• Journal of Mechanical Science and Technology
• /
• 제15권10호
• /
• pp.1356-1368
• /
• 2001

In this paper, the model reference adaptive control (MRAC) of a flexible structure is investigated. Any mechanically flexible structure is inherently distributed parameter in nature, so that its dynamics are described by a partial, rather than ordinary, differential equation. The MRAC problem is formulated as an initial value problem of coupled partial and ordinary differential equations in weak form. The well-posedness of the initial value problem is proved. The control law is derived by using the Lyapunov redesign method on an infinite dimensional filbert space. Uniform asymptotic stability of the closed loop system is established, and asymptotic tracking, i. e., convergence of the state-error to zero, is obtained. With an additional persistence of excitation condition for the reference model, parameter-error convergence to zero is also shown. Numerical simulations are provided.

• International Journal of Precision Engineering and Manufacturing
• /
• 제3권4호
• /
• pp.87-93
• /
• 2002

In this study, basic concepts of magnet were introduced, and dynamic characteristics of magnet coupling were explored. Based on these characteristics, it was proposed how to analyze transverse and torsional vibrations of a spindle system with magnet coupling. Proposed theoretical approaches were applied to a precision power transmission system machined for this study, and the transverse and torsional vibrations were simulated. The force on magnet coupling was shown as a form of nonlinear function of the gap and the eccentricity. Also, the form of torque transmitted by magnet coupling was considered as a sinusoidal function. Main spindle connected to a coupling of a follower part was assumed to be a rigid body. Nonlinear partial differential equation was derived to be as a function of angular displacement. By using the equation, torsional vibration analysis of a spindle system with magnet coupling was performed. Free and forced vibration analyses of a spindle system with magnetic coupling were explored by using FEM.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 1989년도 하계종합학술대회 논문집
• /
• pp.552-556
• /
• 1989

The line equations can be expressed by a set of nonhomogeneous differential equation where forcing terms of these equations have been adopted. Equivalent-circuit representations of this paper are derived from solutions of the equations. The contribution of the external wave to the line is expressed in terms of ideal sources in the form of a cascade connection to the line. These representations art conveniently applicable to the various types of transmission lines because these Lines can often be written in the form of a chain matrix.

• 대한전기학회논문지
• /
• 제45권3호
• /
• pp.399-406
• /
• 1996

This paper presents a method of hierarchical state estimation of the time-varying linear systems via Block-pulse function(BPF). When we estimate the state of the systems where noise is considered, it is very difficult to obtain the solutions because minimum error variance matrix having a form of matrix nonlinear differential equations is included in the filter gain calculation. Therefore, hierarchical approach is adapted to transpose matrix nonlinear differential equations to a sum of low order state space equation from and Block-pulse functions are used for solving each low order state space equation in the form of simple and recursive algebraic equation. We believe that presented methods are very attractive nd proper for state estimation of time-varying linear systems on account of its simplicity and computational convenience. (author). 13 refs., 10 figs.

• Interaction and multiscale mechanics
• /
• 제1권3호
• /
• pp.329-337
• /
• 2008

This paper presents the derivation of the generalized governing equations in theory of elasticity, their weak forms and the some applications in the numerical analysis of structural mechanics. Unlike the differential equations in classical elasticity theory, the generalized equations of the equilibrium and compatibility equations presented here take the form of integral equations, and the generalized equilibrium equations contain the classical differential equations and the boundary conditions in a single equation. By using appropriate test functions, the weak forms of these generalized governing equations can be established. It can be shown that various variational principles in structural analysis are merely the special cases of these weak forms of generalized governing equations in elasticity. The present weak forms of elasticity equations extend greatly the choices of the trial functions for approximate solutions in the numerical analysis of various engineering problems. Therefore, the weak forms of generalized governing equations in elasticity provide a powerful modeling tool in the computational structural mechanics.

• Structural Engineering and Mechanics
• /
• 제14권1호
• /
• pp.71-84
• /
• 2002

A finite element formulation for the time-domain analysis of linear transient elastodynamic problems is presented based on the weak form obtained by applying the Galerkin's method to the integro-differential equations which contain the initial conditions implicitly and does not include the inertia terms. The weak form is extended temporally under the assumptions of the constant and linear time variations of field variables, since the time-stepping algorithms such as the Newmark method and the Wilson ${\theta}$-method are not necessary, obtaining two kinds of implicit finite element equations which are tested for numerical accuracy and convergency. Three classical examples having finite and infinite domains are solved and numerical results are compared with the other analytical and numerical solutions to show the versatility and accuracy of the presented formulation.

• Coupled systems mechanics
• /
• 제12권4호
• /
• pp.337-364
• /
• 2023

The Rayleigh wave propagation is considered in the structure of the functionally graded piezoelectric material (FGPM) layer over the elastic substrate. The elastic substrate loosely bonds the layer through a corrugated interface, whereas its upper boundary is also corrugated but stress-free. Additionally, the solutions for the FGPM layer and substrate are derived using the fundamental variable separable approach to convert the partial differential equation to an ordinary differential equation. The results with boundary conditions lead to dispersion relations for the electrically open and electrically short cases in the determinant form. The outcomes have been numerically analyzed using a specific model. The findings were presented in the form of graphs, which were created using Mathematica 7. Graphs are plotted for variations in wavenumber and phase velocity. The outcomes may help measure interface defects and design Surface Acoustic Wave (SAW) devices.

• 대한본초학회지
• /
• 제29권4호
• /
• pp.61-67
• /
• 2014

Objectives : To present a differential standard of Armeniacae Semen and Persicae Semen that are easily confused. Methods : It was planed a differential standard form through outer appearance of the original plant, outer appearance in the form of each medicines and the appearance of the interior form through a microscope for each samples. Using an standard compound amygdalin, each samples have been analyzed by HPLC and TLC. Results : It was possible to distinguish the orignal plant between Armeniacae Semen and Persicae Semen through its leaf shape and calyx type. In Outer appearance in the form of each medicines, there was no difference pre-existing method(measuring length and width). In vascular pattern of the surface, however, there was a clear difference that Armeniacae Semen was developed more reticulated branches than Persicae Semen. In appearance through a microscope, it has not been possible to find a clear difference in the per original plant. However, there was a clear difference between Armeniacae Semen(1 layer) and Persicae Semen(3 layer) in inner albubemen cell. In TLC analysis, there was no difference in the pattern between samples. But in HPLC analysis, Armeniacae Semen showed amygdalin content higher on average. Conclusions : It will be possible to find various differences in the outer appearance of the original plant, the outer appearance in the form of each medicines, the appearance of the interior form through a microscope and physical and chemical research component.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제15권1호
• /
• pp.57-72
• /
• 2008

This paper is concerned with the numerical solutions to steady state nonlinear elliptical partial differential equations (PDE) of the form $u_{xx}+u_{yy}+Du_{x}+Eu_{y}+Fu=G$, where D, E, F are functions of x, y, u, $u_{x}$, and $u_{y}$, and G is a function of x and y. Dirichlet boundary conditions in a rectangular region are considered. We propose alternating direction shooting method for solving such nonlinear PDE. Numerical results show that the alternating direction shooting method performed better than the commonly used linearized iterative method.

• 대한수학회논문집
• /
• 제12권3호
• /
• pp.645-653
• /
• 1997

We study centrally symmetric orthogonal polynomials satisfying an admissible partial differential equation of the form $$ Au_{xx} + 2Bu_{xy} + Cu_{yy} + Du_x + Eu_y = \lambda_n y, $$ where $A, B, \cdots, E$ are polynomials independent of n and $\lambda_n$ is the eignevalue parameter depending on n. We show that they are either the product of Hermite polymials or the circle polynomials up to a complex linear change of variables. Also we give some properties of them.