• Title/Summary/Keyword: Modal-force Equation

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Design of a decoupled PID controller via MOCS for seismic control of smart structures

  • Etedali, Sadegh;Tavakoli, Saeed;Sohrabi, Mohammad Reza
    • Earthquakes and Structures
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    • v.10 no.5
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    • pp.1067-1087
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    • 2016
  • In this paper, a decoupled proportional-integral-derivative (PID) control approach for seismic control of smart structures is presented. First, the state space equation of a structure is transformed into modal coordinates and parameters of the modal PID control are separately designed in a reduced modal space. Then, the feedback gain matrix of the controller is obtained based on the contribution of modal responses to the structural responses. The performance of the controller is investigated to adjust control force of piezoelectric friction dampers (PFDs) in a benchmark base isolated building. In order to tune the modal feedback gain of the controller, a suitable trade-off among the conflicting objectives, i.e., the reduction of maximum modal base displacement and the maximum modal floor acceleration of the smart base isolated structure, as well as the maximum modal control force, is created using a multi-objective cuckoo search (MOCS) algorithm. In terms of reduction of maximum base displacement and story acceleration, numerical simulations show that the proposed method performs better than other reported controllers in the literature. Moreover, simulation results show that the PFDs are able to efficiently dissipate the input excitation energy and reduce the damage energy of the structure. Overall, the proposed control strategy provides a simple strategy to tune the control forces and reduces the number of sensors of the control system to the number of controlled stories.

Selection of Connection Position to Change Dynamic Characteristic of Structure (동특성 변경을 위한 구조물의 결합 위치 선정)

  • Kim, Kyung-Won;Park, Youn-Sik;Kim, Sung-Hoon;Kim, Jin-Hee;Rhee, Ju-Hun;Hwang, Do-Soon
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.13 no.12
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    • pp.930-937
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    • 2003
  • This research deals with how to select connection positions of two substructures to be synthesized. The goal of this research is to find optimal connection positions in order to maximize the fundamental natural frequency of the synthesized structure. The natural frequencies of a connected structure are obtained by modal-force equations. Optimal connection positions can be selected through optimization process. In the optimization process, the natural frequencies of a connected structure are set to object function value and connection positions become design variables. The method described above is applied to synthesis problems of plates, which is initially conducted for FE models and verified through experiments. Especially in experiments. FRF(frequency response function) s are obtained by means of the Modal Testing technique to be used in modal-force equations for synthesizing. Once the substructures are synthesized. the Modal Testing technique is again applied to spot-welded structure using the result from the optimization procedure. It is found that the fundamental natural frequency of the synthesized structure with the optimized result gives higher value than those with the initially given connection positions.

Selection of Connection Position to Change Dynamic Characteristic of Structure (동특성 변경을 위한 구조물의 결합 위치 선정)

  • 김경원;박윤식;박영진
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2003.05a
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    • pp.65-71
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    • 2003
  • This research deals with how to select connection positions of two substructures to be synthesized. The goal of this research is to find optimal connection positions in order to maximize the fundamental natural frequency of the synthesized structure. The natural frequencies of a connected structure are obtained by modal-force equations. Optimal connection positions can be selected through optimization process. In the optimization process, the natural frequencies of a connected structure are set to object function value and connection positions become design variables. The method described above is applied to synthesis problems of plates, which is initially conducted for FE models and verified through experiments. Especially in experiments, FRE(frequency Response function)s are obtained by means of the Modal Testing technique to be used in modal-force equations for synthesizing. Once the substructures are synthesized, the Modal Testing technique is again applied to spot-welded structure using the result from the optimization procedure. It is found that the fundamental natural frequency of the synthesized structure with the optimized result gives higher value than those with the initially given connection positions.

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Non-spillover control design of tall buildings in modal space

  • Fang, J.Q.;Li, Q.S.;Liu, D.K.
    • Wind and Structures
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    • v.2 no.3
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    • pp.189-200
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    • 1999
  • In this paper, a new algorithm for active control design of structures is proposed and investigated. The algorithm preserves the decoupling property of the modal vibration equation and eliminates the spillover problem, which is the main shortcoming in the independent modal space control(IMSC) algorithm. With linear quadratic regulator(LQR) control law, the analytical solution of algebraic Riccati equation and the optimal actuator control force are obtained, and the control design procedure is significantly simplified. A numerical example for the control design of a tall building subjected to wind loads demonstrates the effectiveness of the proposed algorithm in reducing the acceleration and displacement responses of tall buildings under wind actions.

Active control of a flexible structure with time delay

  • Cai, Guo-Ping;Yang, Simon X.
    • Structural Engineering and Mechanics
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    • v.20 no.2
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    • pp.191-207
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    • 2005
  • Time delay exists inevitably in active control, which may not only degrade the system performance but also render instability to the dynamic system. In this paper, a novel active controller is developed to solve the time delay problem in flexible structures. By using the independent modal space control method, the differential equation of the controlled mode with time delay is obtained from the time-delay system dynamics. Then it is discretized and changed into a first-order difference equation without any explicit time delay by augmenting the state variables. The modal controller is derived based on the augmented system using the discrete variable structure control method. The switching surface is determined by minimizing a discrete quadratic performance index. The modal coordinate is extracted from sensor measurements and the actuator control force is converted from the modal one. Since the time delay is explicitly included throughout the entire controller design without any approximation, the system performance and stability are guaranteed. Numerical simulations show that the proposed controller is feasible and effective in active vibration control of dynamic systems with time delay. If the time delay is not explicitly included in the controller design, instability may occur.

Applicaion of Sensitivity Formulation to Analyze the Dynamic Response due to the Excitation Force for the Undamped Vibration of Cantilever Beam (외팔보의 비감쇠 진동시 가진력에 의한 동적 반응의 민감도 정식화 및 해석)

  • Yun, Seong-Ho
    • Journal of the Korean Society of Manufacturing Process Engineers
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    • v.19 no.11
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    • pp.29-34
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    • 2020
  • In this study, a sensitivity formulation was applied to analyze the dynamic response due to the effect of the excitation force for the undamped vibration of the cantilever beam. The theoretically fundamental formulations were derived considering an eigenvalue problem and its modal analysis to govern the second order algebraic differential equation in terms of the change in the modal coordinate with respect to the design parameters. A representative physical quantity pertaining to the dynamic response, that is, the rate of change in the dynamic displacement, was observed by changing the design variables, such as the cross-sectional area of the beam. The numerical results were obtained at various locations, considering the application of the external forces and observation of the dynamic displacement. When the detection position was closer to the free end of the cantilever beam, the sensitivity of the dynamic displacement was higher, as predicted through the oscillating motion of the beam. The presented findings can provide guidance to compute the dynamic sensitivity for a flexibly connected structure under dynamic excitations.

The effect of Local Vibration Modes on the Flutter (국부진동모드가 플러터해석에 미치는 영향연구)

  • Shin, Young-Sug;Kim, Heon-Ju;Kim, Seong-Tae;Kim, Jae-Young;Hwang, Chul-Ho
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.39 no.10
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    • pp.919-926
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    • 2011
  • The fin of high speed air vehicle is composed of skins and strong skeletons. In the flutter analysis, the eigenmodes of a fin are used for evaluating the unsteady aerodynamic force and the modal approach is applied for solving the flutter equation in both time and frequency domain. Therefore, the proper eigenmodes used for a modal flutter analysis should be chosen. For the appropriate choice of eigenmodes, when there exist local modes of a skin in the high modes, the effects of those modes on the unsteady aerodynamic force and flutter characteristics are anlalyzed.

A Study for The Comparison of Structural Damage Detection Method Using Structural Dynamic Characteristic Parameters (구조 동특성 파라미터를 이용한 구조물 손상 탐색기법 비교 연구)

  • Choi, Byoung-Min;Woo, Ho-Kil
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.17 no.3 s.120
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    • pp.257-263
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    • 2007
  • Detection of structural damage is an inverse problem in structural engineering. There are three main questions in the damage detection: existence, location and extent of the damage. In concept, the natural frequency and mode shapes of any structure must satisfy an eigenvalue problem. But, if a potential damage exists in a structure, an error resulting from the substitution of the refined analytical finite element model and measured modal data into the structural eigenvalue equation will occur, which is called the residual modal forces, and can be used as an indicator of potential damage in a structure. In this study, a useful damage detection method is proposed and compared with other two methods. Two degree-of-freedom system and Cantilever beam are used to demonstrate the approach. And the results of three introduced method are compared.

Element Design of Balancing Shaft for Reducing the Vibration in Engine Module (엔진진동 저감을 위한 밸런싱샤프트의 요소설계 기법 연구)

  • Kim, Chan-Jung;Beak, Gyoung-Won;Lee, Bong-Hyun;Kim, Gi-Hoon
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2005.05a
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    • pp.615-620
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    • 2005
  • Vibration in Engine module could be reduced by introducing a balance shaft module which has one or more unbalanced rotors. The unbalanced rotor is unbalanced in one direction that act as a opposite direction of the inertia force or moment triggered by engine component so that the largest order factor in vibration is efficiently decreased The ability of balance shaft to reduce the order element of engine component is investigated by a vehicle testing that is focused on comparing the vibration with balance shaft to that of without balance shaft. One of the commonly adapted balance shaft is tested by modal scheme for indemnifying the dynamic characteristics and an, the modal information is used for a clue to design the balance shaft module. The essential equation deriving the design parameters of unbalanced rotor is also presented for two cases, 3 in-ling and 4 in-ling cylinder model. Finally, the overall design process is explained with flow chart.

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Development of Truck Crane Analysis Program with Boom Flexibility (붐의 유연성을 고려한 트럭크레인의 설계 전용 동력학 해석 프로그램 개발)

  • 박찬종
    • Journal of the Korean Society of Manufacturing Technology Engineers
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    • v.7 no.6
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    • pp.28-35
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    • 1998
  • Computer simulation technique has been applied on the various engineering fields to reduce cost and development period. On this paper, we introduce a crane analysis program. Using this program, we can predict reaction force of each part or supporting force of truck crane on a personal computer system with out exclusive knowledge of multi-body dynamics. In order to consider the effect of boom flexibility according to each working condition, flexible dynamic theory is applied to the program. Actual crane model is analyzed on special work condition using this program and the results are compared with those of rigid boom model.

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