• 대한조선학회논문집
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• 제42권2호
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• pp.124-128
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• 2005

This paper describes motion stability of a spar platform with and without a damping plate in regular waves. The heave and pitch motion equation is derived in terms of Mathieu equation and the stability diagram is obtained. It is shown that the spar platform with damping plate has smaller unstable region than that without damping plate in the stability diagram. Model tests are carried out to verify the mathematical analysis. Under the condition that the pitch natural period is approximately double the heave natural period and the heave motion is amplified at heave resonance, unstable pitch motions are evoked. However the unstable motion is stabilized in cases of spar platform with damping plate. Therefore the damping plate is an effective device to stabilize the motion of spar platform.

• 대한수학회보
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• 제59권1호
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• pp.73-82
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• 2022

Let K be a field of characteristic zero. We first show that images of the linear derivations and the linear 𝓔-derivations of the polynomial algebra K[x] = K[x₁, x₂, …, x_n] are ideals if the products of any power of eigenvalues of the matrices according to the linear derivations and the linear 𝓔-derivations are not unity. In addition, we prove that the images of D and 𝛿 are Mathieu-Zhao spaces of the polynomial algebra K[x] if D = ∑ⁿ_i=1 (a_ix_i + b_i)∂_i and 𝛿 = I - 𝜙, 𝜙(x_i) = λ_ix_i + 𝜇_i for a_i, b_i, λ_i, 𝜇_i ∈ K for 1 ≤ i ≤ n. Finally, we prove that the image of an affine 𝓔-derivation of the polynomial algebra K[x₁, x₂] is a Mathieu-Zhao space of the polynomial algebra K[x₁, x₂]. Hence we give an affirmative answer to the LFED Conjecture for the affine 𝓔-derivations of the polynomial algebra K[x₁, x₂].

• 대한수학회보
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• 제32권2호
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• pp.367-372
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• 1995

In 1955 Singer and Wermer [12] proved that every bounded derivation on a commutative Banach algebra maps into its radical. They conjectured that the continuity of the derivation in their theorm can be removed. In 1988 Thomas [13] proved their conjecture ; Every derivation on a commutative Banach algebra maps into its radical. For noncommutative versions, in 1984 B. Yood [15] proved that the continuous derivations on Banach algebras satisfing [D(a),b] $\in$ Rad(A) for all a, b $\in$ A have the radical range, where [a,b] will be denote the commutator ab-ba. In 1990 M.Bresar and J.Vukman [1] have generlized Yood's result, that is, the continuous linear Jordan derivation on Banach algebra that satisfies [D(a),a] $\in$ Rad(A) for all a $\in$ A has the radical range. In next year Mathieu and Murphy [5] proved that every bounded centralizing derivation on Banach algebras has its image in the radical. Mathieu and Runde [6] removed the boundedness of that.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1995년도 추계학술대회논문집; 한국종합전시장, 24 Nov. 1995
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• pp.142-147
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• 1995

Dynamic characteristics of current collection system is one of the major factors which decide the performance of high speed train. To find good design parameters of the current collection system design guide is prepared through the engineering analysis in this study. The analysis starts from the statics of catenary system which results in the sinusoidal variation of stiffness, which is inherently nonlinear Mathieu equation. Simple physical models of rigid trolley wire and Mathieu equation are considered. To simulate the dynamic response of current collection system, numerical integration based on central difference method and modal analysis are presented. The calculated results of central difference method show superior to those of Euler based algorithm.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2012년도 추계학술대회 논문집
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• pp.229-230
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• 2012

The free flexural vibration of a cantilever plate partially submerged in a fluid is investigated. The fluid is assumed to be inviscid and irrotational. The virtual mass matrix is derived by solving the boundary-value problem related to the fluid motion using elliptical coordinates. The introduction of the elliptical coordinates naturally leads to the use of the Mathieu function. Hence, the virtual mass matrix which reflects the effect of the fluid on the natural vibration characteristics is expressed in analytical form in terms of the Mathieu functions. The virtual mass matrix is then combined with the dynamic model of a thin rectangular plate obtained by using the Rayleigh-Ritz method. This combination is used to analyze the natural vibration characteristics of a partially submerged cantilever plate qualitatively. Also, the non-dimensionalized added virtual mass incremental factors for a partially submerged cantilever plate are presented to facilitate the easy estimation of natural frequencies of a partially submerged cantilever plate. The numerical results validate the proposed approach.

• 한국자동차공학회논문집
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• 제5권1호
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• pp.69-78
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• 1997

Main sources of the vibration in gear driving system are transmission error and backlash. Transmission error is the difference of the rotation between driving and driven gear due to tooth deformation and profile error. Vibro-impacts induced by backlash between meshing gears lead to excessive vibration and noise in many geared rotation systems. Nonlinear dynamic characteristics of the gear driving system due to transmi- ssion error and backlash are investigated. Transmission error is calculated for spur gear. Nonlinear equation of motion for the gear driving system is developed with the calculated transmission error and backlash. Numerical analysis of the equation and the experimental results show the existence of meshing frequency, superharmonic compon- ents. Instability of the gear driving motion is found on the basis of Mathieu equation. Rattle vibration due to backlash is also discussed on the basis if nonlinear jump phenomenon.

• Ocean Systems Engineering
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• 제9권2호
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• pp.157-177
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• 2019

Studies on motion response of a vessel is of great interest to researchers, since a long time. But intensive researches on stability of vessel during motion under dynamic conditions are few. A numerical model of vessel is developed and responses are analyzed in head, beam and quartering sea conditions. Variation of response amplitude operator (RAO) of vessel based on Strip Theory for different wave heights is plotted. Validation of results was done experimentally and numerical results was considered to obtain effect of damping on vessel stability. A scale model ratio of 1:125 was used which is suitable for dimensions of wave flume at National Institute of Technology Calicut. Stability chart are developed based on Mathieu's equation of stability. Ince-Strutt chart developed can help to capture variations of stability with damping.

• Structural Engineering and Mechanics
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• 제61권4호
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• pp.497-510
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• 2017

A framed structure may be composed of two sub-structures, which are linked by a hinged joint. One sub-structure is the primary system and the other is the secondary system. The primary system, which is subjected to the periodic external load, can give rise to an auto-parametric resonance of the second system. Considering the geometric-stiffness effect produced by the axially internal force, the element equation of motion is derived by the extended Hamilton's principle. The element equations are then assembled into the global non-homogeneous Mathieu-Hill equations. The Newmark's method is introduced to solve the time-history responses of the non-homogeneous Mathieu-Hill equations. The energy-growth exponent/coefficient (EGE/EGC) and a finite-time Lyapunov exponent (FLE) are proposed for determining the auto-parametric instability boundaries of the structural system. The auto-parametric instabilities are numerically analyzed for the two frames. The influence of relative stiffness between the primary and secondary systems on the auto-parametric instability boundaries is investigated. A phenomenon of the "auto-parametric internal resonance" (the auto-parametric resonance of the second system induced by a normal resonance of the primary system) is predicted through the two numerical examples. The risk of auto-parametric internal resonance is emphasized. An auto-parametric resonance experiment of a ${\Gamma}$-shaped frame is conducted for verifying the theoretical predictions and present calculation method.

• 대한수학회지
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• 제40권2호
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• pp.307-317
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• 2003

For linear operators between Banach algebras "spectral boundedness" is derived from ordinary boundedness by substituting spectral radius for norm. The interplay between this concept and some of its near relatives is conspicuous in a result of Curto and Mathieu.

• 한국정보디스플레이학회:학술대회논문집
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• 한국정보디스플레이학회 2002년도 International Meeting on Information Display
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• pp.122-126
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• 2002

Measuring color precisely requires the use of a colorimeter whose spectral response is as close as possible to the CIE response. Some techniques such as the NIST 4-color method can improve the precision. but under given conditions, the results can be worse.