• The Journal of the Acoustical Society of Korea
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• v.20 no.4
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• pp.54-61
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• 2001

Magnetostrictive materials have nonlinear elasto-magnetic properties. However the constitutive equations to describe the nonlinear properties are not available, yet. In this study we develope the equation in magnetostrictive materials by use of piezomagnetic constitutive equation which is quasi-linearized. With the wave equation, we determine the propagation velocity inside the magnetostrictive materials when a plane wave propagates along a given magnetic field. Validity of the calculated velocity is verified through comparison with experimental velocity measurement results for the most representative magnetostrictive materials. Terfenol-D.

• Journal of the Korean Mathematical Society
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• v.61 no.4
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• pp.621-657
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• 2024

In this study, the numerical solution of a space-fractional Burgers' equation with initial and boundary conditions is considered. This equation is the simplest nonlinear model for diffusive waves in fluid dynamics. It occurs in a variety of physical phenomena, including viscous sound waves, waves in fluid-filled viscous elastic pipes, magneto-hydrodynamic waves in a medium with finite electrical conductivity, and one-dimensional turbulence. The proposed QBS/CNG technique consists of the Galerkin method with a function basis of quadratic B-splines for the spatial discretization of the space-fractional Burgers' equation. This is then followed by the Crank-Nicolson approach for time-stepping. A linearized scheme is fully constructed to reduce computational costs. Stability analysis, error estimates, and convergence rates are studied. Finally, some test problems are used to confirm the theoretical results and the proposed method's effectiveness, with the results displayed in tables, 2D, and 3D graphs.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.6
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• pp.907-917
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• 1997

The purpose of this study is to design an anti-sway motion for industrial overhead cranes which transport objects on a horizontal plane by adjusting movements of a trolley motor and a girder motor. The movement of a hoist motor has not been considered at this time since its role was assumed to move objects only vertically, therefore, not to affect the swing motion of objects. The dynamic behavior of the swing motion shows nonlinear characteristics, which makes the design of anti-sway motion controller difficult. First of all, the nonlinear state equation for the motion of industrial overhead cranes has been derived. Then they have been linearized about normal operating states determined by the dynamic characteristics of motor motion-acceleration, constant speed, and deceleration, and deceleration, during transportation. The partial state feedback control algorithm based on this linearized state equation has been developed on order to suppress the swing motion. The simulation results have demonstrated satisfactory performance of the proposed controller.

• Journal of Advanced Navigation Technology
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• v.4 no.1
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• pp.45-49
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• 2000

A GPS measurement solution, in general, is obtained as a least squares solution since the measurement includes errors such as clock errors, ionospheric and tropospheric delays, multipath effect etc. Because of the nonlinearity of the measurement equation, we utilize the nonlinear Newton algorithm to obtain a least squares solution, or mostly, use its linearized algorithm which is more convenient and effective. In this study we developed a fixed point algorithm and proved its availability to replace the nonlinear Newton algorithm and the linearized algorithm. A nonlinear Newton algorithm and a linearized algorithm have the advantage of fast convergence, while their initial values have to be near the unknown solution. On the contrary, the fixed point algorithm provides more reliable but slower convergence even if the initial values are quite far from the solution. Therefore, two types of algorithms may be combined to achieve better performance.

• Proceedings of the KIEE Conference
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• 2000.11d
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• pp.765-768
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• 2000

Linearization of the biped dynamic equations and design of linear controller for the linearized equations are studied in this paper. The biped robot with inverted pendulum type trunk, used to stabilize the dynamic balancing of the biped robot during dynamic walking period, is modelled with 14 DOF and simulated. Despite of well defined linear control theories so far, the linear control methods was limited to the applications for a walking robot, because they have been inherently strong nonlinear properties, such as a modeling parameter uncertainties, external forces as noise, inertial and Coriolis terms by three dimensional modeling and so on. To linearize the nonlinear equations of motion of biped robot on MIMO and time varying linear equations of motion, 1st order Taylor series is used to formulate the linear equation. And a 2nd order numerical perturbation method Is used to approximate partial differential equations. Using the linearized equations of motion, a linear controller is designed by pole placement method with feed forward compensation. Using the obtained linearized equations and linear controller, the continuous walking simulation is performed.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.281-295
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• 2005

The purpose of this paper is to study a class of delay differential equations with two delays. First, we consider the existence of periodic solutions for some delay differential equations. Second, we investigate the local stability of the zero solution of the equation by analyzing the corresponding characteristic equation of the linearized equation. The exponential stability of a perturbed delay differential system with a bounded lag is studied. Finally, by choosing one of the delays as a bifurcation parameter, we show that the equation exhibits Hopf and saddle-node bifurcations.

• The Journal of the Acoustical Society of Korea
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• v.17 no.4E
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• pp.3-10
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• 1998

This paper concerns the dynamical behavior, in probabilistic sense, of a feedforward neural network performing auto association for novelty. Networks of retinotopic topology having a one-to-one correspondence between and output units can be readily trained using back-propagation algorithm, to perform autoassociative mappings. A novelty filter is obtained by subtracting the network output from the input vector. Then the presentation of a "familiar" pattern tends to evoke a null response ; but any anomalous component is enhanced. Such a behavior exhibits a promising feature for enhancement of weak signals in additive noise. As an analysis of the novelty filtering, this paper shows that the probability density function of the weigh converges to Gaussian when the input time series is statistically characterized by nonsymmetrical probability density functions. After output units are locally linearized, the recursive relation for updating the weight of the neural network is converted into a first-order random differential equation. Based on this equation it is shown that the probability density function of the weight satisfies the Fokker-Planck equation. By solving the Fokker-Planck equation, it is found that the weight is Gaussian distributed with time dependent mean and variance.

• Journal of the Korean Chemical Society
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• v.40 no.6
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• pp.409-414
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• 1996

The limit of applicability of Navier-Stokes equation to stationary plane shock-waves is examined by using the principle of minimum entropy production of linear irreversible thermodynamics. In order to obtain analytic results, the equation is linearized near the equilibrium of downstream. Results show that the solution of Navier-Stokes equation which fits the boundary condition of far downstream flow is consistent with the thermodynamic requirement within the first order when the solution is expanded around the M=1, where M is the Mach number of upstream speed.

• International Journal of Automotive Technology
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• v.6 no.4
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• pp.375-381
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• 2005

This paper presents linear algebraic equations in the form of recursive formula to compute elastokinematic characteristics of a suspension system. Conventional methods of elastokinematic analysis are based on nonlinear kinematic constrant equations and force equilibrium equations for constrained mechanical systems, which require complicated and time-consuming implicit computing methods to obtain the solution. The proposed linearized elastokinematic equations in the form of recursive formula are derived based on the assumption that the displacements of elastokinematic behavior of a constrained mechanical system under external forces are very small. The equations can be easily computerized in codes, and have the advantage of sharing the input data of existing general multi body dynamic analysis codes. The equations can be applied to any form of suspension once the type of kinematic joints and elastic components are identified. The validity of the method has been proved through the comparison of the results from established elastokinematic analysis software. Error estimation and analysis due to piecewise linear assumption are also discussed.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1087-1094
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• 2016

On a compact n-dimensional manifold M, it has been conjectured that a critical point of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of unit volume, is Einstein. In this paper, after derivng an interesting curvature identity, we show that the conjecture is true in dimension three and four when g is weakly Einstein. In higher dimensional case $n{\geq}5$, we also show that the conjecture is true under an additional Ricci curvature bound. Moreover, we prove that the manifold is isometric to a standard n-sphere when it is n-dimensional weakly Einstein and the kernel of the linearized scalar curvature operator is nontrivial.