• Structural Engineering and Mechanics
• /
• 제29권5호
• /
• pp.531-550
• /
• 2008

This paper adopts the numerical assembly method (NAM) to determine the exact solutions of natural frequencies and mode shapes of a multi-span and multi-step beam carrying a number of various concentrated elements including point masses, rotary inertias, linear springs, rotational springs and springmass systems. First, the coefficient matrix for an intermediate station with various concentrated elements, cross-section change and/or pinned support and the ones for the left-end and right-end supports of a beam are derived. Next, the overall coefficient matrix for the entire beam is obtained using the numerical assembly technique of the conventional finite element method (FEM). Finally, the exact solutions for the natural frequencies of the vibrating system are determined by equating the determinant of the last overall coefficient matrix to zero and the associated mode shapes are obtained by substituting the corresponding values of integration constants into the associated eigenfunctions.

• Smart Structures and Systems
• /
• 제26권3호
• /
• pp.361-371
• /
• 2020

Exact solution for nonlinear behavior of clamped-clamped functionally graded (FG) buckled beams is presented. The effective material properties are considered to vary along the thickness direction according to exponential-law form. The in-plane inertia and damping are neglected, and hence the governing equations are reduced to a single nonlinear fourth-order partial-integral-differential equation. The von Kármán geometric nonlinearity has been considered in the formulation. Galerkin procedure is used to obtain a second order nonlinear ordinary equation with quadratic and cubic nonlinear terms. Based on the mode of the corresponding linear problem, which readily satisfy the boundary conditions, the frequencies for the nonlinear problem are obtained using the Jacobi elliptic functions. The effects of various parameters such as the Young's modulus ratio, the beam slenderness ratio, the vibration amplitude and the magnitude of axial load on the nonlinear behavior are examined.

• 대한기계학회논문집B
• /
• 제24권5호
• /
• pp.694-698
• /
• 2000

In the cylindrical coordinate, the origin r = 0 plays a role of the singularity and thus much care is needed to treat near-origin region. This work presents a new numerical scheme which is derived from the exact solution under the one-dimensional assumption in the radial direction. It is shown that the near-origin region can be properly treated by the radial-exponential scheme, whereas the numerical results from the conventional exponential scheme deviate considerably from the exact solution. Over the region of small ($ {\delta}r_e/r_e$ the present radial-exponential scheme turns out to be almost the same as the exponential scheme.

• 한국철도학회:학술대회논문집
• /
• 한국철도학회 2005년도 추계학술대회 논문집
• /
• pp.1165-1170
• /
• 2005

In order to perform the spatial buckling analysis of the curved beam element with nonsymmetric thin-walled cross section, exact static stiffness matrices are evaluated using equilibrium equations and force-deformation relations. Contrary to evaluation procedures of dynamic stiffness matrices, 14 displacement parameters are introduced when transforming the four order simultaneous differential equations to the first order differential equations and 2 displacement parameters among these displacements are integrated in advance. Thus non-homogeneous simultaneous differential equations are obtained with respect to the remaining 8 displacement parameters. For general solution of these equations, the method of undetermined parameters is applied and a generalized linear eigenvalue problem and a system of linear algebraic equations with complex matrices are solved with respect to 12 displacement parameters. Resultantly displacement functions are exactly derived and exact static stiffness matrices are determined using member force-displacement relations. The buckling loads are evaluated and compared with analytic solutions or results by ABAQUS's shell element.

• 한국전산구조공학회:학술대회논문집
• /
• 한국전산구조공학회 2002년도 봄 학술발표회 논문집
• /
• pp.43-50
• /
• 2002

Main goal of this study is to develop MATLAB programming for exact analysis of distortional deformation of the straight box girder. For this purpose, a theory for distortional deformation theory is firstly summarized and then a BEF (Beam on Elastic Foundation) theory is presented using analogy of the corresponding variables. Finally, the governing equation of the beam-column element on elastic foundation is derived. An element stiffness matrix of the beam element is established via a generalized linear eigenvalue problem. In order to verify the efficiency and accuracy of the element using exact dynamic stiffness matrix, buckling loads for the continuous beam structures with elastic foundation and distortional deformations of box girders are calculated.

• Structural Engineering and Mechanics
• /
• 제38권2호
• /
• pp.195-210
• /
• 2011

Bernoulli-Euler beam theory is used to develop an exact dynamic stiffness matrix for the flexural-torsional coupled motion of a three-dimensional, axially loaded, thin-walled beam of doubly asymmetric cross-section. This is achieved through solution of the differential equations governing the motion of the beam including warping stiffness. The uniform distribution of mass in the member is also accounted for exactly, thus necessitating the solution of a transcendental eigenvalue problem. This is accomplished using the Wittrick-Williams algorithm. Finally, examples are given to confirm the accuracy of the theory presented, together with an assessment of the effects of axial load and loading eccentricity.

• 대한전기학회논문지
• /
• 제45권2호
• /
• pp.256-264
• /
• 1996

In this paper, the decentralized suboptimal H$_{2}$ filtering problem is considered. An additional term is added to the centralized optimal H$_{2}$ filter so that the whole filter is decentralized. We derive a necessary and sufficient condition for existence of proposed decentralized filters By employing the solution procedure for the exact model matching problem, we obtain a set of decentralized H$_{2}$ filters, and choose a suboptimal filter from this set of decentralized H$_{2}$ filters.

• Journal of Electrical Engineering and Technology
• /
• 제13권5호
• /
• pp.2116-2124
• /
• 2018

Magnetic levitation system with the advantages of non-contact, no friction and no wear can satisfy the requirement of high precision and high speed positioning. In this paper, magnetic levitation positioning stage which mainly consists of planar coil and HALBACH permanent magnet array and its control and driving system are designed. Magnetic levitation system is a highly nonlinear and strongly coupled complex system and its control performance can be influenced by the uncertainty and external disturbance. So exact feedback linearization method is used to realize exact linearization and decoupling, and a strategy of sliding mode control based on disturbance observer is proposed to compensate the uncertainty and external disturbance. Detailed proofs of observer's convergence property and system stability are derived. Both the simulation and experiment results verify the effectiveness of sliding mode control algorithm based on disturbance observer.

• 한국전기전자재료학회:학술대회논문집
• /
• 한국전기전자재료학회 2000년도 추계학술대회 논문집
• /
• pp.267-270
• /
• 2000

This paper describes measurement of relative permittivity of illite found in young-dong area. A measurement of relative permittivity of illite used to cylindrical cavity resonators with moveable cap. A concentric dielectric-rod inserted cylindrical cavity resonator and an exact field representation of travelling wave mode are introduced for measurement of relative permittivity. The exact electromagnetic fields in cylindrical cavity with concentric dielectric rod is analysed. A relative permittivity of dielectric in cavity is calculated by analyzing the characteristic equation. The characteristic equation is solved by using the ContourPlot graph of Mathematica. We know that the field representation of travelling mode is exact. As a result, relative permittivity of dielectric materials were 7.820 at sample-1 and 7.894 at sample-2.

• International Journal of Aeronautical and Space Sciences
• /
• 제3권1호
• /
• pp.39-49
• /
• 2002

This paper presents a robust tracker design method that is specific to the trajectories of target aircraft. This method assumes that representative trajectories of the target aircraft are available. The exact trajectories known to the tracker enables the incorporation of the exact data in the tracker design instead of the measurement data. An estimator is designed to have acceptable performance in tracking a finite number of different target trajectories with a capability to trade off the mean and maximum errors between the exact trajectories and the estimated or predicted trajectories. Constant estimator gains that minimize the cost functions related to the estimation or prediction error are computed off-line from an iterative algorithm. This tracker design method is applied to the longitudinal motion tracking of target aircraft.