• Transactions of the Korean Society of Mechanical Engineers
• /
• v.17 no.8
• /
• pp.1963-1970
• /
• 1993

A simple technique to decouple the modal equations of motion of a linear nonclassically damped system is to neglect the off-diagonal elements of the modal damping matrix. This is called the decoupling approximation. It has generally been conceived that smallness of off-diagonal elements relative to the diagonal ones would validate its use. In this study, the relationship between elements of the modal damping matrix and the error arising from the decoupling approximation is explored. It is shown that the enhanced diagonal dominance of the modal damping matrix need not diminish the error. In fact, the error may even increase. Moreover, the error is found to be strongly dependent on the exitation. Therefore, within the practical range of engineering applications, diagonal dominance of the modal damping matrix would not be sufficient to supress the effect of modal coupling.

• Journal of applied mathematics & informatics
• /
• v.27 no.3_4
• /
• pp.943-953
• /
• 2009

In this paper, we give the lower and upper bounds for inverse elements of strictly diagonally dominant seventh-diagonal matrices, and improve the bounds on [SIAM. J. matrix Anal.App1.20(1999)820-837].

• PNF and Movement
• /
• v.21 no.1
• /
• pp.87-94
• /
• 2023

Purpose: The present study aims to investigate the effects of a diagonal exercise pattern on selective activation of the upper extremity muscles using both normalization and isolation methods. Methods: In total, 17 asymptomatic subjects participated in this study. During the two diagonal patterns of exercise (diagonals 1 and 2), muscular activities of the upper trapezius (UT), lower trapezius (LT), serratus anterior (SA), anterior deltoid (AD), and infraspinatus (IS) were measured. The collected data were analyzed in two ways, according to the dominance of muscle activities (%Isolation) and according to normalized activities (%MVIC). Results: There were significant differences in LT, SA, AD, and IS between %MVIC and %Isolation (p<0.05), and the diagonal 1 pattern of exercise showed significantly more LT activities compared with the diagonal 2 pattern (p<0.05). Further, except for LT, there were no significant differences in muscle activities between the diagonal 1 and 2 exercises. Conclusion: The present study suggests that a diagonal pattern of exercise is advantageous for strengthening shoulder muscles, but caution is needed when applying to patients requiring selective strengthening. Regarding both the concentric and eccentric phases of exercise, there was no significant difference in muscular activation, except in LT, between the two diagonal patterns of exercises.

• IE interfaces
• /
• v.6 no.2
• /
• pp.151-169
• /
• 1993

In this research, we proposed "coefficient of inequality" as a measure of distributional inequality for an alternative, which is defined as the area between the diagonal line from 0 to 1 and the Lorenz curve of the given alternative. Next, we showed theoretical relationship between stochastic dominance and the coefficient of inequality as a means to determine the preferred alternative when decision is made with incomplete information about decision maker's utility function. Then, two experiments were performed to test subject‘s attitude toward risk. The results of the experiments support the idea that when a decision maker is risk averse or risk prone, he/she can use the coefficient of inequality as a decision rule to choose the preferred alternative instead of using stochastic dominance. Thus, according to decision maker’s attitude toward risk, the decision rule proposed here can be used as a valuable aid in decision making under uncertainty with incomplete information.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.23 no.6
• /
• pp.703-712
• /
• 1999

This paper suggests an automatic elliptic grid generation method that is well-suited for the numerical mapping of complex geometries which are easily obtained from general CAD programs. An LBLADI solver is used for the governing mapping equations to have the strong diagonal dominance. The full boundary control method is adopted to determine the control functions of the equations, which allows the control of the grid regarding spacing and angle control at all boundary surfaces. The solution method presented here provides the capability of mapping very complicated geometries by defining grid point locations only along the boundaries. In the automated elliptic grid generation procedure, it is showed that strong diagonal dominance is essential to achieve successful mapping irrespective of the initial grid condition provided. To demonstrate the robustness of this method, it is applied to the thermal flow like the natural convection between eccentric cylinders. The results agree well with others.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.23 no.2
• /
• pp.198-209
• /
• 1999

This study reports the selection of dependent variables for momentum equations in general curvilinear coordinates. Catesian, covariant and contravariant velocity components were examined for the dependent variable. The focus of present study is confined to staggered grid system Each dependent variable selected for momentum equations are tested for several flow fields. Results show that the selection of Cartesian and covariant velocity components intrinsically can not satisfy mass conservation of control volume unless additional converting processes ore used. Also, Cartesian component can only be used for the flow field in which main-flow direction does not change significantly. Convergence rate for the selection of covariant velocity component decreases quickly as with the increase of non-orthogonality of grid system. But the selection of contravariant velocity component reduces the total mass residual of discretized equations rapidly to the limit of machine accuracy and the solutions are insensitive to the main-flow direction.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.25 no.11
• /
• pp.1500-1508
• /
• 2001

This paper represents the importance of dependent variables in non-orthogonal curvilinear coordinates just as the importance of those variables of convective scheme and turbulence model in computational fluid dynamics. Each of Cartesian, physical covariant and physical contravariant velocity components was tested as the dependent variables of momentum equations in the staggered grid system. In the flow past a circular cylinder, the results were computed to use each of three variables and compared to experimental data. In the skewed driven cavity flow, the results were computed to check the grid dependency of the variables. The results used in Cartesian and physical contravariant components of velocity in cylinder flow show the nearly same accuracy. In the case of Cartesian and contravariant component, the same number of vortex was predicted in the skewed driven cavity flow. Vortex strength of Cartesian component case has about 30% lower value than that of the other two cases.

• The Transactions of the Korean Institute of Electrical Engineers D
• /
• v.54 no.1
• /
• pp.17-25
• /
• 2005

This paper provides sufficient conditions for the robustness of Affine linear TFM(Transfer Function Matrix) MIMO (Multi-Input Multi-Output) uncertain systems based on Rosenbrock's DNA (Direct Nyquist Array). The parametric uncertainty is modeled through a Affine TFM MIMO description, and the unstructured uncertainty through a bounded perturbation of Affine polynomials. Gershgorin's theorem and concepts of diagonal dominance and GB(Gershgorin Bands) are extended to include model uncertainty. For this type of parametric robust performance we show robustness of the Affine TFM systems using Nyquist diagram and GB, DNA(Direct Nyquist Array). Multiloop PI/PB controllers can be tuned by using a modified version of the Ziegler-Nickels (ZN) relations. Simulation examples show the performance and efficiency of the proposed multiloop design method.

• Journal of Urban Science
• /
• v.7 no.1
• /
• pp.55-61
• /
• 2018

Long bridges, such as suspension bridges and diagonal bridges, are complex phenomena that show different behaviors depending on the shape and rigidity of the cross sections, such as wind vibrations and liquid vibrations from earthquakes in liquid storage containers. This is called the lower skirt on the lower side of the bridge, and the installation of lower skirt is effective for release and vortex vibrations caused by rapid winds, and that increases the stability of the wind resistance of the bridge. Optimal shape and installation of the lower skirt is also essential to make maximum wind speed effect of the lower skirt. Therefore, this study proposes a numerical analysis method to control the vibration of a bridge by calculating the optimal installation angle of an optimal lower skirt according to the optimal control theory and this study evaluates the impact on the optimal control system by minimizing the dominance equation with an evaluation function,which is an indicator for evaluating the optimal control theory state.

• Journal of Korean Society of Transportation
• /
• v.1 no.1
• /
• pp.64-81
• /
• 1983

소비자 행태에 관한 신고전 경제이론을 통행수요의 분석에 그대로 적용하는데 문제 가 되는 특기 사항으로는 운임이외에 통행시간과 같은 서어비스 질도 통행수단의 선택에 영 향을 미친다는 점과 특정 두지점간의 통행에서 동일한 소비자도 여러 수송수단을 이용한다 는 점을 들수 있다. 본 연구의 주제는 이와같은 통행수요의 독특한 특성을 반영할 수 있는 소비자의 효용최대화모형의 설정과 이 모형에서 유도된 수요함수의 구조를 분석함에 있다. 상술하면, 통행시간 가치의 불확실성 아래에서 효용을 극대화하는 의사결정문제를 Stochastic Programming 모형으로 표현하였다. 또한 이 모형에서 유도된 특성 통행수단의 수요함수는 이 수단이 가장 유리한 시간가치의 범위에 대한 부정적분으로 표현되며 이 적분 범위와 피적분함수는 모든 경쟁수단의 운임과 통행수단의 함수로 정의됨을 증명하였다. 또 한 수요함수는 통행수요에 관한 통계분석모형에서 묵시적으로 가정되고 있는 통행수단간 대 체성(Property of gross substitute)과 대각방향우세성(Property of diagonal dominance)등의 특성을 가지고 있음을 보여 주었다.