• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.759-771
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• 2020

In this article, a hybrid class of the q-Hermite based Apostol type Frobenius-Genocchi polynomials is introduced by means of generating function and series representation. Several important formulas and recurrence relations for these polynomials are derived via different generating function methods. Furthermore, we consider some relationships for q-Hermite based Apostol type Frobenius-Genocchi polynomials of order α associated with q-Apostol Bernoulli polynomials, q-Apostol Euler polynomials and q-Apostol Genocchi polynomials.

• Structural Engineering and Mechanics
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• v.67 no.4
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• pp.385-390
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• 2018

An incongruity is underlined about the analysis of Timoshenko beams subjected to concentrated loads modelled through the use of generalized functions. While for Euler-Bernoulli beams this modeling always leads to effective results, on the contrary, the contemporary assumptions of concentrated external moment, interpreted as a generalized function (doublet), and of shear deformation determine inconsistent discontinuities in the deflection laws. A physical/theoretical explanation of this not-neglecting incongruity is given in the text.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.8-13
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• 1993

This paper presents deterministic and adaptive control laws for two-link flexible arm. The flexible arm has considerable structural flexibility. Because of its flexbility, dynamic equations are very complex and difficult to get, dynamic equations for two-link flexible arm are derived from Bernoulli-Euler beam theory and Lagrangian equation. Using the fact that matrix is skew symmetric, controllers which have a simplified structure with less computational burden are proposed by using Lyapunov stability theory.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.547-551
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• 1996

In this paper, robust vibration control of a one-link flexible robot arm based on variable structure system is discussed. We derive dynamic equations of it using a Lagrangian assumed modes method based on Bernoulli-Euler Beam theory. The optimal sliding surface is designed and the problem of chattering is also solved by the adoption of a continuous control law within a small neighborhood of the switching hyperplane.

• Honam Mathematical Journal
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• v.36 no.2
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• pp.263-273
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• 2014

Ever since Euler solved the so-called Basler problem of ${\zeta}(2)=\sum_{n=1}^{\infty}1/n^2$, numerous evaluations of ${\zeta}(2n)$ ($n{\in}\mathbb{N}$) as well as ${\zeta}(2)$ have been presented. Very recently, Ritelli [61] used a double integral to evaluate ${\zeta}(2)$. Modifying mainly Ritelli's double integral, here, we aim at evaluating certain interesting alternating series.

• Journal of Mechanical Science and Technology
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• v.19 no.9
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• pp.1753-1760
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• 2005

The pseudo spectral method is applied to the free vibration analysis of double-span Timoshenko beams. The analysis is based on the Chebyshev polynomials. Each section of the double-span beam has its own basis functions, and the continuity conditions at the intermediate support as well as the boundary conditions are treated separately as the constraints of the basis functions. Natural frequencies are provided for different thickness-to-length ratios and for different span ratios, which agree with those of Euler-Bernoulli beams when the thickness-to-length ratio is small but deviate considerably as the thickness-to-length ratio grows larger.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11a
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• pp.394.1-394
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• 2002

The purpose of this paper is to investigate the natural frequencies and mode shapes of tapered beams with general boundary condition(translational and rotational elastic support) at one end and carrying a tip mass of rotatory inertia at the other end. The beam model is based on the classical Bernoulli-Euler beam theory which neglects the effects of rotatory inertia and shear deformation. (omitted)

• Proceedings of the IEEK Conference
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• 1999.11a
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• pp.703-706
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• 1999

In this paper, robust vibration control of a one-link flexible robot arm based on variable structure system is discussed. We derive dynamic equations of it using a Lagragian assumed modes method based on Bernoulli-Euler beam theory. The optimal sliding surface is designed and the problem of chattering is also solved by the adoptation of a continuous control law within a small neighborhood of the switching hyperplane.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1995.04a
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• pp.56-60
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• 1995

본 연구에서는 기존의 연구에서 다룬바 없는 분포하중의 경우에 대해 스펙트럴요소법을 적용하기 위해 1) 힘과 변위와의 관계를 이용하여 Bernoulli-Euler보와 1차원 Timoshenko-Mindlin평판에 대한 스펙트럴요소를 유도하고 2) 스펙트럴 요소법을 이용하여 분포하중을 받는 이들 구조물의 동적거동을 해석하고자 한다.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.315-322
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• 2014

In this paper, we observe the behavior of complex roots of the tangent polynomials $T_n(x)$, using numerical investigation. By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the tangent polynomials $T_n(x)$. Finally, we give a table for the solutions of the tangent polynomials $T_n(x)$.