• Title/Summary/Keyword: mode shape and natural frequency

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Experimental study of extracting artificial boundary condition frequencies for dynamic model updating

  • Hou, Chuanchuan;Mao, Lei;Lu, Yong
    • Smart Structures and Systems
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    • v.20 no.2
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    • pp.247-261
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    • 2017
  • In the field of dynamic measurement and structural damage identification, it is generally known that modal frequencies may be measured with higher accuracy than mode shapes. However, the number of natural frequencies within a measurable range is limited. Accessing additional forms of modal frequencies is thus desirable. The present study is concerned about the extraction of artificial boundary condition (ABC) frequencies from modal testing. The ABC frequencies correspond to the natural frequencies of the structure with a perturbed boundary condition, but they can be extracted from processing the frequency response functions (FRF) measured in a specific configuration from the structure in its existing state without the need of actually altering the physical support condition. This paper presents a comprehensive experimental investigation into the measurability of the ABC frequencies from physical experiments. It covers the testing procedure through modal testing, the data processing and data analysis requirements, and the FRF matrix operations leading to the extraction of the ABC frequencies. Specific sources of measurement errors and their effects on the accuracy of the extracted ABC frequencies are scrutinised. The extracted ABC frequencies are subsequently applied in the damage identification in beams by means of finite element model updating. Results demonstrate that it is possible to extract the first few ABC frequencies from the modal testing for a variety of artificial boundary conditions incorporating one or two virtual pin supports, and the inclusion of ABC frequencies enables the identification of structural damages without the need to involve the mode shape information.

Algebraic Method for Computation of Natural Frequency and Mode Shape Sensitivities (고유진동수와 모드의 민감도를 계산하기 위한 대수적 방법)

  • Jung, Gil-Ho;Kim, Dong-Ok;Lee, Chong-Won;Lee, In-Won
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.21 no.5
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    • pp.707-718
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    • 1997
  • This paper presents an efficient numerical method for the computation of eigenpair derivatives for a real symmetric eigenvalue problem with distinct and multiple eigenvalues. The method has a very simple algorithm and gives an exact solution. Furthermore, it saves computer sotrage and CPU time. The algorithm preserves not only the symmetricity but also the band width of the matrices, allowing efficient computer storage and solution techniques. Results from the proposed method for calculating the eigenpair derivatives are compared with those from Rudisill and Chu's method and Nelson's method which is known efficient one in the case of distinct natural frequencies. As an example to demonstrate the efficiency of the proposed method in the case of distinct eigenvalues, a cantilever plate is considered. The design parameter of the cantilever plate is its thickness. For the eigenvalue problem with multiple natural frequencies, the adjacent eigenvectors are used in the algebraic equation as side conditions, lying adjacent to the multiplicity of multiple natural frequency distinct eigenvalues, which appear when design parameter varies. A cantilever beam is used to demonstrate the efficiency of the proposed method in the case of multiple natural frequencies. Results form the proposed method for calculating the eigenpair derivatives are compared with those from Dailey's method(an amendation of Ojalvo's work) which finds the exact eigenvector derivatives. The design parameter of the cantilever beam is its height. Data is presented showing the amount of CPU time used to compute the first ten eigenpair derivatives by each method. It is important to note that the numerical stability of the proposed method is proved.

High Precision Measurement for String Resonator used in FBG Strain Sensors (광섬유 브래그 격자 변형률 센서용 현공진기의 고정밀 측정)

  • 이영균;송인천;정성호;이병하;이선규
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 2001.04a
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    • pp.135-139
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    • 2001
  • This paper describes a string resonator that is used for the interrogation system of a Fiber Bragg Grating(FBG) strain sensor. The strain on the fiber piece is calculated from the measured frequency based on that the natural frequency of a string is a function of the applied absolute strain. Existing research considered a fiber as a string, but a fiber is not a string in the strict sense due to its bending stiffness, thus the fiber should be modeled as a beam accompanied with an axial force. In the vibration modeling, the relationship between the strain and the natural frequency is derived, and then the resonance condition is described in terms of both the phase and the mode shape for sustaining resonant motion. Several experiments verify the effectiveness of the proposed model of the fiber. The performance of the string resonator is analyzed by measuring the frequency change according to the applied strains in the dynamic range of 1100$\mu\varepsilon$ referred to the displacement from capacitance sensor. From the experimental results, the implemented string resonator provides the accuracy of $\pm$3$\mu\varepsilon$, the quasi-static resolution of ~0.1$\mu\varepsilon$(rms) which amount to be $\pm$0.17$\mu\textrm{m}$ and ~6nm respectively, in case of fiber length of 56mm. For a dynamic strain, it can provide the accuracy of ~3$\mu\varepsilon$ until the frequency comes to 8Hz. As a consequence, the string resonator proposed for FBG sensor provides the high accuracy and the high resolution in strain measurement, and also it is expecting to be used, for the application, to not only strain but also displacement measuring device.

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Effects of Design Conditions in Five Pad Tilting Pad Bearing on the Lateral Vibration Characteristics of Small Gas Turbine (5패드 틸팅 패드 베어링의 설계 조건 변화가 소형 가스터빈의 횡진동 특성에 미치는 영향)

  • Ha, Jin-Woong;Myung, Ji-Ho;Suk, Jhin-Ik;Lee, An-Sung;Kim, Young-Cheol
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.21 no.8
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    • pp.752-760
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    • 2011
  • In tilting pad bearing design process, the selection of the proper configuration type of either a load-between-pad(LBP) or load-on-pad(LOP) as well as preload and pivot offset conditions is to be carefully considered. Also the bearing needs to be designed in order to be suited for the rotor-bearing system and operating condition. In this paper, it is observed that the dynamic characteristics in a five pad tilting pad bearing for the LBP and the LOP configurations are influenced by the variation of preload and pivot offset. In this context, rotor dynamic analysis of the 5 MW industrial gas turbine supported by the tilting pad bearing at the front and roller bearing at the rear is carried out based on the dynamic coefficients of the tilting pad bearing investigated. The result shows that two rigid body critical modes experience various changes according to the influence of the tilting pad bearing uniquely applied to one side of this machine. Mainly, the second critical speed, the rigid body mode of conical shape with high whirling in the tilting pad bearing, is significantly changed by preload and pivot offset regardless of the LBP and LOP configurations. And, the first critical mode, the rigid body mode of conical shape with high whirling in the roller bearing, is sensitively affected by preload applied to the LOP configuration and by its asymmetric dynamic properties.

Effects of Design Conditions in Five Pad Tilting Pad Bearing on the Lateral Vibration Characteristics of Small Gas Turbine (5패드 틸팅 패드 베어링의 설계 조건 변화가 소형 가스터빈의 횡진동 특성에 미치는 영향)

  • Ha, Jin-Woong;Myung, Ji-Ho;Suk, Jhin-Ik;Lee, An-Sung;Kim, Young-Cheol
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2011.04a
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    • pp.425-432
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    • 2011
  • In tilting pad bearing design process, the selection of the proper configuration type of either a Load-Between-Pad (LBP) or Load-On-Pad (LOP) as well as preload and pivot offset conditions is to be carefully considered. Also the bearing needs to be designed in order to be suited for the rotor-bearing system and operating condition. In this paper, it is observed that the dynamic characteristics in a 5 pad tilting pad bearing for the LBP and the LOP configurations are influenced by the variation of preload and pivot offset. In this context, rotor dynamic analysis of the 5MW industrial gas turbine supported by the tilting pad bearing at the front and roller bearing at the rear is carried out based on the dynamic coefficients of the tilting pad bearing investigated. The result shows that two rigid body critical modes experience various changes according to the influence of the tilting pad bearing uniquely applied to one side of this machine. Mainly, the second critical speed, the rigid body mode of conical shape with high whirling in the tilting pad bearing, is significantly changed by preload and pivot offset regardless of the LBP and LOP configurations. And, the first critical mode, the rigid body mode of conical shape with high whirling in the roller bearing, is sensitively affected by preload applied to the LOP configuration and by the its asymmetric dynamic properties.

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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.

Vibration measures for local structures through modal tests (모달시험을 통한 국부 구조물 방진대책 수립)

  • Kwon, Jong Hyun;Kim, Mun Su;Yang, Sung Boong;Lee, Won Seok;Lee, Bong Min
    • Special Issue of the Society of Naval Architects of Korea
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    • 2017.10a
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    • pp.14-18
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    • 2017
  • The Lashing bridge and radar mast of ship are upright structures so they are generally exposed to excessive vibration. Recently, the use of low speed main engines for improving fuel efficiency has been increasing, and the excitation frequencies of the main engine are moving to the low frequency band. If the excitation frequencies are coincident with the natural frequencies of the local structure, excessive vibration occurs during main engine operating condition. The modal test is to experimentally determine resonance frequency, mode shape, and damping, which are vibration characteristics of a mechanical structure under dynamic external force. Through this study, the vibration characteristics of the structure are obtained by modal tests and the low vibration measure is applied to the local structures.

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Modal Test of Missile Structure with Live Warhead and Propellant (활성탄 전기체 동특성 시험기법 연구)

  • Kang, Hwi-Won;Jeon, Byoung-Hee;Yang, Myung-Seog
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2005.11b
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    • pp.57-60
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    • 2005
  • Modal parameters of a structure are the important factor to control the missile maneuver. In general, a dummy structure is used for the modal test of missile structure instead of the real warhead and propellant because there may be the danger of a explosion by the electric shock of test equipment, such as the exciter and the power amplifier. However, the modal testing of a real missile structure is required to acquire the modal parameters and to analyze the missile performance accurately. The new test system and technique are developed to get rid of the danger and secure the safety during the testing. This test system is made of with the computer network system and controlled remote from test site. Using His new test system, the modal test of real missile structure is performed successfully and its validity is proven.

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Dynamic Characteristics of Cable-Stayed Anchorage considering Cracks at Bolt and Welding Connection (용접 및 볼트 연결부 균열을 고려한 사장교 케이블 정착부의 동특성 해석)

  • Kim, Chul Young;Kim, Sung Bo;Jung, Woo Tai
    • Journal of Korean Society of Steel Construction
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    • v.11 no.4 s.41
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    • pp.351-362
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    • 1999
  • Damage detection methods which utilize the change in dynamic characteristics are very hard to apply to large civil structures since local damage hardly affects global dynamic characteristics. But, if there is a very important and critical member and we focus only on the local behavior of it, it would be possible to detect damage from the change in local dynamic characteristics, such as natural frequencies and mode shapes .In this study, the cable anchorage part of a cable-stayed bridge under construction is modeled and analyzed by commercial finite element program, ABAQUS. It has both welding and bolting connections with a cable and a stiffening plate, and has a possible high stress concentration portions in it. Several damage scenarios such as crack through the welding or crack through the bolting connection are examined. The result shows that the local natural frequencies of the damaged member decrease up to 16% compared with that of the undamaged member. It is concluded that there is quite a high feasibility that the damage of the cable anchorage can be detected by measuring local dynamic characteristics.

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The Design and Dynamic Characteristics Analysis of the Grinder Bed using Epoxy-Granite (에폭시-그래나이트재를 이용한 연삭기 베드의 설계 및 동특성 해석)

  • 박영일
    • Journal of the Korean Society of Manufacturing Technology Engineers
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    • v.8 no.2
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    • pp.62-72
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    • 1999
  • In this study, the griding machine bed was designed and analyzed by using epoxy-granite. Finite element technique was employed to design and analyze the composite bed structure. Von Mises stress and relative displacements between a tool and a workpiece were checked to compare a cast iron bed structure with a composite bed structure. Dynamic features of structures were also studied according to the process of modal analysis through natural frequency and mode shape measurement. Another improved model was also designed using the accumulation of knowledge based on the use of the structural analysis and experiments. Comparing with the cast iron bed structure, the composite bed structure maintains better functions.

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