• Title/Summary/Keyword: Nonlinear equations

Search Result 2,291, Processing Time 0.03 seconds

Active Handling Control of the Differential Brake System Using Fuzzy Controller (퍼지제어기를 이용한 차동브레이크 시스템의 능동 조향제어)

  • 윤여흥;장봉춘;이성철
    • Journal of the Korean Society for Precision Engineering
    • /
    • v.20 no.5
    • /
    • pp.82-91
    • /
    • 2003
  • Vehicle dynamics control (VDC) has been a breakthrough and become a new terminology for the safety of a driver and improvement of vehicle handling. This paper examines the usefulness of a brake steer system (BSS), which uses differential brake forces for steering intervention in the context of VDC, In order to help the car to turn, a yaw moment can be achieved by altering the left/right and front/rear brake distribution. The steering function achieved through BSS can then be used to control lateral position in an unintended road departure system. An 8-DOF non-linear vehicle model including STI tire model will be validated using the equations of motion of the vehicle, and the non-linear vehicle dynamics. Since fuzzy logic can consider the nonlinear effect of vehicle modeling, fuzzy controller is designed to explore BSS feasibility, by modifying the brake distribution through the control of the yaw rate of the vehicle. The control strategies developed will be tested by simulation of a variety of situation; the possibility of VDC using BSS is verified in this paper.

Numerical Study on the Radiation of Intake Noise from Internal Combustion Engine by Using Essentially Non-Oscillatory Schemes (ENO기법을 이용한 연소 엔진 흡기계 소음의 방사에 관한 수치적 연구)

  • 김용석;이덕주
    • Journal of KSNVE
    • /
    • v.8 no.2
    • /
    • pp.239-250
    • /
    • 1998
  • Traditionally, intake noise from internal combustion engine has not recevied much attention compared to exhaust noise. But nowadays, intake noise is a major contributing factor to automotive passenger compartment noise levels. The main objective of this paper is to identify the mechanism of generation, propagation and radiation of the intake noise. With a simplest geometric model, one of the main noise sources for the intake stroke is found to be the pressure surge, which is generated after intake valve closing. The pressure surge, which has the nonlinear acoustic behavior, propagates and radiates with relatively large amplitude. In this paper, unsteady compressible Navier-Stokes equations are employed for the intake stroke of axisymmetric model having a single moving cylinder and a single moving intake valve. To simulate the periodic motion of the piston and the valve, unsteady deforming mesh algorithm is employed and Thompson's non-reflecting boundary condition is applied to the radiation field. In order to resolve the small amplitude waves at the radiation field, essentially non-oscillatory(ENO) schemes with an artificial compression method (ACM) are used.

  • PDF

Analysis of Flexible Media Using ALE Finite Element Method (ALE 유한요소법을 이용한 유연매체의 거동해석)

  • Jee, Jung-Geun;Jang, Yong-Hoon;Park, No-Cheol;Park, Young-Pil
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
    • /
    • 2007.05a
    • /
    • pp.247-250
    • /
    • 2007
  • Flexible media such as the paper, the film, etc. are thin, light and very flexible. They behave in geometrically nonlinear. Any of small force makes large deformation. So we must including aerodynamic effect when its behavior is predicted. Thus, it becomes fully coupled fluid-structure interaction(FSI) problem. In FSI problems, where the fluid mesh near the structure undergoes large deformations and becomes unacceptably distorted, which drive the time step to a very small value for explicit calculations, the arbitrary Lagrangian-Eulerian(ALE) methods or rezoning are used to create a new undistorted mesh for the fluid domain, which allows the calculations to continue. In this paper, FE sheet model considering geometric nonlinearity is formulated to simulate the behavior of the flexible media. Aerodynamic force to the media by surrounding air is calculated by solving the incompressible Navier-Stokes equations. Q2Q1(Taylor-Hood) element which means biquadratic for velocity and bilinear for pressure is used for fluid domain. Q2Q1 element satisfies LBB condition and any stabilization technique is not needed. In this paper, cantilevered sheet in the viscous incompressible Navier-Stokes flow is simulated to check the mesh motion and numerical integration scheme, and then falling paper in the air is simulated and the effects of some representative parameters are investigated.

  • PDF

Uncertainty Assessment using Monte Carlo Simulation in Net Thrust Measurement at AETF

  • Lee, Bo-Hwa;Lee, Kyung-Jae;Yang, In-Young;Yang, Soo-Seok;Lee, Dae-Sung
    • International Journal of Aeronautical and Space Sciences
    • /
    • v.8 no.2
    • /
    • pp.126-131
    • /
    • 2007
  • In this paper, Monte Carlo Simulation (MCS) method was used as an uncertainty assessment tool for air flow, net thrust measurement. Uuncertainty sources of the net thrust measurement were analyzed, and the probability distribution characteristics of each source were discussed. Detailed MCS methodology was described including the effect of the number of simulation. Compared to the conventional sensitivity coefficient method, the MCS method has advantage in the uncertainty assessment. The MCS is comparatively simple, convenient and accurate, especially for complex or nonlinear measurement modeling equations. The uncertainty assessment result by MCS was compared with that of the conventional sensitivity coefficient method, and each method gave different result. The uncertainties in the net thrust measurement by the MCS and the conventional sensitivity coefficient method were 0.906% and 1.209%, respectively. It was concluded that the first order Taylor expansion in the conventional sensitivity coefficient method and the nonlinearity of model equation caused the difference. It was noted that the uncertainty assessment method should be selected carefully according to the mathematical characteristics of the model equation of the measurement.

Mathematical Modeling of Combustion Characteristics in HVOF Thermal Spray Processes(I): Chemical Composition of Combustion Products and Adiabatic Flame Temperature (HVOF 열용사 프로세스에서의 연소특성에 관한 수학적 모델링(I): 연소생성물의 화학조성 및 단열화염온도)

  • Yang, Young-Myung;Kim, Ho-Yeon
    • Journal of the Korean Society of Combustion
    • /
    • v.3 no.1
    • /
    • pp.21-29
    • /
    • 1998
  • Mathematical modeling of combustion characteristics in HVOF thermal spray processes was carried out on the basis of equilibrium chemistry. The main objective of this work was the development of a computation code which allows to determine chemical composition of combustion products, adiabatic flame temperature, thermodynamic and transport properties. The free energy minimization method was employed with the descent Newton-Raphson technique for numerical solution of systems of nonlinear thermochemical equations. Adiabatic flame temperature was calculated by using a Newton#s iterative method incorporating the computation module of chemical composition. The performance of this code was verified by comparing computational results with data obtained by ChemKin code and in the literature. Comparisons between the calculated and measured flame temperatures showed a deviation less than 2%. It was observed that adiabatic flame temperature augments with increase in combustion pressure; the influence was significant in the region of low pressure but becomes weaker and weaker with increase in pressure. Relationships of adiabatic flame temperature, dissociation ratio and combustion pressure were also analyzed.

  • PDF

A Numerical Study on the Aerodynamic Characteristics of a Bus-Like Bluff Body - Effect of Turbulence Model and Discretisation Scheme - (버스형상 무딘물체의 공력특성에 관한 수치해석적 고찰 - 난류모델과 이산화법의 영향 -)

  • 김민호;국종영;천인범
    • Transactions of the Korean Society of Automotive Engineers
    • /
    • v.11 no.3
    • /
    • pp.115-123
    • /
    • 2003
  • With the advent of high performance computers and more efficient numerical algorithms, computational fluid dynamics(CFD) has come out as a modem alternative for reducing the use of wind tunnels test in automotive engineering. However, in spite of the fact that many competent researchers have made all their talents in developing turbulence model over since the past dozen or more years, it has been an important impediment in using the CFD effectively to design machinery and to diagnose or to improve engineering problems in the industry since the turbulence model has been acting as the Achilles' tendon in aspect of the reliability even to this time. In this study, Reynolds-averaged Wavier-Stokes equations were solved to simulate an incompressible turbulent flow around a bus-like bluff body near ground plane. In order to investigate the effect of the discretisation schemes and turbulence model on the aerodynamic forces several turbulence models with five convective difference schemes are adopted. From the results of this study, it is clear that choice of turbulence model and discretisation scheme profoundly affects the computational outcome. The results also show that the adoption of RNG $k-\varepsilon$ turbulence model and nonlinear quadratic turbulence model with the second order accurate discretisation scheme predicts fairly well the aerodynamic coefficients.

Optimum time history analysis of SDOF structures using free scale of Haar wavelet

  • Mahdavi, S.H.;Shojaee, S.
    • Structural Engineering and Mechanics
    • /
    • v.45 no.1
    • /
    • pp.95-110
    • /
    • 2013
  • In the recent decade, practical of wavelet technique is being utilized in various domain of science. Particularly, engineers are interested to the wavelet solution method in the time series analysis. Fundamentally, seismic responses of structures against time history loading such as an earthquake, illustrates optimum capability of systems. In this paper, a procedure using particularly discrete Haar wavelet basis functions is introduced, to solve dynamic equation of motion. In the proposed approach, a straightforward formulation in a fluent manner is derived from the approximation of the displacements. For this purpose, Haar operational matrix is derived and applied in the dynamic analysis. It's free-scaled matrix converts differential equation of motion to the algebraic equations. It is shown that accuracy of dynamic responses relies on, access of load in the first step, before piecewise analysis added to the technique of equation solver in the last step for large scale of wavelet. To demonstrate the effectiveness of this scheme, improved formulations are extended to the linear and nonlinear structural dynamic analysis. The validity and effectiveness of the developed method is verified with three examples. The results were compared with those from the numerical methods such as Duhamel integration, Runge-Kutta and Wilson-${\theta}$ method.

Stochastic thermo-mechanically induced post buckling response of elastically supported nanotube-reinforced composite beam

  • Chaudhari, Virendra Kumar;Shegokar, Niranjan L.;Lal, Achchhe
    • Advances in aircraft and spacecraft science
    • /
    • v.4 no.5
    • /
    • pp.585-611
    • /
    • 2017
  • This article covenants with the post buckling witticism of carbon nanotube reinforced composite (CNTRC) beam supported with an elastic foundation in thermal atmospheres with arbitrary assumed random system properties. The arbitrary assumed random system properties are be modeled as uncorrelated Gaussian random input variables. Unvaryingly distributed (UD) and functionally graded (FG) distributions of the carbon nanotube are deliberated. The material belongings of CNTRC beam are presumed to be graded in the beam depth way and appraised through a micromechanical exemplary. The basic equations of a CNTRC beam are imitative constructed on a higher order shear deformation beam (HSDT) theory with von-Karman type nonlinearity. The beam is supported by two parameters Pasternak elastic foundation with Winkler cubic nonlinearity. The thermal dominance is involved in the material properties of CNTRC beam is foreseen to be temperature dependent (TD). The first and second order perturbation method (SOPT) and Monte Carlo sampling (MCS) by way of CO nonlinear finite element method (FEM) through direct iterative way are offered to observe the mean, coefficient of variation (COV) and probability distribution function (PDF) of critical post buckling load. Archetypal outcomes are presented for the volume fraction of CNTRC, slenderness ratios, boundary conditions, underpinning parameters, amplitude ratios, temperature reliant and sovereign random material properties with arbitrary system properties. The present defined tactic is corroborated with the results available in the literature and by employing MCS.

A high-order gradient model for wave propagation analysis of porous FG nanoplates

  • Shahsavari, Davood;Karami, Behrouz;Li, Li
    • Steel and Composite Structures
    • /
    • v.29 no.1
    • /
    • pp.53-66
    • /
    • 2018
  • A high-order nonlocal strain gradient model is developed for wave propagation analysis of porous FG nanoplates resting on a gradient hybrid foundation in thermal environment, for the first time. Material properties are assumed to be temperature-dependent and graded in the nanoplate thickness direction. To consider the thermal effects, uniform, linear, nonlinear, exponential, and sinusoidal temperature distributions are considered for temperature-dependent FG material properties. On the basis of the refined-higher order shear deformation plate theory (R-HSDT) in conjunction with the bi-Helmholtz nonlocal strain gradient theory (B-H NSGT), Hamilton's principle is used to derive the equations of wave motion. Then the dispersion relation between frequency and wave number is solved analytically. The influences of various parameters (such as temperature rise, volume fraction index, porosity volume fraction, lower and higher order nonlocal parameters, material characteristic parameter, foundations components, and wave number) on the wave propagation behaviors of porous FG nanoplates are investigated in detail.

Solution for a circular tunnel in strain-softening rock with seepage forces

  • Wei, Luo;Zo, Jin-feng;An, Wei
    • Geomechanics and Engineering
    • /
    • v.22 no.6
    • /
    • pp.553-564
    • /
    • 2020
  • In this study, a simple numerical approach for a circular tunnel opening in strain-softening surrounding rock is proposed considering out-of-plane stress and seepage force based on Biot's effective stress principle. The plastic region of strain-softening surrounding rock was divided into a finite number of concentric rings, of which the thickness was determined by the internal equilibrium equation. The increments of stress and strain for each ring, starting from the elastic-plastic interface, were obtained by successively incorporating the effect of out-of-plane stress and Biot's effective stress principle. The initial value of the outmost ring was determined using equilibrium and compatibility equations. Based on the Mohr-Coulomb (M-C) and generalized Hoek-Brown (H-B) failure criteria, the stress-increment approach for solving stress, displacement, and plastic radius was improved by considering the effects of Biot's effective stress principle and the nonlinear degradation of strength and deformation parameters in plastic zone incorporating out-of-plane stress. The correctness of the proposed approach is validated by numerical simulation.