• Title, Summary, Keyword: Free vibration

### Free Vibration Analysis of Arbitrarily Shaped Plates with Free Edges Using Non-dimensional Dynamic Influence Functions (무차원 동영향 함수를 이용한 자유단 경계를 가진 임의 형상 평판의 자유진동해석)

• 강상욱;김일순;이장무
• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.10
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• pp.821-827
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• 2003
• The so-called boundary node method (or NDIF method) that was developed by the authors has been extended for free vibration analysis of arbitrarily shaped plates with free edges. Since the proposed method requires no interpolation functions. no integration Procedure is needed on boundary edges of the plates and only a small amount of numerical calculation is involved, compared with FEM and BEM. In order to explain tile reason why spurious eigenvalues are generated when the NDIF method is applied to free plates, the NDIF method has been considered for free vibration analysis of both a fixed string and a free beam. Finally, verification examples show that natural frequencies obtained by the present method agree well with those given by an exact method or a numerical method (ANSYS).

### Application of Numerical Differentiations in Free Vibration Analysis (자유진동 해석에서 수치미분의 응용)

• 이병구;안대순;강희종;김권식
• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• pp.814-818
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• 2003
• This paper deals with the application of numerical differentiation in free vibration analysis. In the free vibration analysis, the derivative values of the given function are certainly used in calculation of structural parameters. For deriving the derivative values, both the time and labor are needed when the structures consist of non-linear geometries such as arches or curved beams. From this viewpoint, the numerical differentiation scheme is applied into the free vibration analysis. The numerical results obtained from the numerical differentiations are agreed very well with those obtained from the exact derivatives by analytical method. It is expected that the numerical differentiations can be utilized practically in the free vibration analysis.

### Free Vibration Analysis of an Annular Plate by the Independent Coordinate Coupling Method (독립좌표연성법을 이용한 원환판의 자유진동해석)

• Heo, Seok;Kwak, Moon-K.
• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.5
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• pp.564-571
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• 2008
• This paper is concerned with the free vibration analysis of an annular plate with boundary conditions of simply supported-free, clamped-free and free-free, respectively. Exact solutions for the natural frequency and mode of an annular plate can be obtained by solving the differential equation but other methods such as the Rayleigh-Ritz method and the finite element method can be also used. In this research, we applied the Independent Coordinate Coupling Method(ICCM) to the annular plate and prove that the ICCM can accurately predict the natural frequency and mode shape of the annular plate. The numerical results show that the ICCM can be used effectively for the free vibration problem of plate with a hole compared to the Rayleigh-Ritz method and the finite element method.

### Free vibration analysis of tapered beam-column with pinned ends embedded in Winkler-Pasternak elastic foundation

• Civalek, Omer;Ozturk, Baki
• Geomechanics and Engineering
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• v.2 no.1
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• pp.45-56
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• 2010
• The current study presents a mathematical model and numerical method for free vibration of tapered piles embedded in two-parameter elastic foundations. The method of Discrete Singular Convolution (DSC) is used for numerical simulation. Bernoulli-Euler beam theory is considered. Various numerical applications demonstrate the validity and applicability of the proposed method for free vibration analysis. The results prove that the proposed method is quite easy to implement, accurate and highly efficient for free vibration analysis of tapered beam-columns embedded in Winkler- Pasternak elastic foundations.

### Free Vibration and Dynamic Stability of the Axially Moving Continuum with Time-varying Length (축방향으로 이동하며 길이가 변하는 연속체의 자유 진동 및 동적 안정성)

• 사재천;이민형;이승엽
• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.4
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• pp.272-279
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• 2002
• The time-dependent frequency and energy of free vibration of the spagetti problem, that is the axially moving continuum with time-varying length, are investigated. Exact expressions for the natural frequency and time-varying vibration energy are derived by dealing with traveling waves. The vibration period increases with increasing length, but the free vibration energy decreases. When the string undergoes retraction, the vibration energy increases with time. The free response of the time-varying string is represented by superposing two traveling waves.

### Free Vibration Analysis of Timoshenko Arcs with Elastic Supports Using Transfer of Influence Coefficient (영향계수의 전달을 이용한 탄성 지지된 티모센코 호의 자유진동 해석)

• Choi, Myung-Soo;Yeo, Dong-Jun
• Journal of Power System Engineering
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• v.21 no.2
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• pp.70-76
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• 2017
• When Timoshenko arcs considering the shear deformation and rotatory inertia have elastic supports, the authors analyze in-plane free vibration of them by the transfer influence coefficient method. This method finds the natural frequencies of them using the transfer of influence coefficient after obtaining the transfer matrix of arc element from numerical integration of the differential equations governing the vibration of arc. In this study, two computer programs were made by the transfer influence coefficient method and the transfer matrix method for analyzing free vibration of Timoshenko arcs. From numerical results of four computational models, we confirmed that the transfer influence coefficient method is a reliable method when analyzing the free vibration of Timoshenko arcs. In particular, the transfer influence coefficient method is a effective method when analyzing the free vibration of arcs with rigid supports.

### Free Vibration Analysis of a Circular Plate with an Eccentric Circular Hole by the Independent Coordinate Coupling Method (독립좌표연성법을 이용한 편심 된 원형 구멍을 갖는 원판의 자유진동해석)

• Heo, Seok;Kwak, Moon-K.
• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.6
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• pp.681-689
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• 2008
• This paper is concerned with the free vibration analysis of a circular plate with an eccentric circular hole by the Independent coordinate coupling method(ICCM). It was proved in the previous study that the ICCM can accurately predict the natural frequencies and mode shapes of the annular plates and can also be used for the free vibration analysis of the simply-supported circular plate with an eccentric circular hole. In this study, the clamped and free boundary conditions were considered for the circular plate. The numerical results show that the ICCM can be used effectively for the free vibration problem of circular plate with an eccentric hole compared to the finite element method.

### Free Vibration Analysis of Arbitrarily Shaped Polygonal Plates with Free Edges by Considering the Phenomenon of Stress Concentration at Corners (꼭지점에서의 응력 집중 현상을 고려한 자유단 경계조건을 가진 임의 다각형 형상 평판의 자유 진동 해석)

• Kang, Sang-Wook
• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.3
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• pp.220-225
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• 2007
• Free vibration analysis using the method of NDIF (non-dimensional dynamic influence function), which was developed by the author, is extended to arbitrarily shaped polygonal plates with free edges. Local Cartesian coordinate systems are employed to apply the free boundary condition to nodes distributed along the edges of the plate of interest. Furthermore, a new way for applying the free boundary condition to nodes located at corners of the plate is for the first time introduced by considering the phenomenon of stress concentration at the corners. Two case studies show that the proposed method is valid and accurate when the eigenvalues by the proposed method are compared to those by FEM(ANSYS).

### The effect of internal axial forces of a cantilever beam with a lumped mass at its free end

• Zhang, Jinfu
• Coupled systems mechanics
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• v.7 no.3
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• pp.321-331
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• 2018
• When a cantilever beam with a lumped mass at its free end undergoes free transverse vibration, internal axial forces are produced in the beam. Such internal axial forces have an effect on free transverse vibration of the beam. This effect is studied in this paper. The equations of motion for the beam in terms of the generalized coordinates including the effect are derived. The method for determining free transverse vibration of the beam including the effect is presented. In numerical simulations, the results of free transverse vibration of the free end of the beam including and not including the effect are obtained. Based on comparison between the results obtained, the conclusions concerning the effect are given.

### Torsional Free Vibration Analysis of Propulsion Shafting of Training Ship SAEDONGBAEK by Sylvester-Transfer Stiffness Coefficient Mehtod (실베스터-전달강성계수법에 의한 실습선 새동백호 추진축계의 비틀림 자유진동 해석)

• Kim, Myung-Jun;Wang, Woo-Gyeong;Yeo, Dong-Jun;Choi, Myung-Soo
• Journal of Power System Engineering
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• v.22 no.6
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• pp.11-19
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• 2018
• In this study, the authors examine the propulsion shafting of the training ship SAEDONGBAEK and perform modeling to analyze the torsional free vibration of the shafting. In this paper, the computational algorithm for analyzing the torsional free vibration of the shafting with a reduction gear is formulated by the sylvester-transfer stiffness coefficient method (S-TSCM) that is a recently developed and a powerful method in free vibration analysis. According to the state of the controllable pitch propeller of the shafting and the temperature of the elastic coupling, the torsional free vibration of the shafting is performed by the S-TSCM. The authors examine the changes of the natural frequencies and natural modes which are the results of the torsional free vibration analysis of the shafting.