• Title/Summary/Keyword: modes of vibration

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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.

Prediction of elastic constants of Timoshenko rectangular beams using the first two bending modes

  • Chen, Hung-Liang (Roger);Leon, Guadalupe
    • Structural Engineering and Mechanics
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    • v.80 no.6
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    • pp.657-668
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    • 2021
  • In this study, a relationship between the resonance frequency ratio and Poisson's ratio was proposed that can be used to directly determine the elastic constants. Using this relationship, the frequency ratio between the 1st bending mode and 2nd bending mode for any rectangular Timoshenko beam can be directly estimated and used to determine the elastic constants efficiently. The exact solution of the Timoshenko beam vibration frequency equation under free-free boundary conditions was determined with an accurate shear shape factor. The highest percent difference for the frequency ratio between the theoretical values and the estimated values for all the beam dimensions studied was less than 0.02%. The proposed equations were used to obtain the elastic constants of beams with different material properties and dimensions using the first two measured transverse bending frequencies. Results show that using the equations proposed in this study, the Young's modulus and Poisson's ratio of rectangular Timoshenko beams can be determined more efficiently and accurately than those obtained from industry standards such as ASTM E1876-15 without the need to test the torsional vibration.

PID Control of a flexible robot rotating in vertical plane (수직면에서 회전운동을 하는 탄성로봇의 PID 제어)

  • Kang, Junwon;Oh, Chaeyoun;Kim, Kiho
    • Journal of the Korean Society for Precision Engineering
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    • v.14 no.11
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    • pp.34-41
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    • 1997
  • This paper presents a technique to control a very flexible robot moving in a vertical plane. The flexible robot is modeled as an Euler-Bernoulli beam. Elastic deformation is approximated using the assmed modes method. A comparison function which satisfies all geometric and natural boundary conditions of a cantilever beam with an end mass is used as an assumed mode shape. Lagrange's equation is utilized for the development of a discretized model. A control algorithm is developed using a simple PID cnotrol tech- nique. The proportional, integral and deivative control gains are determined based on the dominant pole placement method and tuned to show no overshoot and no steady state error, and short settling time. The effectiveness of the developed control scheme is showed in the hub angular diaplacement control experiment. Three different end masses are uned in the experiment. The experimental results show that developed control algorithm is very effective showing little overshoot, no steady state error, and less than 2.5 second settl- ing time in case of having an end mass which is equivalent to 45% of the manipulator mass. Also the experimental results show that the residual vibration fo the end point is effectively controlled.

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Study on Dynamic Characteristic and Safety of 45m Steel Box Railway Bridge according to Girder hight and Ballast (강상형 철도교의 도상종류와 형고에 따른 동특성 및 안정성 연구)

  • Yun, Ji-Hong;Choi, Kwon-Young;Kwon, Ku-Sung;An, Ju-Ok;Chung, Won-Seok
    • Proceedings of the KSR Conference
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    • 2011.10a
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    • pp.3147-3155
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    • 2011
  • Railway bridges are highly susceptible to resonance due to the equidistant axle load with constant speed of train. Thus, it is inevitable verify dynamic characteristics and quantities against dynamic guidelines. Recently, various new-type bridges are developed and applies to medium span length between 30m and 40m. However, just steel box girder bridge is under review for span length between 45m and 50m without development any new technologies. This study investigate the dynamic properties and safety of steel box railway bridge having span length 45m in alternative girder hight and kind of ballast. Numerical analysis is performed time series analysis by mode superposition using calculated natural vibration frequency and mode after carry out a free vibration analysis and extract modal parameter to higher modes. The results are then compared to various dynamic stability standards toward target bridge's dynamic stability analysis. The result of this study is expected as a reference for design railway bridges.

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Structure Excitation by Using Beating (맥놀이 현상을 이용한 구조물 진동 가진)

  • Choi, Young-Chul;Park, Jin-Ho;Yoon, Doo-Byoung
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.19 no.10
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    • pp.1028-1033
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    • 2009
  • To detect faults and monitor thinning on a pipe, many people use ultra sonic sensors that are operated in high frequency range. Because there are many modes in high frequency range, it is difficult to find faults and monitor pipe thinning on a structure. If we deal with signals in a low frequency range which include only A0 wave and S0 wave, the information of monitoring and diagnosis can be easily obtained. In this paper, the technique for exciting low frequency range using ultra sonic sensors is proposed. The main idea of the proposed method comes from the beat phenomenon. The beat frequency is equal to the absolute value of the difference in frequency of the two waves. If the beat frequency is tuned by two ultra waves, we can excite A0 mode and S0 mode of structures. To verify the proposed method, we have performed a steel plate and pipe experiments. Experimental results show that two ultra sonic sensors can well excite low frequency range.

Forced Response Analyses of a Bladed Disk with Friction Dampers (마찰감쇠기가 있는 블레이드디스크의 강제진동해석)

  • Yoo, Jae-Han;Lee, In
    • Journal of the Korean Society of Propulsion Engineers
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    • v.14 no.5
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    • pp.15-23
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    • 2010
  • To reduce the vibration levels, additional dissipation elements such as dry friction dampers are sometimes integrated into bladed disk assembly. In this study, forced response analysis systems for a tuned bladed disk with friction dampers were developed and verified. For the efficient nonlinear vibration analysis, multi-harmonic balanced method and cyclic boundary condition were used. Also, mode shapes obtained using fictitious mass method were used to describe the motion of the structures with the concentrated structural nonlinearity, friction damper. The relative convergence of fictitious mass and traditional unconstrained modes were compared.

Acoustic Scattering from Circular Cylinder by Periodic Sources (주기적인 음원에 의한 원형 실린더의 음향 산란)

  • Lee, Duck-Joo;Kim, Yong-Seok
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.17 no.1 s.118
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    • pp.41-47
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    • 2007
  • Scattering fields of two dimensional acoustic waves by a circular cylinder are investigated. The present numerical approach for the acoustic scattering problem has difficulties of numerical robustness, long-time stability and suitability of far-field boundary treatments. The time-dependent periodic acoustic source is used to analyze Interference patterns between incident waves and waves reflected by the cylinder. Characteristic boundary algorithms coupled with 4th order Modified-Flux-Approach ENO(essentially non-oscillatory) schemes are employed in generalized coordinates to examine the effect of the wane frequency on the interference patterns. Non-reflecting boundary conditions, which is crustal for accurate computations of aeroacoustic problems, are used not to contaminate scattering fields by reflected waves at the outer boundary. Computed scattering fields show the circumferential acoustic modes generated by interacting between acoustic sources and scattered waves. At a lower frequency, the wave passes almost straight through the cylinder without Interacting with circular cylinder. Simulation results are presented and compared with the analytic solution. Computed RMS-pressure distribution on the cylinder wall is good agreement with exact solution.

Wave Models and Experimental Studies of Beam-plate-beam Coupled Systems for a Mid-frequency Analysis (중주파수 대역 해석을 위한 Beam-plate-beam 연성 구조물의 웨이브 모형 연구와 시험적 규명)

  • Yoo, Ji-Woo;Thompson, D.J.;Ferguson, N.S.
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.17 no.2 s.119
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    • pp.121-129
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    • 2007
  • There has been much effort to find suitable methods for structural analysis in the mid-frequency region where traditional low frequency methods have increasing uncertainties whilst statistical energy analysis is not strictly applicable. Systems consisting of relatively stiff beams coupled to flexible plates have a particularly broad mid-frequency region where the beams support only a few modes whilst the plate has a high modal density and modal overlap. A system of two parallel beams coupled to a plate is investigated based on the wave method, which is an approximate method. Muller's method is utilised for obtaining complex roots of a dispersion wave equation, which does not converge in the conventional wave method based on a simple iteration. The wave model is extended from a single-beam-plate system, to a plate with two identical beams which is modelled using a symmetric-antisymmetric technique. The important hypothesis that the coupled beam wavenumber is sufficiently smaller than the plate free wavenumber is experimentally verified. Finally, experimental results such as powers and energy ratios show the validity of the analytical wave models.

Inertia Latch Design for Micro Optical Disk Drives (초소형 광디스크 드라이브용 관성 래치 설계)

  • 김경호;김유성;이승엽;유승헌;김수경
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2003.05a
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    • pp.1157-1164
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    • 2003
  • Dynamic Load/unload (L/UL) mechanism is an alternative to the contact start stop (CSS) technology which eliminates stiction and wear failure modes associated with CSS. Other benefits of L/UL include increased areal density due to smooth disk surfaces, thinner overcoats, and lower head flying height Improved shock resistance due to elimination of head slap, and reduced power consumption. Inertia latch mechanism becomes important for mobile disk drives because of non operating shock performance. Various types of latch designs have been introduced in hard disk drives to limit a rotary actuator from sudden uncontrolled motion. In this paper, a single spring inertia latch is introduced for a small form optical disk drive, which uses a rotary actuator for moving an optical pick-up. A new small inertia latch with single spring is designed to ensure both feasible and small size. The shock performance of the new inertia latch is experimentally verified.

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Harmonic Response Estimation Method on the Lévy Plate with Two Opposite Edges Having Free Boundary Conditions (마주보는 양단이 자유 경계조건을 갖는 Lévy 판의 조화 응답 해석)

  • Park, Nam-Gyu;Suh, Jung-Min;Jeon, Kyeong-Lak
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.23 no.11
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    • pp.943-950
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    • 2013
  • This paper discusses a harmonic response estimation method on the L$\acute{e}$vy plate with two opposite edges simply supported and the other two edges having free boundary conditions. Since the equation of motion of the plate is not self-adjoint, the modes are not orthogonal to each other on the domain. Noting that the L$\acute{e}$vy plate can be expressed using one term sinusoidal function that is orthogonal to other sinusoidal functions, this paper suggested the calculation method that is equivalent to finding a least square error minimization solution of the finite number of algebraic equations. Example problems subjected to a distributed area loading and a distributed line loading are defined and their solutions are provided. The solutions are compared to those of the commercial code, ANSYS. According to the verification results, it is expected that the suggested method will be useful to predict the forced response on the L$\acute{e}$vy plate with the distributed area or line loading conditions.