• Title/Summary/Keyword: dynamic stiffness matrix

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Static and dynamic analysis of circular beams using explicit stiffness matrix

  • Rezaiee-Pajand, Mohammad;Rajabzadeh-Safaei, Niloofar
    • Structural Engineering and Mechanics
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    • v.60 no.1
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    • pp.111-130
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    • 2016
  • Two new elements with six degrees of freedom are proposed by applying the equilibrium conditions and strain-displacement equations. The first element is formulated for the infinite ratio of beam radius to thickness. In the second one, theory of the thick beam is used. Advantage of these elements is that by utilizing only one element, the exact solution will be obtained. Due to incorporating equilibrium conditions in the presented formulations, both proposed elements gave the precise internal forces. By solving some numerical tests, the high performance of the recommended formulations and also, interaction effects of the bending and axial forces will be demonstrated. While the second element has less error than the first one in thick regimes, the first element can be used for all regimes due to simplicity and good convergence. Based on static responses, it can be deduced that the first element is efficient for all the range of structural characteristics. The free vibration analysis will be performed using the first element. The results of static and dynamic tests show no deficiency, such as, shear and membrane locking and excessive stiff structural behavior.

A Study on the Coupled Shaft-torsional and Blade-bending Vibrations in the Flexible Rotor-coupling-blade System (유연체 로터-커플링-블레이드 시스템의 로터 축과 블레이드의 연성 진동에 관한 연구)

  • Oh, Byung-Young;Lee, Sun-Sook;Yoon, Hyungwon;Cha, Seog-Ju;Na, Sungsoo
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.15 no.9 s.102
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    • pp.1023-1029
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    • 2005
  • In this paper, a dynamic model for the rotor shaft-coupling-blade system was developed. The blades are attached to a disk and driven by an electric motor shaft which is flexible in torsion. We assumed that the shaft torsional flexibility was lumped in the flexible coupling which is usually adopted in rotor systems. The Lagrangian approach with the small deformation theory for both blade-bending and shaft-torsional deformations was employed for developing the equation of the motion. The Assumed Modes Method was used for estimating the blade transverse deflection. The numerical results highlight the effects of both structural damping of the system and the torsional stiffness of the flexible coupling to the dynamic response of the blade. The results showed strong coupling between the blade bending and shaft torsional vibrations in the form of inertial nonlinearity, stiffness hardening and softening.

Selection of Nodes and Modes for Reduced Modeling of Substructures (부분구조물의 축약 모델링을 위한 절점 및 모드의 선정)

  • Hwang, Woo Seok
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.25 no.4
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    • pp.232-237
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    • 2015
  • Complex dynamic systems are composed of several subsystems. Each subsystems affect the dynamics of other subsystems since they are connected to each other in the whole system. Theoretically, we can derive the exact mass and stiffness matrix of a system if we have the natural frequencies and mode shapes of that system. In real situation, the modal parameters for the higher modes are not available and the number of degree of freedom concerned are not so high. This paper shows a simple method to derive the mass and stiffness matrix of a system considering the connecting points of subsystems. Since the accuracy of reconstructed structure depends on the selection of node and mode, the rule for selection of node and mode are derived from the numerical examples.

Geometric Nonlinear Analysis of Flexible Media Using $C^1$ Beam Element ($C^1$보요소를 이용한 유연매체의 기하비선형 해석)

  • Jee, Jung-Geun;Hong, Sung-Kwon;Jang, Yong-Hoon;Park, No-Cheol;Park, Young-Pil
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2005.05a
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    • pp.326-329
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    • 2005
  • In the development of sheet-handling .machinery, it is important to predict the static and dynamic behavior of the sheets with a high degree of reliability because the sheets are fed and stacked at suck a high speed flexible media behaves geometric nonlinearity of large displacement and small strain. In this paper, static analysis of flexible media are performed by FEM considering geometric nonlinearity. Linear stiffness matrix and geometric nonlinear stiffness matrix based m the updated Lagrangian approach are derived using $C^1$ beam element and numerical simulations are performed by Updated Newton-Raphson(UNR) method.

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Dynamic Analysis of Rotating Turbomachine Blades Including Coriolis Effect (코리올리 영향을 고려한 회전하는 터보기계 블레이드의 동특성 해석)

  • Lee, Jin-Gap
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.23 no.11 s.170
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    • pp.2067-2077
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    • 1999
  • Recently, turbomachine blades are becoming larger and more flexible, it is necessary to calculate natural frequencies of a rotating blades for avoiding resonance. This problem is complicated by the fact that blades are tapered, twisted and curved. To keep with this demands, the designer must rely on more exact methods of calculation. In this paper, natural frequencies of a single straight or curved blade with variable R.P.M. are calculated by a stiffness matrix method. Results of investigation on the correspondence between the calculated and other values of the literature are described. The calculated values are agree with the other values but with a small error. Furthermore, the influence of Coriolis force on the natural frequency for rotating, curved turbo blades is described.

Stochastic finite element analysis of structural systems with partially restrained connections subjected to seismic loads

  • Cavdar, Ozlem;Bayraktar, Alemdar;Cavdar, Ahmet;Kartal, Murat Emre
    • Steel and Composite Structures
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    • v.9 no.6
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    • pp.499-518
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    • 2009
  • The present paper investigates the stochastic seismic responses of steel structure systems with Partially Restrained (PR) connections by using Perturbation based Stochastic Finite Element (PSFEM) method. A stiffness matrix formulation of steel systems with PR connections and PSFEM and MCS formulations of structural systems are given. Based on the formulations, a computer program in FORTRAN language has been developed, and stochastic seismic analyses of steel frame and bridge systems have been performed for different types of connections. The connection parameters, material and geometrical properties are assumed to be random variables in the analyses. The Kocaeli earthquake occurred in 1999 is considered as a ground motion. The connection parameters, material and geometrical properties are considered to be random variables. The efficiency and accuracy of the proposed SFEM algorithm are validated by comparison with results of Monte Carlo simulation (MCS) method.

Analysis and Control of the Flexible Multibody System Using MATLAB (MATLAB을 이용한 유연 다물체 시스템의 해석 및 제어)

  • Jung, Sung-Pil;Park, Tae-Won
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.32 no.5
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    • pp.437-443
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    • 2008
  • In this paper, analysis and control of the flexible multibody system using MATLAB is presented. The equations of motion of a flexible body are derived in terms of the modal coordinate. The rigid-flexible multibody dynamic solver is developed. Finite element information required to analyze motion of flexible bodies is imported from ANSYS. The modified finite element data, such as modal mass matrix, modal stiffness matrix and constraint mode shapes, is calculated in the solver. Since the solver is developed using MATLAB, it is very easy to connect with SIMULINK which is widely used to control motion of the multibody system. Several simulations are implemented to verify the developed solver. A control example is carried out and the usefulness of the developed solver is demonstrated.

Exact Distortional Deformation Analysis of Steel Box Girders (강상자형 거더의 엄밀한 단면변형(Distortion) 해석)

  • 진만식;곽태영;이준석;김문영
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2002.04a
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    • pp.43-50
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    • 2002
  • Main goal of this study is to develop MATLAB programming for exact analysis of distortional deformation of the straight box girder. For this purpose, a theory for distortional deformation theory is firstly summarized and then a BEF (Beam on Elastic Foundation) theory is presented using analogy of the corresponding variables. Finally, the governing equation of the beam-column element on elastic foundation is derived. An element stiffness matrix of the beam element is established via a generalized linear eigenvalue problem. In order to verify the efficiency and accuracy of the element using exact dynamic stiffness matrix, buckling loads for the continuous beam structures with elastic foundation and distortional deformations of box girders are calculated.

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Computer Program for the solution of the Soil-Structure-Interaction Problem using the Boundary Element Method : SSI2D/3D (경계요소법을 이용한 구조물과 지반사이의 동적상호 작용 해석 전산 프로그램 : SSI2D/3D)

  • Huh, Young
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 1989.04a
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    • pp.17-21
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    • 1989
  • SSI2D/3D is a computer program to calculate dynamic stiffness matrix of the foundation for soil-structure-interaction problem in frequency demain. It is written in FORTRAN 77 and applicable to two or three dimensional situations. In this paper the program structure is summarized. Two examples aye shown to demonstrate the possibilities of the Boundary Element Method applied to dynamic problems in infinite domains.

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Optimal design of the suspension stiffness in HDD for improving the load/unload performance (램프 로드-언로드 특성 향상을 위한 서스펜션강성 최적설계)

  • 강태식;김태수;이철우
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2003.11a
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    • pp.898-901
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    • 2003
  • In order to get the drive reliability and low Power-consumption characteristics, most of small form factor HDD has und the load/unload mechanism instead of CSS type. Compared with CSS mechanism, the load/unload system has little opportunity of head/media contact during the disk spin-up and down. However, the load/unload mechanism needs the precise integration technology with slider, suspension, ramp and load/unload velocity, and all of these component s should be designed simultaneously, not an individually. In this paper, we focus the design of the suspension stiffness using the specified ABS design. We use the CML software to calculate the load/unload dynamic and use the RSM(Response surface method) to get the optimal condition of the suspension stiffness.

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