• Title, Summary, Keyword: natural mode

### A Mode Sorting Method Using the MAC of a Rotor-bearing System (MAC을 이용한 회전축계 시스템의 모드정렬 방법)

• Lim, Jonghyuk;Kim, Minsung;Lee, Kyuho;Park, Chuljun;Chung, Jintai
• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.25 no.5
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• pp.329-336
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• 2015
• This paper presents a sorting method of mode vectors and natural frequencies about a rotor-journal bearing system. The rotor is solved by the finite element method, the bearing stiffness and damping coefficient are solved by the finite difference method. At any rotation speed section through the eigenvalue analysis of the system, mode vectors and natural frequencies not sorted are confirmed via the Campbell diagram and the MAC(modal assurance criterion). To sort mode vectors and natural frequencies of the section, a mode sorting method is presented through a method of rearranging the MAC of the mode vectors. Finally, the mode vectors and the natural frequencies are sorted by using the presented method, these are verified through the MAC.

### Natural Mode Analysis for Chatter Lobe Estimation (채터로브 계산을 위한 고유모우드 분석법)

• Yoon, Moon-Chul;Cho, Hyun-Deog;Lee, Eung-Soog
• Journal of the Korean Society of Manufacturing Process Engineers
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• v.2 no.2
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• pp.60-66
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• 2003
• For the estimation of chatter lobe boundary it is very important to calculate the natural mode of cutting process. There are many time series algorithms for getting the natural mode of structural endmilling dynamics considering the cutting process. In this study, we have compared several time series methods such as AR algorithm, ARX, ARMAX, ARMA, Box Jenkins, Output Error, Recursive ARX, Recursive ARMAX considering the sampling frequency. As a results, the ARX, ARMAX and IV 4 are more desirable algorithms for the calculation of modal parameters such as natural frequency and damping ratio In endmilling operation. Also these algorithms may be adopted for the natural mode estimation of endmilling operation for chatter lobe prediction.

### Modal Analysis and Testing of a High Head Pump/Turbine Runner (고낙차 수력 펌프/터빈 런너에 대한 진동 모드해석 및 실험)

• 류석주;하현천
• Journal of KSNVE
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• v.8 no.6
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• pp.1062-1068
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• 1998
• This paper describes the vibration characteristics of a high head pump-turbine runner. with nine blades and an outer diameter of 4.410 mm. of the pumped storage power plant. Mode shapes and natural frequencies were obtained by means of both the finite element analysis and modal testing. both in air and in water. The natural frequencies in air were calculated using the finite element method by ANSYS software. In order to confirm calculation results. the natural frequencies and mode shapes of the runner were measured using a hydraulic exciter both in air and in water. Natural frequencies of the pump-turbine runner were found at 174. 310 Hz in air, and at 107. 184 Hz in water. The first mode shape is flat plate mode with two nodal diameter and the second one is also flat plate mode with three nodal diameter. It can be shown that the natural frequencies of the pump-turbine runner in water is reduced approximately 40 ％ due to additional mass effect. Natural frequencies in air predicted by ANSYS software are in good agreement with test results.

### Natural frequencies and mode shapes of thin-walled members with shell type cross section

• Ohga, M.;Shigematsu, T.;Hara, T.
• Steel and Composite Structures
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• v.2 no.3
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• pp.223-236
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• 2002
• An analytical procedure based on the transfer matrix method to estimate not only the natural frequencies but also vibration mode shapes of the thin-walled members composed of interconnected cylindrical shell panels is presented. The transfer matrix is derived from the differential equations for the cylindrical shell panels. The point matrix relating the state vectors between consecutive shell panels are used to allow the transfer procedures over the cross section of the members. As a result, the interactions between the shell panels of the cross sections of the members can be considered. Although the transfer matrix method is naturally a solution procedure for the one-dimensional problems, this method is well applied to thin-walled members by introducing the trigonometric series into the governing equations of the problem. The natural frequencies and vibration mode shapes of the thin-walled members composed of number of interconnected cylindrical shell panels are observed in this analysis. In addition, the effects of the number of shell panels on the natural frequencies and vibration mode shapes are also examined.

### Extension of a semi-analytical approach to determine natural frequencies and mode shapes of a multi-span orthotropic bridge deck

• Rezaiguia, A.;Fisli, Y.;Ellagoune, S.;Laefer, D.F.;Ouelaa, N.
• Structural Engineering and Mechanics
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• v.43 no.1
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• pp.71-87
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• 2012
• This paper extends a single equation, semi-analytical approach for three-span bridges to multi-span ones for the rapid and precise determination of natural frequencies and natural mode shapes of an orthotropic, multi-span plate. This method can be used to study the dynamic interaction between bridges and vehicles. It is based on the modal superposition method taking into account intermodal coupling to determine natural frequencies and mode shapes of a bridge deck. In this paper, a four- and a five-span orthotropic roadway bridge deck are compared in the first 10 modes with a finite element method analysis using ANSYS software. This simplified implementation matches numerical modeling within 2% in all cases. This paper verifies that applicability of a single formula approach as a simpler alternative to finite element modeling.

### A Study on the Vibration Analysis of an Automobile Steering System (승용차 스티어링 칼럼 시스템의 진동해석에 관한 연구)

• 김찬묵;김도연
• Journal of KSNVE
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• v.8 no.3
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• pp.494-503
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• 1998
• In this paper, in order to analyze dynamic characteristics of an automobile steering system consisting of many components, natural frequencies and transfer functions of each component and the total system are found on a FFT analyzer by experiments. Then, the data are transmitted to a commercial package program, CADA-PC. By analyzing the data, the mode shape of each natural frequency and damping values are obtained. Also, the function of a rubber coupling in column and telescoping effects on system are considered. C.A.E commercial programs are used to compare with the results of experiments. For the finite element modeling, I-DEAS is used. Data processing and post processing are operated on NASTRAN and XL, respectively. The ball-bearing and the linkage of shaft with column are modeled by spring element. Stiffness is modified from the results of experiments. The results of those show close agreement. In the mode shape of total system, wheel mode is dominant at lower frequency, while the column mode is main mode at higher. The role of rubber coupling in vibration isolation is clear on mode shape. Telescoping function makes natural frequency of column changed.

### Feedback scope for fault detection and localization

• Hunsang Jung;Park, Youngjin
• 제어로봇시스템학회:학술대회논문집
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• pp.32.6-32
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• 2002
• The damage localization of the structural system using the natural frequency measurement only is proposed. The existing methods use the changes of mode shape, strain mode shape or curvature mode shape before and after the damage occurrence as these shapes carry the geometric information of the structure. Basically, the change of natural frequencies of the structure can be used as the indicator of the damage occurrence but not as the indicator of the damage location as the natural frequency changes does not carry the geometric information of the structure. In this research, the feedback scope method that measures the natural frequency changes of the structure with and without the feedback Ioo...

### Flexural natural vibration characteristics of composite beam considering shear deformation and interface slip

• Zhou, Wangbao;Jiang, Lizhong;Huang, Zhi;Li, Shujin
• Steel and Composite Structures
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• v.20 no.5
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• pp.1023-1042
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• 2016
• Based on Hamilton's principle, the flexural vibration differential equations and boundary conditions of the steel-concrete composite beam (SCCB) with comprehensive consideration of the influences of the shear deformation, interface slip and longitudinal inertia of motion were derived. The analytical natural frequencies of flexural vibration were compared with available results previously observed by the experiments, the results calculated by the FE model and the other similar beam theories available in the open literatures. The comparison results showed that, the calculation results of the analytical and Timoshenko models had a good agreement with the results of the experimental test and FE model. Finally, the influences of shear deformation and interface slip on the flexural natural frequencies of the SCCB were discussed. The shear deformation effect increases with the increase of the mode orders of flexural natural vibration, and the flexural natural frequencies of the higher mode orders ignoring the influence of shear deformations effect would be overestimated. The interface slip effect decrease with the increase of the mode orders of flexural natural vibration, and the influence of the interface slip effect on flexural natural frequencies of the low mode orders is significant. The influence of the degree of shear connection on shear deformation effect is insignificant, and the low order modes of flexural natural vibration are mainly composed of the rotational displacement of cross sections.

### Dynamic Behavior Analysis of Stiffened Cylindrical Shell Filled with Fluid (내부가 유체로 채워진 보강원통쉘의 동적거동 해석)

• Youm, Ki-Un;Yoon, Kyung-Ho;Lee, Young-Shin;Kim, Jong-Kiun
• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.9
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• pp.2875-2886
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• 1996
• This work present the experimental resutls for the free vibration of unstiffened, stiffened cylindrical shell filled with air, half water and full water. The natural frequencies and mode shapes of unstiffened, stiffened cylindrical shell are obtained experimentally also. The natural frequencies of stiffened cylindrical shell were generally highter than those of unstiffened cylindrical shell and natural requencies were decreased as cylindrical shell was filled with water. The effect of circumferential stiffener in the first mode was shown that natural frequency more increased 25% at air environment, 29% at half water environment and 37% at full water than those of unstiffened cylindrical shell, respectively. Also, the natural frequencies were decreased according to the added mass effect of fluid in the shell of unstiffened and stiffened cylindrical shell. The six mode shape results of all cases are simular and given. The natural frequencies are determined for a wide range of parameters : e.g. unstiffened shell, and filled with air, half and full water. The effects of varying the parameters on the free vibration frequencies and mode shapes are discussed.