivity various bioreceptors weree designed. A single chain variable fragment (scFv) was used as a receptor to bind C-reactive protein (CRP). The results of this effort showed that CRP in human serum could be quantitatively detected lower than 1 ng/ml. Aptamers, which were immobilized on gold nanorods, were used to detect mycotoxins. The specific binding of ochratoxin A (OTA) to the aptamer was monitored by the longitudinal wavelength shift of LSPR peak in the UV-Vis spectra resulting from the changes of local refractive index near the GNR surface induced by accumulation of OTA and G-quadruplex structure formation of the aptamer. According to our results, OTA could be quantitatively detected lower than 1 nM level. Additionally, aptamer-functionalized GNR substrate was quite robust and can be regenerated many times by rinsing at 70 OC to remove bound target. During seven times of washing steps, the developed OTA sensing system could be reusable. Moreover, the proposed biosensor exhibited selectivity over other mycotoxins with an excellent recovery for detection in grinded corn samples, suggesting that the proposed LSPR based aptasensor plays an important role in label-free detection of mycotoxins.

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${\lambda}$-calculus (${\lambda}$-연산 소개)

  • Cheong Kye-Seop
    • Journal for History of Mathematics
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    • v.17 no.4
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    • pp.45-64
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    • 2004
  • The lambda calculus is a mathematical formalism in which functions can be formed, combined and used for computation that is defined as rewriting rules. With the development of the computer science, many programming languages have been based on the lambda calculus (LISP, CAML, MIRANDA) which provides simple and clear views of computation. Furthermore, thanks to the "Curry-Howard correspondence", it is possible to establish correspondence between proofs and computer programming. The purpose of this article is to make available, for didactic purposes, a subject matter that is not well-known to the general public. The impact of the lambda calculus in logic and computer science still remains as an area of further investigation.stigation.

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Three-Dimensional Vibration Analysis of Thick Shells of Revolution (두꺼운 축대칭 회전쉘의 3차원적 진동해석)

  • 강재훈;양근혁;장경호
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.15 no.3
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    • pp.399-407
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    • 2002
  • A three-dimensional method of analysis is presented for determining the free vibration frequencies and mode shapes of hollow bodies of revolution (i.e., thick shells), not limited to straight line generators or constant thickness. The middle surface of the shell may have arbitrary curvatures, and the wall thickness may vary arbitrarily. Displacement components$U_\Phi, U_z, U_\theta$ in the meridional, normal and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in$\theta$, and algebraic polynomials in the$\Phi$and z directions. Potential(strain) and kinetic energies of the entire body are formulated, and upper bound values of the frequencies are obtained by minimizing the frequencies. As the degrees of the polynomials are increased, frequencies converge to the exact values. Novel numerical results are presented for two types of thick conical shells and thick spherical shell segments having linear thickness variations. Convergence to four digit exactitude is demonstrated for the first five frequencies of both types of shells. The method is applicable to thin shells, as well as thick and very thick ones.

Drying by Microwave Irradiation of Sewage Waste (도시 하수 폐기물의 고주파 건조)

  • Park, Soo In;Park, Kwang Ha
    • Analytical Science and Technology
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    • v.10 no.6
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    • pp.418-426
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    • 1997
  • Dewatered digested sewage sludge were heated with microwave and their drying characteristics were investigated on the effect of their surface area, shape, diameter and thickness. The drying characteristics of identical samples in a conventional drying oven were studied. In conventional drying, constant rate period was not found and moisture was evaporated with capillary action. Moisture in the sludge was a bound water and free water was not exist. In microwave drying, the falling rate period was divided into two zones. In falling rate drying period, moisture movement occured by diffusion. The evaporation surface area was a significant variable, the greater heating surface area promoted water removal rate over wide region of water content. Drying rate was slow and constant rate drying period was found in wide moisture content region with increasing diameter. Drying characteristics appeared differently in various shape. In microwave heating, first of all temperature of sludge center was increased and was the highest. Temperature in the constant rate drying period was remained constantly at $80{\sim}100^{\circ}C$.

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Three-Dimensional Vibration Analysis of Solid and Hollow Hemispheres Having Varying Thickness (변두께를 갖는 두꺼운 반구형 쉘과 반구헝체의 3차원적 진동해석)

  • 심현주;장경호;강재훈
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.16 no.2
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    • pp.197-206
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    • 2003
  • A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of solid and hollow hemispherical shells of revolution of arbitrary wall thickness having arbitrary constraints on their boundaries. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components μ/sub Φ/, μ/sub z/, and μ/sub θ/ in the meridional, normal, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the Φ and z directions. Potential (strain) and kinetic energies of the hemispherical shells are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies obtained by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Novel numerical results are presented for solid and hollow hemispheres with linear thickness variation. The effect on frequencies of a small axial conical hole is also discussed. Comparisons are made for the frequencies of completely free, thick hemispherical shells with uniform thickness from the present 3-D Ritz solutions and other 3-D finite element ones.