• Earthquakes and Structures
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• v.5 no.3
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• pp.359-378
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• 2013

The problem of identification of multi-component and (or) spatially varying earthquake support motions based on measured responses in instrumented structures is considered. The governing equations of motion are cast in the state space form and a time domain solution to the input identification problem is developed based on the Kalman and particle filtering methods. The method allows for noise in measured responses, imperfections in mathematical model for the structure, and possible nonlinear behavior of the structure. The unknown support motions are treated as hypothetical additional system states and a prior model for these motions are taken to be given in terms of white noise processes. For linear systems, the solution is developed within the Kalman filtering framework while, for nonlinear systems, the Monte Carlo simulation based particle filtering tools are employed. In the latter case, the question of controlling sampling variance based on the idea of Rao-Blackwellization is also explored. Illustrative examples include identification of multi-component and spatially varying support motions in linear/nonlinear structures.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10b
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• pp.100-104
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• 1993

In Part 1, we derived robust stability conditions for an LTI interconnected to time-varying nonlinear perturbations belonging to several classes of nonlinearities. These conditions were presented in terms of positive definite solutions to LMI. In this paper we address a problem of synthesizing feedback controllers for linear time-invariant systems under structured time-varying uncertainties, combined with a worst-case H$_{2}$ performance. This problem is introduced in [7, 8, 15, 35] in case of time-invariant uncertainties, where the necessary conditions involve highly coupled linear and nonlinear matrix equations. Such coupled equations are in general difficult to solve. A convex optimization approach will be employed in this synthesis problem in order to avoid solving highly coupled nonlinear matrix equations that commonly arises in multiobjective synthesis problem. Using LMI formulation, this convex optimization problem can in turn be cast as generalized eigenvalue minimization problem, where an attractive algorithm based on the method of centers has been recently introduced to find its solution [30, 361. In the present paper we will restrict our discussion to state feedback case with Popov multipliers. A more general case of output feedback and other types of multipliers will be addressed in a future paper.

• Smart Structures and Systems
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• v.19 no.2
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• pp.213-224
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• 2017

The electromagnetic field can cause an essential change of the dynamic behavior of the railgun. The evaluation of the dynamics performance of railgun is a mandatory task. Here, a nonlinear electromagnetic force equation of the railgun is given in which the clearance, the thickness and the width of the rail are considered. Based on it, the nonlinear electromechanical coupled dynamics equations of Euler beam rails for the railgun are proposed. Using the equations, the nonlinear free vibration frequency of the railgun is investigated and the effects of the system parameters on the frequency are analyzed. The nonlinear forced responses of the rail to the electromagnetic excitation are investigated as well. The results show that as the nonlinearity of the railgun system is considered, the vibration frequencies of the railgun system increase; as the current in the rail increases, the difference between the natural frequencies and the nonlinear vibration frequencies increases significantly; the nonlinearity of the railgun system is more obvious for smaller distance between the two rails, smaller rail thickness, and smaller stiffness of the elastic foundation; the unstable dynamics state of the rail system occurs when the armature runs to the exit of the railgun. The results are useful for design and application of the railgun system.

• Journal of Advanced Research in Ocean Engineering
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• v.1 no.1
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• pp.14-24
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• 2015

A three-dimensional multidirectional nonlinear numerical wave tank (NWT) based on the Navier-Stokes equations and the Finite Volume Method (FVM) is developed by using the two-phase hydrodynamic flow solver naoe-FOAM-SJTU based on the open source toolbox OpenFOAM. The free surface is capturing with the Volume Of Fluids (VOF). The directional wave including Stokes wave, solitary wave and nonlinear wave are simulated and verified. The multi-directional waves are also simulated with particular wave spectral such as JONSWAP and wave directional spreading function. The obtained numerical results show the capability of the solver to generate different type of multidirectional nonlinear waves accurately. Meanwhile, it implies that the presented NWT can easily extend to model the wave-structures interactions, which will be great help to the offshore structures design.

• International Journal of Ocean System Engineering
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• v.4 no.1
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• pp.49-56
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• 2014

A three-dimensional multidirectional nonlinear numerical wave tank (NWT) based on the Navier-Stokes equations and the Finite Volume Method (FVM) is developed by using the two-phase hydrodynamic flow solver naoe-FOAM-SJTU based on the open source toolbox OpenFOAM. The free surface is capturing with the Volume Of Fluids (VOF). The directional wave including Stokes wave, solitary wave and nonlinear wave are simulated and verified. The multi-directional waves are also simulated with particular wave spectral such as JONSWAP and wave directional spreading function. The obtained numerical results show the capability of the solver to generate different type of multidirectional nonlinear waves accurately. Meanwhile, it implies that the presented NWT can easily extend to model the wave-structures interactions, which will be great help to the offshore structures design.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.412-415
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• 1995

Previously obtained results of L$_{2}$-gain and H$_{\infty}$ control via state feedback of nonlinear systems are extended to a class of nonlinear system with uncertainties. The required information about the uncertainties is that the uncertainties are bounded in Euclidian norm by known functions of the system state. The conditions are characterized in terms of the corresponding Hamilton-Jacobi equations or inequalities (HJEI). An algorithm for finding an approximate local solution of Hamilton-Jacobi equation is given. This results and algorithm are illustrated on a numerical example..

• Proceedings of the KIEE Conference
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• 1996.07b
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• pp.959-961
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• 1996

In this paper, we study the modeling and control of Electro-Magnetic Suspension System with 2 Degree Of Freedom. While the previous researchers considered the control of single rail EMS Systems, we consider the control of two rail EMS Systems. We first derive a simple model to represent the dynamics of EMS System with 2 D.O.F., using the Lagrange's method. The nonlinear equations of motion that we derive are shown to be linearizable by coordinate change and nonlinear static state feedback. The nonlinear static state feedback controller is constructed explicitly.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.983-986
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• 2005

Free vibration characteristics of a curved pipe conveying fluid is studied when the pipe is clamped at both ends. Using the perturbation method, the non-linear governing equations divided into two parts; the steady state non-linear equilibrium equations and the linearized equations of motion in the neighborhood of the equilibrium position. The natural frequencies are computed from the linearized equations of motion. In this study, the equilibrium positions are determined by two types of equations, i.e., (1) the non-linear equations, and (2) the equations obtained by neglecting the non-linear terms. The natural frequencies obtained from the non-linear equilibrium equations are compared to those obtained from the linearized equilibrium equations. From the results, as the fluid velocity increases, the equilibrium position should be determined from the nonlinear equations for the vibration analysis of the curved pipe conveying fluid.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.12
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• pp.1152-1162
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• 2008

This paper deals with the State-Dependent Riccati Equation (SDRE) technique for the design of helicopter nonlinear flight controllers. Since the SDRE controller requires a linear system-like structure for nonlinear motion equations, a state-dependent coefficient (SDC) factorization technique is developed in order to derive the conforming structure from a general nonlinear helicopter dynamic model. Also on-line numerical methods of solving the algebraic Riccati equation are investigated to improve the numerical efficiency in designing the SDRE controllers. The proposed method is applied to trajectory tracking problems of the helicopter and computational tips for a real time application are proposed using a high fidelity rotorcraft mathematical model.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.2
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• pp.25-37
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• 2001

We consider the finite element method applied to nonlinear Sobolev equation with smooth data and demonstrate for arbitrary order ($k{\geq}2$) finite element spaces the optimal rate of convergence in $L_{\infty}\;W^{1,{\infty}}({\Omega})$ and $L_{\infty}(L_{\infty}({\Omega}))$ (quasi-optimal for k = 1). In other words, the nonlinear Sobolev equation can be approximated equally well as its linear counterpart. Furthermore, we also obtain superconvergence results in $L_{\infty}(W^{1,{\infty}}({\Omega}))$ for the difference between the approximate solution and the generalized elliptic projection of the exact solution.