• 제어로봇시스템학회:학술대회논문집
• /
• 1990.10a
• /
• pp.446-450
• /
• 1990

In this paper, we present a method of analysing perturbed linear system by pole sensitivity defined by the rate of pole movement with respect of perturbation. Pole sensitivity give us not only the rate of pole movement but also the directional information of the pole movement. We present a method of design of a LQR by considering the pole sensitivity and show that the suggested method guarantee the stability robustness of parameter perturbation.

• Structural Engineering and Mechanics
• /
• v.27 no.1
• /
• pp.17-32
• /
• 2007

The main source of transverse vibration of a conveyor belt is frictional contact between pulley and belt. Also, environmental characteristics such as natural dampers and springs affect natural frequencies, stability and bifurcation points of system. These phenomena can be modeled by a small velocity fluctuation about mean velocity. Also, viscoelastic foundation can be modeled as the dampers and springs with continuous characteristics. In this study, non-linear vibration of a conveyor belt supported partially by a distributed viscoelastic foundation is investigated. Perturbation method is applied to obtain a closed form analytic solutions. Finally, numerical simulations are presented to show stiffness, damping coefficient, foundation length, non-linearity and mean velocity effects on location of bifurcation points, natural frequencies and stability of solutions.

• KSTLE International Journal
• /
• v.10 no.1_2
• /
• pp.6-12
• /
• 2009

In this study, the effect of oil supply conditions on the dynamic performance of a hydrodynamic journal bearing is analyzed numerically. Axial length, circumferential length and location of oil grooves are considered as oil supply conditions. The perturbation equations of the perturbed film contents are obtained by applying Elrod's universal equation implementing JFO film rupture / reformation boundary conditions to Lund's infinitesimal perturbation method. The dynamic coefficients of a hydrodynamic journal bearing are calculated by solving the perturbation equations, and the linear stability analysis is carried out by using those for a variety of oil supply conditions.

• Kyungpook Mathematical Journal
• /
• v.25 no.2
• /
• pp.127-130
• /
• 1985

• Structural Engineering and Mechanics
• /
• v.44 no.3
• /
• pp.405-416
• /
• 2012

In this study the investigation of large deflections subject in compliant mechanisms is presented using homotopy perturbation method (HPM). The main purpose is to propose a convenient method of solution for the large deflection problem in compliant mechanisms in order to overcome the difficulty and complexity of conventional methods, as well as for the purpose of mathematical modeling and optimization. For simplicity, a cantilever beam of linear elastic material under horizontal, vertical and bending moment end point load is considered. The results show that the applied method is very accurate and capable for cantilever beams and can be used for a large category of practical problems for the aim of optimization. Also the consequence of effective parameters on the large deflection is analyzed and presented.

• Structural Engineering and Mechanics
• /
• v.82 no.2
• /
• pp.191-204
• /
• 2022

A three-mass vehicle model including one rigid mass and two unsprung masses is adopted to predict the vehicle-bridge interaction (VBI) and to establish the nonlinear coupled governing equations. To overcome the numerical instability and large computation problems concerning the vehicle-bridge system, the perturbation method is used to convert the nonlinear coupled governing equations into a set of linear uncoupled equations. Formulas for bridge's natural frequencies considering both the VBI and the dynamic responses of bridge and vehicle are proposed. Compared with the numerical results obtained by the Newmark-β method, the theoretical solutions for natural frequencies and dynamic responses are validated. The effects of the important factors of unsprung mass, vehicle damping, surface irregularity on the natural frequencies and dynamic responses of bridge and vehicle are discussed, based on the theoretical solutions.

• Steel and Composite Structures
• /
• v.24 no.2
• /
• pp.141-149
• /
• 2017

In this study, vibration analysis of fluid conveying microbeams under non-ideal boundary conditions (BCs) is performed. The objective of the present paper is to describe the effects of non-ideal BCs on linear vibrations of fluid conveying microbeams. Non-ideal BCs are modeled as a linear combination of ideal clamped and ideal simply supported boundary conditions by using the weighting factor (k). Non-ideal clamped and non-ideal simply supported beams are both considered to show the effects of BCs. Equations of motion of the beam under the effect of moving fluid are obtained by using Hamilton principle. Method of multiple scales which is one of the perturbation techniques is applied to the governing linear equation of motion. Approximate solutions of the linear equation are obtained and the effects of system parameters and non-ideal BCs on natural frequencies are presented. Results indicate that, natural frequencies of fluid conveying microbeam changed significantly by varying the weighting factor k. This change is more remarkable for clamped microbeams rather than simply supported ones.

• Honam Mathematical Journal
• /
• v.43 no.4
• /
• pp.679-689
• /
• 2021

The first author suggested an exact volume formula of the hypercubes [0, 1]ⁿ clipped by several hyperplanes expressed directly in terms of linear coefficients of the hyperplanes. However, it requires awkward assumptions to apply the formula to various situations. We suggest a concrete method to overcome those restrictions for two or three hyperplanes using 𝜖-perturbation, which gives an exact value applicable for any kind of arrangement of hyperplanes with no consideration.

• Earthquakes and Structures
• /
• v.9 no.1
• /
• pp.221-232
• /
• 2015

In this study, Homotopy Perturbation Method (HPM) is used to solve the nonlinear oscillators with damping. We have considered two strong nonlinear equations to show the application of the method. The Runge-Kutta's algorithm is used to obtain the numerical solution for the problems. The method works very well for the whole range of initial amplitudes and does not demand small perturbation and also sufficiently accurate to both linear and nonlinear physics and engineering problems. Finally to show the accuracy of the HPM, the results have been shown graphically and compared with the numerical solution.

• Nuclear Engineering and Technology
• /
• v.21 no.2
• /
• pp.99-110
• /
• 1989

The optimal control of xenon concentration in a nuclear reactor is posed as a linear quadratic regulator problem with state feedback control. Since it is not possible to measure the state variables such as xenon and iodine concentrations directly, implementation of the optimal state feedback control law requires estimation of the unmeasurable state variables. The estimation method used is based on the Luenberger observer. The set of the reactor kinetics equations is a stiff system. This singularly perturbed system arises from the interaction of slow dynamic modes (iodine and xenon concentrations) and fast dynamic modes (neutron flux, fuel and coolant temperatures). The singular perturbation technique is used to overcome this stiffness problem. The observer-based controller of the original system is effected by separate design of the observer and controller of the reduced subsystem and the fast subsystem. In particular, since in the reactor kinetics control problem analyzed in the study the fast mode dies out quickly, we need only design the observer for the reduced slow subsystem. The results of the test problems demonstrated that the state feedback control of the xenon oscillation can be accomplished efficiently and without sacrificing accuracy by using the observer combined with the singular perturbation method.