• Title/Summary/Keyword: Nonlinear state equations

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Harmonic State Space Modeling of DC Microgrid Systems (직류 마이크로그리드 시스템의 고조파 상태 공간 모델링)

  • Kamalirad, Mohsen;To, Dinh Du;Lee, Dong-Choon
    • Proceedings of the KIPE Conference
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    • 2019.07a
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    • pp.483-484
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    • 2019
  • This paper proposes a harmonic state space (HSS) modeling of DC microgrid. In the HSS model, nonlinear equations for the switched circuit model are transformed into multiple linear equations. The simulation results have shown the HSS modeling is comparable with PSIM simulation.

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A Study on the Steady-State Cornering of a Vehicle Considering Roll Motion (롤 운동을 고려한 차량의 정상상태 선회주행에 관한 연구)

  • 이장무;윤중락;강주석;배상우;탁태오
    • Transactions of the Korean Society of Automotive Engineers
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    • v.5 no.6
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    • pp.89-102
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    • 1997
  • In this study, the steady state cornering behavior of a vehicle is investigated by using a numerical model that has parameters associated with roll motion. The nonlinear characteristics of tire cornering forces and aligning torques are presented in analytical forms using the magic formula. The sets of nonlinear algebraic equations that govern the cornering motion are solved by the Newton-Raphson iteration method. The vehicle design parameters are measured by SPMD(Suspension Parameter Measuring Device), and its results are verified by carrying out a skid pad test. The design parameters that are most affecting the steady state cornering behavior are classified into four factors, and the contributions of the factors to understeer gradient are then calculated.

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ACCURACY AND EFFICIENCY OF A COUPLED NEUTRONICS AND THERMAL HYDRAULICS MODEL

  • Pope, Michael A.;Mousseau, Vincent A.
    • Nuclear Engineering and Technology
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    • v.41 no.7
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    • pp.885-892
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    • 2009
  • This manuscript will discuss a numerical method where the six equations of two-phase flow, the solid heat conduction equations, and the two equations that describe neutron diffusion and precursor concentration are solved together in a tightly coupled, nonlinear fashion for a simplified model of a nuclear reactor core. This approach has two important advantages. The first advantage is a higher level of accuracy. Because the equations are solved together in a single nonlinear system, the solution is more accurate than the traditional "operator split" approach where the two-phase flow equations are solved first, the heat conduction is solved second and the neutron diffusion is solved third, limiting the temporal accuracy to $1^{st}$ order because the nonlinear coupling between the physics is handled explicitly. The second advantage of the method described in this manuscript is that the time step control in the fully implicit system can be based on the timescale of the solution rather than a stability-based time step restriction like the material Courant limit required of operator-split methods. In this work, a pilot code was used which employs this tightly coupled, fully implicit method to simulate a reactor core. Results are presented from a simulated control rod movement which show $2^{nd}$ order accuracy in time. Also described in this paper is a simulated rod ejection demonstrating how the fastest timescale of the problem can change between the state variables of neutronics, conduction and two-phase flow during the course of a transient.

Topology Design Optimization of Nonlinear Thermoelasticity Problems (비선형 열탄성 연성 구조물에 대한 위상 최적설계)

  • 문세준;하윤도;조선호
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2004.10a
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    • pp.347-354
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    • 2004
  • Using an efficient adjoint variable method, we develop a unified design sensitivity analysis (DSA) method considering both steady state nonlinear heat conduction and geometrical nonlinear elasticity problems. Design sensitivity expressions with respect to thermal conductivity and Young's modulus are derived. Beside the temperature and displacement adjoint equations, another coupled one is defined regarding the obtained adjoint displacement field as the adjoint load in temperature field. The developed DSA method is shown to be very efficient and further extended to a topology design optimization method for the nonlinear weakly coupled thermo-elasticity problems using a density approach.

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A Study on the Deadbeat Response Attribute of Nonlinear Systems (비선형시스템의 데드비트응답 특성 연구)

  • Song, Ja-Youn
    • Proceedings of the KIEE Conference
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    • 2001.07d
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    • pp.1993-1995
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    • 2001
  • The subject of nonlinear control is an important area of automatic control. The behavior of nonlinear systems is much more complex. If the operating range of a control system is small, and if the involved nonlinearities are smooth, then the control system may be resonably approximated by a set of linear differential equations. This paper presents the deadbeat response attribute of some nonlinear systems, e.g., magnetic levitation, pendulum, van der pol oscillator etc.. The studied results through the computer simulation are shown a promising attribute of deadbeat response that the outputs of the systems are reached relatively fast the steady state.

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Nonlinear bending of functionally graded porous nanobeam subjected to multiple physical load based on nonlocal strain gradient theory

  • Gao, Yang;Xiao, Wan-shen;Zhu, Haiping
    • Steel and Composite Structures
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    • v.31 no.5
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    • pp.469-488
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    • 2019
  • We in this paper study nonlinear bending of a functionally graded porous nanobeam subjected to multiple physical load based on the nonlocal strain gradient theory. For more reasonable analysis of nanobeams made of porous functionally graded magneto-thermo-electro-elastic materials (PFGMTEEMs), both constituent materials and the porosity appear gradient distribution in the present expression of effective material properties, which is much more suitable to the actual compared with the conventional expression of effective material properties. Besides the displacement function regarding physical neutral surface is introduced to analyze mechanical behaviors of beams made of FGMs. Then we derive nonlinear governing equations of PFGMTEEMs beams using the principle of Hamilton. To obtain analytical solutions, a two-step perturbation method is developed in nonuniform electric field and magnetic field, and then we use it to solve nonlinear equations. Finally, the analytical solutions are utilized to perform a parametric analysis, where the effect of various physical parameters on static bending deformation of nanobeams are studied in detail, such as the nonlocal parameter, strain gradient parameter, the ratio of nonlocal parameter to strain gradient parameter, porosity volume fraction, material volume fraction index, temperature, initial magnetic potentials and external electric potentials.

Two-dimensional curved panel vibration and flutter analysis in the frequency and time domain under thermal and in-plane load

  • Moosazadeh, Hamid;Mohammadi, Mohammad M.
    • Advances in aircraft and spacecraft science
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    • v.8 no.4
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    • pp.345-372
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    • 2021
  • The analysis of nonlinear vibrations, buckling, post-buckling, flutter boundary determination and post-flutter behavior of a homogeneous curved plate assuming cylindrical bending is conducted in this article. Other assumptions include simply-supported boundary conditions, supersonic aerodynamic flow at the top of the plate, constant pressure conditions below the plate, non-viscous flow model (using first- and third-order piston theory), nonlinear structural model with large deformations, and application of mechanical and thermal loads on the curved plate. The analysis is performed with constant environmental indicators (flow density, heat, Reynolds number and Mach number). The material properties (i.e., coefficient of thermal expansion and modulus of elasticity) are temperature-dependent. The equations are derived using the principle of virtual displacement. Furthermore, based on the definitions of virtual work, the potential and kinetic energy of the final relations in the integral form, and the governing nonlinear differential equations are obtained after fractional integration. This problem is solved using two approaches. The frequency analysis and flutter are studied in the first approach by transferring the handle of ordinary differential equations to the state space, calculating the system Jacobin matrix and analyzing the eigenvalue to determine the instability conditions. The second approach discusses the nonlinear frequency analysis and nonlinear flutter using the semi-analytical solution of governing differential equations based on the weighted residual method. The partial differential equations are converted to ordinary differential equations, after which they are solved based on the Runge-Kutta fourth- and fifth-order methods. The comparison between the results of frequency and flutter analysis of curved plate is linearly and nonlinearly performed for the first time. The results show that the plate curvature has a profound impact on the instability boundary of the plate under supersonic aerodynamic loading. The flutter boundary decreases with growing thermal load and increases with growing curvature.

Steady-state Vibration Responses of a Beam with a Nonlinear Boundary Condition (비선형 경계조건을 가진 보의 정상상태 진동응답)

  • Lee, Won-Kyoung;Yeo, Myeong-Hwan
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.21 no.2
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    • pp.337-345
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    • 1997
  • An analysis is presented for the response of a beam constrained by a nonlinear spring to a harmonic excitation. The system is governed by a linear partial differential equation with a nonlinear boundary condition. The method of multiple scales is used to reduce the nonlinear boundary value problem to a system of autonomous ordinary differential equations of the amplitudes and phases. The case of the third-order subharmonic resonance is considered in this study. The autonomous system is used to determine the steady-state responses and their stability.

Experimental identification of nonlinear model parameter by frequency domain method (주파수영역방법에 의한 비선형 모델변수의 실험적 규명)

  • Kim, Won-Jin
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.22 no.2
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    • pp.458-466
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    • 1998
  • In this work, a frequency domain method is tested numerically and experimentally to improve nonlinear model parameters using the frequency response function at the nonlinear element connected point of structure. This method extends the force-state mapping technique, which fits the nonlinear element forces with time domain response data, into frequency domain manipulations. The force-state mapping method in the time domain has limitations when applying to complex real structures because it needd a time domain lumped parameter model. On the other hand, the frequency domain method is relatively easily applicable to a complex real structure having nonlinear elements since it uses the frequency response function of each substurcture. Since this mehtod is performed in frequency domain, the number of equations required to identify the unknown parameters can be easily increased as many as it needed, just by not only varying excitation amplitude bot also selecting excitation frequency domain method has some advantages over the classical force-state mapping technique in the number of data points needed in curve fit and the sensitivity to response noise.

On the Design of the Observers of the Nonlinear System

  • Roh, Dong-Hwi;Park, Se-Yeon;Ryu, Dong-Young;Lee, Hong-Gi
    • Journal of the Korean Institute of Intelligent Systems
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    • v.11 no.7
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    • pp.653-658
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    • 2001
  • In this paper, we find the necessary and sufficient conditions for the discrete time nonlinear system to be transformed into observable canonical form by state coordinates change. Unlike the continuous time case, our theorems give the desired state coordinates change without solving partial differential equations. Also, our approach is applicable to both autonomous systems and control systems by slight change of the definition of the vector field.

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