• Title/Summary/Keyword: Linearized equation

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Vibration Analysis of a Bogie Using Linearized Dynamic Equations of a Multibody System (다물체계의 선형 동역학식을 이용한 대차의 진동 해석)

  • Kang, Juseok
    • Journal of the Korean Society for Railway
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    • v.17 no.5
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    • pp.321-327
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    • 2014
  • In this paper, linear dynamic equations are derived from nonlinear dynamic equations of constrained multibody systems using the QR decomposition method. The derived linear equations are applied to a railway vehicle bogie. The vibration characteristics of the railway vehicle are investigated by calculating the natural mode and transfer function of the bogie frame in relation to rail-roughness input. The main modes of the bogie were found below 35Hz, and the local modes above 198Hz. The magnitude of the vertical transfer function varied with the forward velocity due to vertical and pitch modes, which were influenced by the forward velocity. The magnitude of the lateral transfer function was negligibly small, and the mode in the longitudinal direction was excited for longitudinal transfer function regardless of the forward velocity.

Natural vibrations and hydroelastic stability of laminated composite circular cylindrical shells

  • Bochkareva, Sergey A.;Lekomtsev, Sergey V.
    • Structural Engineering and Mechanics
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    • v.81 no.6
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    • pp.769-780
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    • 2022
  • This paper studies the dynamic behavior of laminated composite circular cylindrical shells interacting with a fluid. The mathematical formulation of the dynamic problem for an elastic body is developed based on the variational principle of virtual displacements and the relations of linear elasticity theory. The behavior of an ideal compressible fluid is described by the potential theory, the equations of which together with boundary conditions are transformed to a weak form. The hydrodynamic pressure exerted by the fluid on the internal surface of the shell is calculated according to the linearized Bernoulli equation. The numerical implementation of the mathematical formulation has been done using the semi-analytical finite element method. The influence of the ply angle and lay-up configurations of laminated composites on the natural vibration frequencies and the hydroelastic stability boundary have been analyzed for shells with different geometrical dimensions and under different kinematic boundary conditions set at their edges. It has been found that the optimal value of the ply angle depends on the level of filling of the shell with a fluid. The obtained results support the view that by choosing the optimal configuration of the layered composite material it is possible to change upwards or downwards the frequency and mode shape, as well as the critical velocity for stability loss over a wide range.

Nonlinear Aeroelastic Analyses of Composite Wing with Flap (플랩을 갖는 복합재 평판 날개의 비선형 공력 탄성학 해석)

  • Shin, Won-Ho;Bae, Jae-Sung;Lee, In
    • Composites Research
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    • v.20 no.1
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    • pp.8-14
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    • 2007
  • Nonlinear aeroelastic analyses of composite wing with flap are performed considering free-play and dynamic stiffness of actuator. Doublet-Hybrid method is used for the calculation of subsonic unsteady aerodynamic forces. Free-play is modeled as a bilinear spring and is linearized by using the describing function method. Dynamic stiffness is obtained from governing equation of gear system and the aeroelastic analyses were performed according to ply-angle of laminate and material. The linear and nonlinear flutter analysis results show that the flutter characteristics are significantly dependent on the free-play and dynamic stiffness. from the nonlinear flutter analysis, various types of limit cycle oscillations are observed in a range of air speeds below or above the linear divergent flutter boundary.

A Study on Viscous Damping System of a Ship with Anti-Rolling Pendulum (안티롤링 진자를 장치한 선박의 점성감쇠계 해석에 대한 연구)

  • Park, Sok-Chu;Jang, Kwang-Ho;Yi, Geum-Joo
    • Journal of Navigation and Port Research
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    • v.41 no.6
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    • pp.365-372
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    • 2017
  • The rolling motion of a floating body makes crews and passengers exhausted and/or applies forces to the structure to cause damage; it might even upset the body. Therefore, almost all ships are equipped with bilge keels for anti-rolling; in special cases, an anti-rolling tank(ART) or fin stabilizer or gyroscope could be installed. But an ART requires a large capacity to install it, and a fin stabilizer and gyroscope need great costs to install and also many expenses to operate. The authors suggest the use of an anti-rolling pendulum(ARP), and they showed that the ARP is effective to reduce rolling by experiments and via a Runge-Kutta analysis. This paper introduces the linearized 2 degrees of freedom with a viscous damping system for a ship equipped with ARP; it also shows the validation of the linearized analysis for the ship's roll motion. The paper proposes an optimum ARP on the basis of the justified model. The case of the 7.7kg model with ship 20g ARP of a mass ratio of 0.26%, is the most effective for reducing roll motion. The paper shows the ARPs with various mass ratios are effective for reducing the roll motion of a ship by free decaying roll experiments.

Methods of Weighting Matrices Determination of Moving Double Poles with Jordan Block to Real Poles By LQ Control (LQ 제어로 조단블록이 있는 중근을 실근으로 이동시키는 가중행렬 결정 방법)

  • Park, Minho
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.21 no.6
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    • pp.634-639
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    • 2020
  • In general, the stability and response characteristics of the system can be improved by changing the pole position because a nonlinear system can be linearized by the product of a 1st and 2nd order system. Therefore, a controller that moves the pole can be designed in various ways. Among the other methods, LQ control ensures the stability of the system. On the other hand, it is difficult to specify the location of the pole arbitrarily because the desired response characteristic is obtained by selecting the weighting matrix by trial and error. This paper evaluated a method of selecting a weighting matrix of LQ control that moves multiple double poles with Jordan blocks to real poles. The relational equation between the double poles and weighting matrices were derived from the characteristic equation of the Hamiltonian system with a diagonal control weighting matrix and a state weighting matrix represented by two variables (ρd, ϕd). The Moving-Range was obtained under the condition that the state-weighting matrix becomes a positive semi-definite matrix. This paper proposes a method of selecting poles in this range and calculating the weighting matrices by the relational equation. Numerical examples are presented to show the usefulness of the proposed method.

A Study on Adsorption of Lead(II) in Wastewater Using Natural Kaolinite (천연 고령토의 폐수 중 납 흡착에 관한 연구)

  • 이종은
    • Journal of Environmental Health Sciences
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    • v.21 no.3
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    • pp.77-86
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    • 1995
  • Lead(II) removal efficiency by natural kaolinite was investigated through laboratory experiments. This study was conducted in two phases-sorption and desorption. In the adsorption study, the influence of sorption kinetics and sorption isotherm and various parameters such as pH, temperature, coexisting other heavy metal ions on the lead adsorption was investigated. And desorption study was carried out in order to find the re-usability of kaolinite as an adsorbent. The results of the study are as follows. 1. Sorption kinetics was investigated under the condition of 2.5 mg/l adsorbent concentration, pH 6.5$\pm$0.05, temperature $30\pm 0.5\circ$C, initial lead(II) concentration 25 mg/l. Adsorption rate was initially rapid and the extent of adsorption arrived at adsorption equilibrium with 73% adsorption efficiency in an hour. 2. The sorption isotherm experiment was made with different initial lead(II) concentration. A linearized Freundlich equation was used to fit the acquired experimental data. As a result, Freundlich constants, the sorption intensity (1/n) was 0.47 and the measure of sorption (k) was 2.44. So, it was concluded that sorption of lead(II) by kaolinite is effective. 3. The effect of pH on lead(II) sorption by kaolinite shows that at a pH of 3, only 6% of the total lead(II) was adsorbed and at a pH 9, 97% of the lead(II) was removed. And the effect of temperature on lead(II) sorption by kaolinite shows that as the temperature increased, the amount of lead(II) sorption per unit weight of kaolinite increased. But the effect was minor (p<0.05). 4. Sorption isotherm of lead coexisting cadmium (II) or zinc (II) was lower than that of lead itself. It was caused by the result of competitive sorption to adsorption site. And there was no difference between the sorption isotherm of cadmium and zinc. 5. In desorption studies, only 5.12% desorption took place in distilled water, while 52.08% in 0.1 N hydrochloric acid. Consequently used kaolinite could be regenerated by hydrochoric acid.

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A Study on Vibration Control Performance of Macpherson Type Semi-Active Suspension System (맥퍼슨 타입 반 능동 현가장치의 진동제어 성능 고찰)

  • Dutta, Saikat;Han, Chulhee;Lee, TaeHoon;Choi, Seung-Bok
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.26 no.2
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    • pp.157-164
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    • 2016
  • The paper studies a comparison analysis of semi-active control strategies for a Macpherson strut type suspension system consisting of MR(magneto-rheological) damper. As a first step, in order to formulate governing, a dynamic full model of a Macpherson strut is developed considering the kinematics. The nonlinear equation of motion of the strut is then linearized around the equilibrium point. A new adaptive moving sliding model controller is developed for fast response of the system. A newly proposed adaptive moving sliding mode control strategy is then compared with conventional sliding mode controller and skyhook controller. The comparison is made for two different types of road inputs; bump and random road profiles showing superior vibration control performance in time and frequency domains.

A Study on the Relation between Towing Force of Tow Vessel and Towing Point and Behavior of Towed Ship (예인력과 피예인선의 예인 지점과 거동에 관한 연구)

  • Nam, Taek-Kun
    • Journal of the Korean Society of Marine Environment & Safety
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    • v.19 no.6
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    • pp.637-642
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    • 2013
  • In this paper, an analysis results of towing force and towing points which are dominating factors to determine the behavior of towed ship are introduced. The towing force and towing points to achive the desired posture and its position of the towed vessel are derived based on simplified dynamics and linearization method. LQR algorithm for posture control is applied to linearized system and numerical simulation is also executed. Force based on COG(cneter of gravity) and gain of controller to achieve desired posture for target vessel are obtained by using Riccati matrix equation and pseudo inverse matrix is applied to analyze the relation between the derived force and its towing point. Based on this analysis method, towing force need to move the towed vessel from its initial position to target position can be calculated. The towing method including towing point and direction is also considered on this method. Finally, the relation between towing force and towing point is confirmed from the analysis and the results can be applied to arrangement of tug boats during salvage works.

Stability Analysis of Shear-Flexible and Semi-Rigid Plane Frames (전단변형효과를 고려한 부분강절 평면뼈대구조의 안정성 해석)

  • Min, Byoung Cheol;Min, Dong Ju;Jung, Myung Rag;Kim, Moon Young
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.31 no.1A
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    • pp.9-18
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    • 2011
  • Generally the connection of structural members is assumed as hinge, rigid and semi-rigid connections. The exact tangent stiffness matrix of a semi-rigid frame element is newly derived using the stability functions considering shear deformations. Also, linearized elastic- and geometric-stiffness matrices of shear deformable semi-rigid frame are newly proposed. For the exact stiffness matrix, an accurate displacement field is introduced by equilibrium equation for beam-column under the bending and the axial forces. Also, stability functions considering sway deformation and force-displacement relations with elastic rotational spring on ends are defined. In order to illustrate the accuracy of this study, various numerical examples are presented and compared with other researcher's results. Lastly, shear deformation and semi-rigid effects on buckling behaviors of structure are parametrically investigated.

Transient Modeling of Single-Electron Transistors for Circuit Simulation (회로 시뮬레이션을 위한 단일전자 트랜지스터의 과도전류 모델링)

  • 유윤섭;김상훈
    • Journal of the Institute of Electronics Engineers of Korea SD
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    • v.40 no.4
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    • pp.1-12
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    • 2003
  • In this study, a regime where independent treatment of SETs in transient simulations is valid has been identified quantitatively. It is found that as in the steady-state case, each SET can be treated independently even in the transient case when the interconnection capacitance is large enough. However, the value of the load capacitance $C_{L}$of the interconnections for the independent treatment of SETs is approximately 10 times larger than that of the steady state case. A compact SET transient model is developed for transient circuit simulation by SPICE. The developed model is based on a linearized equivalent circuit and the solution of master equation is done by the programming capabilities of the SmartSpice. Exact delineation of several simulation time scales and the physics-based compact model make it possible to accurately simulate hybrid circuits in the time scales down to several tens of pico seconds. The simulation time is also shown to depend on the complexity level of the transient model.l.