• Structural Engineering and Mechanics
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• v.35 no.2
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• pp.141-173
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• 2010

In this paper a boundary element method is developed for the general flexural-torsional buckling analysis of Timoshenko beams of arbitrarily shaped cross section. The beam is subjected to a compressive centrally applied concentrated axial load together with arbitrarily axial, transverse and torsional distributed loading, while its edges are restrained by the most general linear boundary conditions. The resulting boundary value problem, described by three coupled ordinary differential equations, is solved employing a boundary integral equation approach. All basic equations are formulated with respect to the principal shear axes coordinate system, which does not coincide with the principal bending one in a nonsymmetric cross section. To account for shear deformations, the concept of shear deformation coefficients is used. Six coupled boundary value problems are formulated with respect to the transverse displacements, to the angle of twist, to the primary warping function and to two stress functions and solved using the Analog Equation Method, a BEM based method. Several beams are analysed to illustrate the method and demonstrate its efficiency and wherever possible its accuracy. The range of applicability of the thin-walled theory and the significant influence of the boundary conditions and the shear deformation effect on the buckling load are investigated through examples with great practical interest.

• International Journal of Automotive Technology
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• v.8 no.2
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• pp.249-258
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• 2007

This paper proposes a method that can be used for the resistance estimation of a PWM (Pulse Width Modulation)-driven solenoid. By using estimated solenoid resistance, the PWM duty ratio was compensated to be proportional to the solenoid current. The proposed method was developed for use with EHB (Electro-Hydraulic Braking) systems, which are essential features of the regenerative braking system of many electric vehicles. Because the HU (Hydraulic Unit) of most EHB systems performs not only ABS/TCS/ESP (Electronic Stability Program) functions but also service braking function, the possible duration of continuous solenoid driving is so long that the generated heat can drastically change the level of solenoid resistance. The current model of the PWM-driven solenoid is further developed in this paper; from this a new resistance equation is derived. This resistance equation is solved by using an iterative method known as the FPT (fixed point theorem). Furthermore, by taking the average of the resistance estimates, it was possible to successfully eliminate the effect of measurement noise factors. Simulation results showed that the proposed method contained a sufficient pass-band in the frequency response. Experimental results also showed that adaptive solenoid driving which incorporates resistance estimations is able to maintain a linear relationship between the PWM duty ratio and the solenoid current in spite of a wide variety of ambient temperatures and continuous driving.

• Ocean Systems Engineering
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• v.12 no.1
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• pp.63-86
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• 2022

A refined projection-based purely Lagrangian meshfree method is presented towards reliable numerical analysis of fluid flow interactions with saturated/unsaturated porous media of uniform/spatially-varying porosities. The governing equations are reformulated on the basis of two-phase mixture theory with incorporation of volume fraction. These principal equations of mixture are discretized in the context of Incompressible SPH (Smoothed Particle Hydrodynamics) method. Associated with the consideration of governing equations of mixture, a new term arises in the source term of PPE (Poisson Pressure Equation), resulting in modified source term. The linear and nonlinear force terms are included in momentum equation to represent the resistance from porous media. Volume increase of fluid particles are taken into consideration on account of the presence of porous media, and hence multi-resolution ISPH framework is also incorporated. The stability and accuracy of the proposed method are thoroughly examined by reproducing several numerical examples including the interactions between fluid flow and saturated/unsaturated porous media of uniform/spatially-varying porosities. The method shows continuous pressure field, smooth variations of particle volumes and regular distributions of particles at the interface between fluid and porous media.

• Journal of the Korean earth science society
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• v.38 no.3
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• pp.173-181
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• 2017

The stability of the steady Rossby-Haurwitz wave (R-H wave) in the nondivergent barotropic model (NBM) on the sphere was investigated with the normal mode method. The linearized NBM equation with respect to the R-H wave was formulated into the eigenvalue-eigenvector problem consisting of the huge sparse matrix by expanding the variables with the spherical harmonic functions. It was shown that the definite threshold R-H wave amplitude for instability could be obtained by the normal mode method. It was revealed that some unstable modes were stationary, which tend to amplify without the time change of the spatial structure. The maximum growth rate of the most unstable mode turned out to be in almost linear proportion to the R-H wave amplitude. As a whole, the growth rate of the unstable mode was found to increase with the zonal- and total-wavenumber. The most unstable mode turned out to consist of more-than-one zonal wavenumber, and in some cases, the mode exhibited a discontinuity over the local domain of weak or vanishing flow. The normal mode method developed here could be readily extended to the basic state comprised of multiple zonalwavenumber components as far as the same total wavenumber is given.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.20 no.5
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• pp.589-597
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• 2011

In this paper, optimal tuning of a cross-coupled controller linked with the feedforward controller and the disturbance observer is studied to improve contouring and tracking accuracy as well as robustness against disturbance. Previously developed integrated design and optimal tuning methods are applied for developing the robust tuning method. Strict mathematical modeling of the multivariable system is formulated as a state-space equation. Identification processes of the servomechanism are conducted for mechanical servo models. An optimal tuning problem to minimize both the contour error and settling time is formulated as a nonlinear constrained optimization problem including the relevant controller parameters of the servo control system. Constraints such as relative stability, robust stability and overshoot, etc. are considered for the optimization. To verify the effectiveness of the proposed optimal tuning procedure, linear and circular motion experiments are performed on the xy-table. Experimental results confirm the control performance and robustness despite the variation of parameters of the mechanical subsystems.

• Ocean Systems Engineering
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• v.2 no.3
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• pp.229-238
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• 2012

We discuss the bi - stability that is possibly exhibited by a liquid free surface in a parametrically - driven two-dimensional (2D) rectangular tank with finite liquid depth. Following the method of adaptive mode ordering, assuming two dominant modes and retaining polynomial nonlinearities up to third-order, a nonlinear finite-dimensional nonlinear modal system approximation is obtained. A "continuation method" of nonlinear dynamics is then used in order to elicit efficiently the instability boundary in parameters' space and to predict how steady surface elevation changes as the frequency and/or the amplitude of excitation are varied. Results are compared against those of the linear version of the system (that is a Mathieu-type model) and furthermore, against an intermediate model also derived with formal mode ordering, that is based on a second - order ordinary differential equation having nonlinearities due to products of elevation with elevation velocity or acceleration. The investigation verifies that, in parameters space, there must be a region, inside the quiescent region, where liquid surface instability is exhibited. There, behaviour depends on initial conditions and a wave form would be realised only if the free surface was substantially disturbed initially.

• Advances in aircraft and spacecraft science
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• v.11 no.1
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• pp.55-81
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• 2024

This paper presents the exact solutions and closed forms for of nonlinear stability and vibration behaviors of straight and curved beams with nonlinear viscoelastic boundary conditions, for the first time. The mathematical formulations of the beam are expressed based on Euler-Bernoulli beam theory with the von Karman nonlinearity to include the mid-plane stretching. The classical boundary conditions are replaced by nonlinear viscoelastic boundary conditions on both sides, that are presented by three elements (i.e., linear spring, nonlinear spring, and nonlinear damper). The nonlinear integro-differential equation of buckling problem subjected to nonlinear nonhomogeneous boundary conditions is derived and exactly solved to compute nonlinear static response and critical buckling load. The vibration problem is converted to nonlinear eigenvalue problem and solved analytically to calculate the natural frequencies and to predict the corresponding mode shapes. Parametric studies are carried out to depict the effects of nonlinear boundary conditions and amplitude of initial curvature on nonlinear static response and vibration behaviors of curved beam. Numerical results show that the nonlinear boundary conditions have significant effects on the critical buckling load, nonlinear buckling response and natural frequencies of the curved beam. The proposed model can be exploited in analysis of macrosystem (airfoil, flappers and wings) and microsystem (MEMS, nanosensor and nanoactuators).

• Journal of the Korean Institute of Intelligent Systems
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• v.26 no.1
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• pp.50-55
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• 2016

This paper discusses a sampled-data controller design problem for nonlinear systems including singular perturbation. The concerned system is assumed to be modeled in Takagi--Sugeno (T--S) form. By introducing a novel Lyapunov function and an identity equation, the stability of the sampled-data closed-loop dynamics of the singularly perturbed T--S fuzzy system is analyzed. The design condition is represented in terms of linear matrix inequalities. A few discussions on the development are made that propose future research topics. Numerical simulation shows the effectiveness of the proposed method.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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• pp.583-590
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• 2002

Point collocation method based on the fast derivatives approximation of meshfree shape function is applied to solid mechanics in this study. Enhanced meshfree approximation with approximated derivative of shape function is reviewed, and formulation of linear elastic solid mechanics by point collocation method is presented. It implies that governing equation of solid mechanics with strong form is directly formulated without no numerical integration cells or grid. The regularity of weight function is not required due to a use of approximated derivative, so we propose the exponential type weight function that is discontinuous in first derivative. The convergence and stability of the proposed method is verified by passing the generalized patch test. Also, the efficiency and applicability of the proposed method in solid mechanics is verified by solving types of solid problems. Numerical results show that not only a use of proposed weight function leads lower error and higher convergence rate than that of the conventional weight functions, but also the improved collocation method with derivative approximation enables to compute the derivatives of shape function very fast and accurately enough to replace the classical direct derivative calculation.

• Nuclear Engineering and Technology
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• v.26 no.4
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• pp.536-547
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• 1994

The state feedback optimal control techniques are used in designing the reactor control system. The mathematical plant model with the temperature feedback effects is established from the one delayed neutron group point kinetics equation and the singly lumped thermal-hydraulic balance equations, and is expressed in terms of state variables. The LQR (Linear Quadratic Regulator) control system is designed, being followed by the LQG (Linear Quadratic Gaussian) design to determine the optimal conditions of rod movement for the desired reactor power responses. And two different servo control schemes, the ordinary feedback system and the order increased regulating system, are proposed for the purpose of input tacking. The general control characteristics such as stability margins and output responses are discussed. Comparing each other, it is found that the order increased regulating system has far better control characteristics than the ordinary feedback system.