• Structural Engineering and Mechanics
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• v.12 no.1
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• pp.85-100
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• 2001

In this paper, an analytical procedure for solving several static and dynamic problems of non-uniform beams is proposed. It is shown that the governing differential equations for several stability, free vibration and static problems of non-uniform beams can be written in the from of a unified self-conjugate differential equation of the second-order. There are two functions in the unified equation, unlike most previous researches dealing with this problem, one of the functions is selected as an arbitrary expression in this paper, while the other one is expressed as a functional relation with the arbitrary function. Using appropriate functional transformation, the self-conjugate equation is reduced to Bessel's equation or to other solvable ordinary differential equations for several cases that are important in engineering practice. Thus, classes of exact solutions of the self-conjugate equation for several static and dynamic problems are derived. Numerical examples demonstrate that the results calculated by the proposed method and solutions are in good agreement with the corresponding experimental data, and the proposed procedure is a simple, efficient and exact method.

• The Journal of the Korea Contents Association
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• v.2 no.4
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• pp.93-98
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• 2002

Functional equations are useful in the experimental science because they play very important role for researchers to formulate mathematical models in general terms, through some not very restrictive equations that only stipulate basic properties of functions showing in these equations, without postulating the exact forms of such functions. Of lots of such functional equations, in this paper we adopt and solve some generalized quadratic functional equation a$^2$f((x+y/a))+b$^2$f((x-y/b)) = 2f(x)+2f(y)

• Structural Engineering and Mechanics
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• v.54 no.4
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• pp.809-827
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• 2015

In this paper, seismic energy response of inelastic steel structures under earthquake excitations is investigated. For this purpose, a numerical procedure based on nonlinear dynamic analysis is developed by considering material, geometric and connection nonlinearities. Material nonlinearity is modeled by the inversion of Ramberg-Osgood equation. Nonlinearity caused by the interaction between the axial force and bending moment is also defined considering stability functions, while the geometric nonlinearity caused by axial forces is described using geometric stiffness matrix. Cyclic behaviour of steel connections is taken into account by employing independent hardening model. Dynamic equation of motion is solved by Newmark's constant acceleration method in the time history domain. Energy response analysis of space frames is performed by using this proposed numerical method. Finally, for the first time, the distribution of the different energy types versus time at the duration of the earthquake ground motion is obtained where in addition error analysis for the numerical solutions is carried out and plotted depending on the relative error calculated as a function of energy balance versus time.

• Steel and Composite Structures
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• v.48 no.2
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• pp.235-250
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• 2023

The present paper examines the stability analysis of the buckling differentiae of the small-scale, non-uniform porosity-dependent functionally graded (PD-FG) tube. The high-order beam theory and nonlocal strain gradient theory are operated for the mathematical modeling of nanotubes based on the Hamilton principle. In this paper, the external radius function is non-uniform. In contrast, the internal radius is uniform, and the cross-section changes along the tube length due to these radius functions based on the four types of useful mathematical functions. The PD-FG material distributions are varied in the radial direction and made with ceramics and metals. The governing partial differential equations (PDEs) and associated boundary conditions are solved via a numerical method for different boundary conditions. The received outcomes concerning different presented parameters are valuable to the design and production of small-scale devices and intelligent structures.

• Journal of the Korean Society of Physical Medicine
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• v.5 no.3
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• pp.413-420
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• 2010

Purpose : The purpose of this study was to demonstrate the effect of trunk stability exercise on various support base and posture on gait speed, static and dynamic balance performance. Methods : Included 17 persons with stroke who were living in the community. Trunk stability exercise program was conducted three times per week, 50 minutes per session, for 8 consecutive weeks. Subjects were tested with 10 m walking test(sec), multidirectional reach test (cm), timed get up and go test(sec) and K.A.T.3000 at both (pre and post treatment) time points. Paired t-test was used to exam mean differences between pre and post treatment by using SPSS 12.0. Results : After 8 weeks exercise program, there were significant differences in gait speed, static and dynamic balance performance(p<0.05). Conclusion : This study have shown that trunk stability exercise on various support base and posture improve physical functions(gait speed, static and dynamic balance performance).

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.89-102
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• 2010

This paper concerns the problem of global robust stability of a time-delay discontinuous system with a positive-defined connection matrix under polytopic-type uncertainty. In order to give the stability condition, we firstly address the existence of solution and equilibrium point based on the properties of M-matrix, Lyapunov-like approach and the theories of differential equations with discontinuous right-hand side as introduced by Filippov. Second, we give the delay-independent and delay-dependent stability condition in terms of linear matrix inequalities (LMIs), and based on Lyapunov function and the properties of the convex sets. One numerical example demonstrate the validity of the proposed criteria.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.10
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• pp.1207-1214
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• 1999

Many papers have recently been presented to develop energy functions for power systems. However, earlier studies adopted case-by-case approaches, which failed to give a general approach to deal with various kinds of generator models. In this paper, two useful theorems are developed regarding the integral relationships of the generator power versus its phasor current and voltage. By using the proposed theorems, an exact energy conservation law can be derived from the complex integral. The proposed energy conservation law, which is free of the generator model, can be utilized to develop energy functions for various kinds of generator models including the speed governors and exciters. An illustrative example is given for a multimachine system with the Eq' model of generator. This thesis also shows a possibility of more accurate and fast stability analysis by using the proposed Energy Conservation Law.

• Transactions of the Korean Society of Automotive Engineers
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• v.4 no.4
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• pp.87-96
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• 1996

The proportional pressure control valve(PCV) is an essential component in the open loop controlled rear wheel steering gear of the four wheel steering(4WS) system on the passenger car. The valve should have versatile functions and higher performance. But, it is hard to find the proportional pressure control valve suitable for the 4WS system. In this paper, the determination of the valve parameters was studied by the stability discrimination and the characteristic analysis for the purpose of the development of a new PCV for the 4WS. The mathematical model of the valve was derived from the valve-cylinder system and the programme for numerical computation was developed. The transfer function of the system was obtained from the mathematical model. The characteristics of the valve were inspected through the experiment and compared to those obtained by numerical method. And then the stability discrimination of the system was done by root locus and the analysis of characteristics was done by the developed programme. From the experiment and the analysis of characteristics was done by the developed programme. From the experiment and the inspection, the appropriation of mathematical model and the usefulness of the programme were confirmed. And the parameters which might affect the performance of the valve can be determined by considering the stability discrimination, the characteristics analysis and required functions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.2
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• pp.137-170
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• 2015

In this paper, we propose and analyze three viral infection models with humoral immunity including an eclipse stage of infected cells. The incidence rate of infection is represented by bilinear incidence and saturated incidence in the first and second models, respectively, while it is given by a more general function in the third one. The neutralization rate of viruses is giv0en by bilinear form in the first two models, while it is given by a general function in the third one. For each model, we have derived two threshold parameters, the basic infection reproduction number which determines whether or not a chronic-infection can be established without humoral immunity and the humoral immune response activation number which determines whether or not a chronic-infection can be established with humoral immunity. By constructing suitable Lyapunov functions we have proven the global asymptotic stability of all equilibria of the models. For the third model, we have established a set of conditions on the threshold parameters and on the general functions which are sufficient for the global stability of the equilibria of the model. We have performed some numerical simulations for the third model with specific forms of the incidence and neutralization rates and have shown that the numerical results are consistent with the theoretical results.

• Journal of the Korean GEO-environmental Society
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• v.16 no.5
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• pp.13-25
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• 2015

This paper proposes an extended model evaluation method that considers not only the model performance but also the model structure and parameter uncertainties in hydrologic modeling. A simple reservoir model (SFM) and distributed kinematic wave models (KWMSS1 and KWMSS2 using topography from 250-m, 500-m, and 1-km digital elevation models) were developed and assessed by three evaluative criteria for model performance, model structural stability, and parameter identifiability. All the models provided acceptable performance in terms of a global response, but the simpler SFM and KWMSS1 could not accurately represent the local behaviors of hydrographs. Moreover, SFM and KWMSS1 were structurally unstable; their performance was sensitive to the applied objective functions. On the other hand, the most sophisticated model, KWMSS2, performed well, satisfying both global and local behaviors. KMSS2 also showed good structural stability, reproducing hydrographs regardless of the applied objective functions; however, superior parameter identifiability was not guaranteed. A number of parameter sets could result in indistinguishable hydrographs. This result indicates that while making hydrologic models complex increases its performance accuracy and reduces its structural uncertainty, the model is likely to suffer from parameter uncertainty.