• Title/Summary/Keyword: Equations of motion

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Study on the Effect of Design Parameters of the Vane Type Inertial Separator Using Commercial CFD Code (상용 CFD 프로그램을 사용한 베인형 관성분리기의 설계인자 영향 검토)

  • Lee, Dap-Yeon;Lew, Jae-Moon
    • Journal of the Society of Naval Architects of Korea
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    • v.54 no.6
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    • pp.470-475
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    • 2017
  • Since the intake air of gas turbine engine of marine purpose contains water particles, inertial separator for separating the air and water particles are provided. Saw type and wave type separator are now used to separate inflow water particle from the gas. In this paper, the design parameters of saw type separator are studied by numerical simulations. Using the commercial CFD program, Star-CCM+, Lagrangian-Eulerian method was used to perform the analysis of two phase flow of the mist in the air. This method solves Reynolds-Averaged Navier-Stokes equations in Eulerian framework for the continuous phase, while solves equation of motion for individual particles in Lagrangian framework. Lagrangian multiphase method was applied to monitor the particles of different sizes and shapes and to verify collision between particles by chasing particles. Water particles were injected through injectors located at the inlet of the separator and escape mode was used which assumes that the particles attached on the surface of inertial separator were removed from the simulation, effectively escaping the solution domain. Through the numerical computations with the inlet condition of constant water particle size in the wetness fraction of 85%, efficiency of eliminating the water particle and the pressure drop between the inlet and outlet were examined.

The effect of impact with adjacent structure on seismic behavior of base-isolated buildings with DCFP bearings

  • Bagheri, Morteza;Khoshnoudiana, Faramarz
    • Structural Engineering and Mechanics
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    • v.51 no.2
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    • pp.277-297
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    • 2014
  • Since the isolation bearings undergo large displacements in base-isolated structures, impact with adjacent structures is inevitable. Therefore, in this investigation, the effect of impact on seismic response of isolated structures mounted on double concave friction pendulum (DCFP) bearings subjected to near field ground motions is considered. A non-linear viscoelastic model of collision is used to simulate structural pounding more accurately. 2-, 4- and 8-story base-isolated buildings adjacent to fixed-base structures are modeled and the coupled differential equations of motion related to these isolated systems are solved in the MATLAB environment using the SIMULINK toolbox. The variation of seismic responses such as base shear, displacement in the isolation system and superstructure (top floor) is computed to study the impact condition. Also, the effects of variation of system parameters: isolation period, superstructure period, size of seismic gap between two structures, radius of curvature of the sliding surface and friction coefficient of isolator are contemplated in this study. It is concluded that the normalized base shear, bearing and top floor displacement increase due to impact with adjacent structure. When the distance between two structures decreases, the base shear and displacement increase comparing to no impact condition. Besides, the increase in friction coefficient difference also causes the normalized base shear and displacement in isolation system and superstructure increase in comparison with bi-linear hysteretic behavior of base isolation system. Totally, the comparison of results indicates that the changes in values of friction coefficient have more significant effects on 2-story building than 4- and 8-story buildings.

Buckling and free vibration analysis of tapered FG- CNTRC micro Reddy beam under longitudinal magnetic field using FEM

  • Mohammadimehr, M.;Alimirzaei, S.
    • Smart Structures and Systems
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    • v.19 no.3
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    • pp.309-322
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    • 2017
  • In this paper, the buckling, and free vibration analysis of tapered functionally graded carbon nanotube reinforced composite (FG-CNTRC) micro Reddy beam under longitudinal magnetic field using finite element method (FEM) is investigated. It is noted that the material properties of matrix is considered as Poly methyl methacrylate (PMMA). Using Hamilton's principle, the governing equations of motion are derived by applying a modified strain gradient theory and the rule of mixture approach for micro-composite beam. Micro-composite beam are subjected to longitudinal magnetic field. Then, using the FEM, the critical buckling load, and natural frequency of micro-composite Reddy beam is solved. Also, the influences of various parameters including ${\alpha}$ and ${\beta}$ (the constant coefficients to control the thickness), three material length scale parameters, aspect ratio, different boundary conditions, and various distributions of CNT such as uniform distribution (UD), unsymmetrical functionally graded distribution of CNT (USFG) and symmetrically linear distribution of CNT (SFG) on the critical buckling load and non-dimensional natural frequency are obtained. It can be seen that the non-dimensional natural frequency and critical buckling load decreases with increasing of ${\beta}$ for UD, USFG and SFG micro-composite beam and vice versa for ${\alpha}$. Also, it is shown that at the specified value of ${\alpha}$ and ${\beta}$, the dimensionless natural frequency and critical buckling load for SGT beam is more than for the other state. Moreover, it can be observed from the results that employing magnetic field in longitudinal direction of the micro-composite beam increases the natural frequency and critical buckling load. On the other hands, by increasing the imposed magnetic field significantly increases the stability of the system that can behave as an actuator.

Geometrically nonlinear dynamic analysis of FG graphene platelets-reinforced nanocomposite cylinder: MLPG method based on a modified nonlinear micromechanical model

  • Rad, Mohammad Hossein Ghadiri;Shahabian, Farzad;Hosseini, Seyed Mahmoud
    • Steel and Composite Structures
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    • v.35 no.1
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    • pp.77-92
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    • 2020
  • The present paper outlined a procedure for geometrically nonlinear dynamic analysis of functionally graded graphene platelets-reinforced (GPLR-FG) nanocomposite cylinder subjected to mechanical shock loading. The governing equation of motion for large deformation problems is derived using meshless local Petrov-Galerkin (MLPG) method based on total lagrangian approach. In the MLPG method, the radial point interpolation technique is employed to construct the shape functions. A micromechanical model based on the Halpin-Tsai model and rule of mixture is used for formulation the nonlinear functionally graded distribution of GPLs in polymer matrix of composites. Energy dissipation in analyses of the structure responding to dynamic loads is considered using the Rayleigh damping. The Newmark-Newton/Raphson method which is an incremental-iterative approach is implemented to solve the nonlinear dynamic equations. The results of the proposed method for homogenous material are compared with the finite element ones. A very good agreement is achieved between the MLPG and FEM with very fine meshing. In addition, the results have demonstrated that the MLPG method is more effective method compared with the FEM for very large deformation problems due to avoiding mesh distortion issues. Finally, the effect of GPLs distribution on strength, stiffness and dynamic characteristics of the cylinder are discussed in details. The obtained results show that the distribution of GPLs changed the mechanical properties, so a classification of different types and volume fraction exponent is established. Indeed by comparing the obtained results, the best compromise of nanocomposite cylinder is determined in terms of mechanical and dynamic properties for different load patterns. All these applications have shown that the present MLPG method is very effective for geometrically nonlinear analyses of GPLR-FG nanocomposite cylinder because of vanishing mesh distortion issue in large deformation problems. In addition, since in proposed method the distributed nodes are used for discretization the problem domain (rather than the meshing), modeling the functionally graded media yields to more accurate results.

A four-unknown refined plate theory for dynamic analysis of FG-sandwich plates under various boundary conditions

  • Menasria, Abderrahmane;Kaci, Abdelhakim;Bousahla, Abdelmoumen Anis;Bourada, Fouad;Tounsi, Abdeldjebbar;Benrahou, Kouider Halim;Tounsi, Abdelouahed;Adda Bedia, E.A.;Mahmoud, S.R.
    • Steel and Composite Structures
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    • v.36 no.3
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    • pp.355-367
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    • 2020
  • The current work, present dynamic analysis of the FG-sandwich plate seated on elastic foundation with various kinds of support using refined shear deformation theory. The present analytical model is simplified which the unknowns number are reduced. The zero-shear stresses at the free surfaces of the FG-sandwich plate are ensured without introducing any correction factors. The four equations of motion are determined via Hamilton's principle and solved by Galerkin's approach for FG-sandwich plate with three kinds of the support. The proposed analytical model is verified by comparing the results with those obtained by other theories existing in the literature. The parametric studies are presented to detect the various parameters influencing the fundamental frequencies of the symmetric and non-symmetric FG-sandwich plate with various boundary conditions.

A Study of the Location and Shape of the Ship using GPS (GPS를 이용한 선박 위치 및 자세 형상 제어 연구)

  • Park, Jung-Won;Kim, Han-Sil
    • Journal of the Institute of Electronics Engineers of Korea SC
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    • v.48 no.4
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    • pp.86-93
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    • 2011
  • The ship movement implies current position, wave, wind, and its other factors. We need to know exactly the location and the shape of the ship and control its motion because of these effects. In order to control the small ship according to the movement of the large ship, the position and shape of the ship should be given first. In this paper we propose the method with which we know the current status of the ship without dynamic equations of the ship. There are several methods to track the system such as optical, radio frequency, radar, camera, and infrared light. We propose the movement of the ship using the GPS absolute axis. But, the genuine error by the GPS itself and the movement of the ship cause the result of the GPS of not being accurate. This paper reduces the error of the location and the shape of the ship and gives the exact values of the ship movements even if the GPS implies some error itself.

A frequency tracking semi-active algorithm for control of edgewise vibrations in wind turbine blades

  • Arrigan, John;Huang, Chaojun;Staino, Andrea;Basu, Biswajit;Nagarajaiah, Satish
    • Smart Structures and Systems
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    • v.13 no.2
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    • pp.177-201
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    • 2014
  • With the increased size and flexibility of the tower and blades, structural vibrations are becoming a limiting factor towards the design of even larger and more powerful wind turbines. Research into the use of vibration mitigation devices in the turbine tower has been carried out but the use of dampers in the blades has yet to be investigated in detail. Mitigating vibrations will increase the design life and hence economic viability of the turbine blades and allow for continual operation with decreased downtime. The aim of this paper is to investigate the effectiveness of Semi-Active Tuned Mass Dampers (STMDs) in reducing the edgewise vibrations in the turbine blades. A frequency tracking algorithm based on the Short Time Fourier Transform (STFT) technique is used to tune the damper. A theoretical model has been developed to capture the dynamic behaviour of the blades including the coupling with the tower to accurately model the dynamics of the entire turbine structure. The resulting model consists of time dependent equations of motion and negative damping terms due to the coupling present in the system. The performances of the STMDs based vibration controller have been tested under different loading and operating conditions. Numerical analysis has shown that variation in certain parameters of the system, along with the time varying nature of the system matrices has led to the need for STMDs to allow for real-time tuning to the resonant frequencies of the system.

Stochastic stability control analysis of an inclined stay cable under random and periodic support motion excitations

  • Ying, Z.G.;Ni, Y.Q.;Duan, Y.F.
    • Smart Structures and Systems
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    • v.23 no.6
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    • pp.641-651
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    • 2019
  • The stochastic stability control of the parameter-excited vibration of an inclined stay cable with multiple modes coupling under random and periodic combined support disturbances is studied by using the direct eigenvalue analysis approach based on the response moment stability, Floquet theorem, Fourier series and matrix eigenvalue analysis. The differential equation with time-varying parameters for the transverse vibration of the inclined cable with control under random and deterministic support disturbances is derived and converted into the randomly and deterministically parameter-excited multi-degree-of-freedom vibration equations. As the stochastic stability of the parameter-excited vibration is mainly determined by the characteristics of perturbation moment, the differential equation with only deterministic parameters for the perturbation second moment is derived based on the $It{\hat{o}}$ stochastic differential rule. The stochastically and deterministically parameter-excited vibration stability is then determined by the deterministic parameter-varying response moment stability. Based on the Floquet theorem, expanding the periodic parameters of the perturbation moment equation and the periodic component of the characteristic perturbation moment expression into the Fourier series yields the eigenvalue equation which determines the perturbation moment behavior. Thus the stochastic stability of the parameter-excited cable vibration under the random and periodic combined support disturbances is determined directly by the matrix eigenvalues. The direct eigenvalue analysis approach is applicable to the stochastic stability of the control cable with multiple modes coupling under various periodic and/or random support disturbances. Numerical results illustrate that the multiple cable modes need to be considered for the stochastic stability of the parameter-excited cable vibration under the random and periodic support disturbances, and the increase of the control damping rather than control stiffness can greatly enhance the stochastic stability of the parameter-excited cable vibration including the frequency width increase of the periodic disturbance and the critical value increase of the random disturbance amplitude.

Vibrational characteristics of sandwich annular plates with damaged core and FG face sheets

  • Xi, Fei
    • Steel and Composite Structures
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    • v.44 no.1
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    • pp.65-79
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    • 2022
  • The main goal of this paper is to study the vibration of damaged core laminated annular plates with FG face sheets based on a three-dimensional theory of elasticity. The structures are made of a damaged isotropic core and two external face sheets. These skins are strengthened at the nanoscale level by randomly oriented Carbon nanotubes (CNTs) and are reinforced at the microscale stage by oriented straight fibers. These reinforcing phases are included in a polymer matrix and a three-phase approach based on the Eshelby-Mori-Tanaka scheme and on the Halpin-Tsai approach, which is developed to compute the overall mechanical properties of the composite material. In this study the effect of microcracks on the vibrational characteristic of the sandwich plate is considered. In particular, the structures are made by an isotropic core that undergoes a progressive uniform damage, which is modeled as a decay of the mechanical properties expressed in terms of engineering constants. These defects are uniformly distributed and affect the central layer of the plates independently from the direction, this phenomenon is known as "isotropic damage" and it is fully described by a scalar parameter. Three complicated equations of motion for the sectorial plates under consideration are semi-analytically solved by using 2-D differential quadrature method. Using the 2-D differential quadrature method in the r- and z-directions, allows one to deal with sandwich annular plate with arbitrary thickness distribution of material properties and also to implement the effects of different boundary conditions of the structure efficiently and in an exact manner. The fast rate of convergence and accuracy of the method are investigated through the different solved examples. The sandwich annular plate is assumed to have any arbitrary boundary conditions at the circular edges including simply supported, clamped and, free. Several parametric analyses are carried out to investigate the mechanical behavior of these multi-layered structures depending on the damage features, through-the-thickness distribution, and boundary conditions.

Effect of the Acceleration and Deceleration on the Dynamic Characteristics of an Air Stage (에어 스테이지의 동적 특성에 미치는 가속도 및 감속도의 영향)

  • Park, Sang Joon;Lee, Jae Hyeok;Park, Sang-Shin;Kim, Gyu Ha
    • Tribology and Lubricants
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    • v.36 no.1
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    • pp.39-46
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    • 2020
  • Air stages are usually applied to precision engineering in sectors such as the semiconductor industry owing to their excellent performance and extremely low friction. Since the productivity of a semiconductor depends on the acceleration and deceleration performance of the air stage, many attempts have been made to improve the speed of the stage. Even during sudden start or stop sequences, the stage should maintain an air film to avoid direct contact between pad and the rail. The purpose of this study is to quantitatively predict the dynamic behavior of the air stage when acceleration and deceleration occur. The air stage is composed of two parts; the stage and the guide-way. The stage transports objects to the guideway, which is supported by an externally pressurized gas bearing. In this study, we use COMSOL Multiphysics to calculate the pressure of the air film between the stage and the guide-way and solve the two-degree-of-freedom equations of motion of the stage. Based on the specified velocity conditions such as the acceleration time and the maximum velocity of stage, we calculate the eccentricity and tilting angle of the stage. The result shows that the stiffness and damping of the gas bearing have non-linear characteristics. Hence, we should consider the operating conditions in the design process of an air stage system because the dynamic behavior of the stage becomes unstable depending on the maximum velocity and the acceleration time.