• Title/Summary/Keyword: Non-linear Equation

Search Result 591, Processing Time 0.024 seconds

Calculation of Wave Deformation and Wave Induced Current around an Underwater Shoal by Boussinesq Equation (Boussinesq 방정식을 이용한 수중 천퇴에서의 파랑변형 및 파랑류 계산)

  • Chun Insik;Seong Sangbong;Kim Guidong;Sim Jaeseol
    • Journal of Korean Society of Coastal and Ocean Engineers
    • /
    • v.17 no.3
    • /
    • pp.202-212
    • /
    • 2005
  • In the design of an of offshore structure located near an underwater shoal, the same amount of attention given to the wave height may have to be put to the wave induced current as well since some of the wave energy translates to the current. In the present study, two numerical models each based on the nonlinear Boussinesq equation and the linear mild slope equation are applied to calculate the wave deformation and secondly induced current around a shoal. The underwater shoal in Vincent and briggs' experiment (1989) is used here, and all non-breaking wave conditions of the experiment with various monochromatic and unidirectional or multidirectional spectral wave incidences are concerned. Both numerical models clearly showed wave induced currents symmetrically farmed along the centerline over the shoal. The calculated wave heights along a preset line also generally showed very nice agreements with the experimental values.

The Effect of Fiber Volume Fraction Non-uniformity in Thickness Direction on the Buckling Load of Cylindrical Composite Lattice Structures (두께 방향 섬유체적비 불균일이 원통형 복합재 격자 구조 좌굴하중에 미치는 영향)

  • Kong, Seung-Taek;Jeon, Min-Hyeok;Kim, In-Gul;Lee, Sang-Woo
    • Composites Research
    • /
    • v.34 no.2
    • /
    • pp.129-135
    • /
    • 2021
  • In this paper, in order to examine the effect of fiber volume fraction non-uniformity in thickness direction on the buckling load of cylindrical composite lattice structures, we modified the equation of buckling load of the cylindrical composite lattice structures proposed by Vasiliev. The thickness of each layer of the rib was varied by fiber volume fraction, and material properties were applied differently by using the rule of mixture. Also, we performed linear buckling analysis by varying the structure size, thickness, and average value of the fiber volume fraction of finite element model. Finally, by comparing the calculation results of the buckling load of the equivalent model using the modified buckling load equation and the results of the finite element analysis, we found that the fiber volume fraction non-uniformity in thickness direction can reduce the buckling load of the cylindrical composite lattice structure.

Theoretical modelling of post - buckling contact interaction of a drill string with inclined bore-hole surface

  • Gulyayev, V.I.;Andrusenko, E.N.;Shlyun, N.V.
    • Structural Engineering and Mechanics
    • /
    • v.49 no.4
    • /
    • pp.427-448
    • /
    • 2014
  • At present, the time of easy oil and gas is over. Now, the largest part of fossil fuels is concentrated in the deepest levels of tectonic structures and in the sea shelves. One of the most cumbersome operations of their extraction is the bore-hole drilling. In connection with austere tectonic and climate conditions, their drivage every so often is associated with great and diversified technological difficulties causing emergencies on frequent occasions. As a rule, they are linked with drill string accidents. A key role in prediction of these situations should play methods of theoretical modelling. For this reason, there is a growing need for development and implementation of new numerical methods for computer simulation of critical and post-critical behavior of drill strings (DSs). In this paper, the processes of non-linear deforming of a DS in cylindrical cavity of a deep bore-hole are considered. On the basis of the theory of curvilinear flexible rods, non-linear constitutive differential equations are deduced. The effects of the longitudinal non-uniform preloading, action of torque and interaction between the DS and the bore-hole surface are taken into account. Owing to the use of curvilinear coordinates in the constraining cylindrical surface and a specially chosen concomitant reference frame, it became possible to separate the desired variables and to reduce the total order of the equation system. To solve it, the method of continuation the solution by parameter and the transfer matrix technique are applied. As a result of the completed numerical analysis, the critical states of the DS loading in the cylindrical channels of inclined bore-holes are found. It is shown that the modes of the post-critical deforming of the DS are associated with its irregular spiral curving prevailing in the zone of bottom-hole-assembly. The possibility of invariant state generation during post-critical deforming is established, condition of its bifurcation is formulated. It is shown that infinite variety of loads can correspond to one geometrical configuration of the DS. They differ each from other by contact force functions.

The 3-Axis Attitude Stabilization System Design of Picosat Hausat-1 (극소형 위성 HAUSAT-1의 3축 자세 안정화 시스템 설계)

  • Seo,Seung-Won;Jeong,Nam-Suk;Jang,Yeong-Geun
    • Journal of the Korean Society for Aeronautical & Space Sciences
    • /
    • v.31 no.7
    • /
    • pp.100-111
    • /
    • 2003
  • The HAUSAT-1(Hankuk Aviation University SATellite-1) will orbit at the altitude of 650km-800 km with 65 or 98 degree inclination angle. The effects of magnetic field and Earth gravity are more predominant than other space disturbances because the HAUSAT-1 will be positioned in LEO(Low Earth Orbit). The HAUSAT-1 design implements a magnetic control system and gravity-stable system which implement the solar panel deployment system. The simulation using MATLAB was performed to make sure the attitude stability of HAUSAT-1, which is based on the 8th order magnetic field model and non-linear equations of disturbances and the HAUSAT-1 attitude. The stability is investigated for two different HAUSAT-1 configurations and attitude which are affected by disturbances through simulation. The results for gravity-gradient stable and non gravity-gradient stable system are compared. Methodology of attitude stabilization was explored to develop an effective attitude control system for the HAUSAT-1 using magnetic torquers.

Wave load resistance of high strength concrete slender column subjected to eccentric compression

  • Jayakumar, M.;Rangan, B.V.
    • Structural Engineering and Mechanics
    • /
    • v.50 no.3
    • /
    • pp.287-304
    • /
    • 2014
  • A computer based iterative numerical procedure has been developed to analyse reinforced high strength concrete columns subjected to horizontal wave loads and eccentric vertical load by taking the material, geometrical and wave load non-linearity into account. The behaviour of the column has been assumed, to be represented by Moment-Thrust-Curvature relationship of the column cross-section. The formulated computer program predicts horizontal load versus deflection behaviour of a column up to failure. The developed numerical model has been applied to analyse several column specimens of various slenderness, structural properties and axial load ratios, tested by other researchers. The predicted values are having a better agreement with experimental results. A simplified user friendly hydrodynamic load model has been developed based on Morison equation supplemented with a wave slap term to predict the high frequency non-linear impulsive hydrodynamic loads arising from steep waves, known as ringing loads. A computer program has been formulated based on the model to obtain the wave loads and non-dimensional wave load coefficients for all discretised nodes, along the length of column from instantaneous free water surface to bottom of the column at mud level. The columns of same size and material properties but having different slenderness ratio are analysed by the developed numerical procedure for the simulated wave loads under various vertical thrust. This paper discusses the results obtained in detail and effect of slenderness in resisting wave loads under various vertical thrust.

New Stability Conditions for Positive Time-Varying Discrete Interval System with Interval Time-Varying Delay Time (구간 시변 지연시간을 갖는 양의 시변 이산 구간 시스템의 새로운 안정 조건)

  • Han, Hyung-Seok
    • Journal of Advanced Navigation Technology
    • /
    • v.18 no.5
    • /
    • pp.501-507
    • /
    • 2014
  • A dynamic system is called positive if any trajectory of the system starting from non-negative initial states remains forever non-negative for non-negative controls. In this paper, new sufficient conditions for asymptotic stability of the interval positive time-varying linear discrete-time systems with time-varying delay in states are considered. The considered time-varying delay time has an interval-like bound which has minimum and maximum delay time. The proposed conditions are established by using a solution bound of the Lyapunov equation and they are expressed by simple inequalities which do not require any complex numerical algorithms. An example is given to illustrate that the new conditions are simple and effective in checking stability for interval positive time-varying discrete systems.

Asian Stock Markets Analysis: The New Evidence from Time-Varying Coefficient Autoregressive Model

  • HONGSAKULVASU, Napon;LIAMMUKDA, Asama
    • The Journal of Asian Finance, Economics and Business
    • /
    • v.7 no.9
    • /
    • pp.95-104
    • /
    • 2020
  • In financial economics studies, the autoregressive model has been a workhorse for a long time. However, the model has a fixed value on every parameter and requires the stationarity assumptions. Time-varying coefficient autoregressive model that we use in this paper offers some desirable benefits over the traditional model such as the parameters are allowed to be varied over-time and can be applies to non-stationary financial data. This paper provides the Monte Carlo simulation studies which show that the model can capture the dynamic movement of parameters very well, even though, there are some sudden changes or jumps. For the daily data from January 1, 2015 to February 12, 2020, our paper provides the empirical studies that Thailand, Taiwan and Tokyo Stock market Index can be explained very well by the time-varying coefficient autoregressive model with lag order one while South Korea's stock index can be explained by the model with lag order three. We show that the model can unveil the non-linear shape of the estimated mean. We employ GJR-GARCH in the condition variance equation and found the evidences that the negative shocks have more impact on market's volatility than the positive shock in the case of South Korea and Tokyo.

Experimental studies on the axisymmetric sphere-wall interaction in Newtonian and non-Newtonian fluids

  • Lee, Sang-Wang;Sohn, Sun-Mo;Ryu, Seung-Hee;Kim, Chongyoup;Song, Ki-Won
    • Korea-Australia Rheology Journal
    • /
    • v.13 no.3
    • /
    • pp.141-148
    • /
    • 2001
  • In this research, experimental studies leave been performed on the hydrodynamic interaction between a spherical particle and a plane wall by measuring the force between the particle and wall. To approach the system as a resistance problem, a servo-driving system was set-up by assembling a microstepping motor, a ball screw and a linear motion guide for the particle motion. Glycerin and dilute solution of polyacrylamide in glycerin were used as Newtonian and non-Newtonian fluids, respectively. The polymer solution behaves like a Boger fluid when the concentration is 1,000 ppm or less. The experimental results were compared with the asymptotic solution of Stokes equation. The result shows that fluid inertia plays all important role in the particle-wall interaction in Newtonian fluid. This implies that the motion of two particles in suspension is not reversible even in Newtonian fluid. In non-Newtonian fluid, normal stress difference and viscoelasticity play important roles as expected. In the dilute solution weak shear thinning and the migration of polymer molecules in the inhomogeneous flow field also affect the physic of the problem.

  • PDF

Flapwise and non-local bending vibration of the rotating beams

  • Mohammadnejad, Mehrdad;Saffari, Hamed
    • Structural Engineering and Mechanics
    • /
    • v.72 no.2
    • /
    • pp.229-244
    • /
    • 2019
  • Weak form integral equations are developed to investigate the flapwise bending vibration of the rotating beams. Rayleigh and Eringen nonlocal elasticity theories are used to investigate the rotatory inertia and Size-dependency effects on the flapwise bending vibration of the rotating cantilever beams, respectively. Through repetitive integrations, the governing partial differential equations are converted into weak form integral equations. The novelty of the presented approach is the approximation of the mode shape function by a power series which converts the equations into solvable one. Substitution of the power series into weak form integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of the non-trivial solution for resulting system of equations. Accuracy of the proposed method is verified through several numerical examples, in which the influence of the geometry properties, rotatory inertia, rotational speed, taper ratio and size-dependency are investigated on the natural frequencies of the rotating beam. Application of the weak form integral equations has made the solution simpler and shorter in the mathematical process. Presented relations can be used to obtain a close-form solution for quick calculation of the first five natural frequencies of the beams with flapwise vibration and non-local effects. The analysis results are compared with those obtained from other available published references.

A semi-active stochastic optimal control strategy for nonlinear structural systems with MR dampers

  • Ying, Z.G.;Ni, Y.Q.;Ko, J.M.
    • Smart Structures and Systems
    • /
    • v.5 no.1
    • /
    • pp.69-79
    • /
    • 2009
  • A non-clipped semi-active stochastic optimal control strategy for nonlinear structural systems with MR dampers is developed based on the stochastic averaging method and stochastic dynamical programming principle. A nonlinear stochastic control structure is first modeled as a semi-actively controlled, stochastically excited and dissipated Hamiltonian system. The control force of an MR damper is separated into passive and semi-active parts. The passive control force components, coupled in structural mode space, are incorporated in the drift coefficients by directly using the stochastic averaging method. Then the stochastic dynamical programming principle is applied to establish a dynamical programming equation, from which the semi-active optimal control law is determined and implementable by MR dampers without clipping in terms of the Bingham model. Under the condition on the control performance function given in section 3, the expressions of nonlinear and linear non-clipped semi-active optimal control force components are obtained as well as the non-clipped semi-active LQG control force, and thus the value function and semi-active nonlinear optimal control force are actually existent according to the developed strategy. An example of the controlled stochastic hysteretic column is given to illustrate the application and effectiveness of the developed semi-active optimal control strategy.