• Title/Summary/Keyword: out-of-plane vibration

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Effect of Initial Uniform Moment on Lateral Free Vibration of Arches (등분포 모멘트를 받는 아치의 횡 자유진동)

  • 염응준;한택희;임남형;강영종
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2002.10a
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    • pp.3-10
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    • 2002
  • Recently, arches are used structurally because of their high in-plane stiffness and strength, which result from their ability to transmit most of the applied loading by axial forces actions, so that the bending actions are reduced. On the other hand, the resistances of arches to (out-of-plane,) flexural-torsional behavior depend on the rigidities EI/sub y/, for lateral bending, GJ for Uniform torsion, and EI/sub w/ for warping torsion which are related to axial stress for flexural-torsional behavior. The resistance of an arch to out-of-plane behavior may be reduced by its in-plane curvature, and so it may require significant lateral bracing. Thus. it is supposed that In-plane preloading which cause an axial stress, have an effect on out-of-plane free vibration behavior of arches. Because axial stresses caused increase or decrease out-of-plane stiffness. But study about this substance is insufficient. In this thesis, We will study an effect of preloading on lateral free vibration of arches, using finite element method based on Kang and Yoo's curved beam theory (about curved beam element have 7 degree of freedom including warping) with FORTRAN programming.

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Linear Stability Analysis of an Out-of-plan Motion of Vibration of a Two Degree-of-freedom with Contact Stiffness (마찰기인 접촉 강성을 가지는 2-자유도계 면외 방향 진동 시스템의 선형 안정성 해석)

  • Joe, Yong-goo;Shin, Ki-hong;Lee, Hyun-young;Oh, Jae-Eung;Lee, Su-Gab
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.15 no.3 s.96
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    • pp.259-265
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    • 2005
  • A two-degree-of-freedom out-of-plane model with contact stiffness is presented to describe dynamical interaction between the pad and disc of a disc brake system. It is assumed that the out-of-plane motion of the system depends on the friction force acting along the in-plane direction. Dynamic friction coefficient is modelled as a function of both in-plane relative velocity and out-of-plane normal force. When the friction coefficient depends only on the relative velocity, the contact stiffness has the role of negative stiffness. The results of stability analysis show that the stiffness of both pad and disc is equally important. Complex eigen value analysis is conducted for the case that the friction coefficient is also dependent on the normal force. The results further verify the importance of the stiffness. It has also been found that increasing the gradient of friction coefficient with respect to the normal force makes the system more unstable.

Out-of-plane Free Vibration Analysis of Curved Timoshenko Beams by the Pseudospectral Method

  • Lee, Jinhee
    • International Journal of Precision Engineering and Manufacturing
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    • v.5 no.2
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    • pp.53-59
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    • 2004
  • The pseudospectral method is applied to the analysis of out-of$.$plane free vibration of circularly curved Timoshenko beams. The analysis is based on the Chebyshev polynomials and the basis functions are chosen to satisfy the boundary conditions. Natural frequencies are calculated for curved beams of circular cross sections under hinged-hinged, clamped-clamped and hinged-clamped end conditions. The present method gives good accuracy with only a limited number of collocation points.

Dynamics of a Micro Three-Axis Ring Gyroscope (마이크로 3축 링 자이로스코프의 동역학)

  • Choi, Sang-Hyun;Kim, Chang-Boo
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2002.11b
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    • pp.37-43
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    • 2002
  • In this paper, we analyse and present mechanical dynamic characteristics of a micro-machined vibrating silicon ring gyroscope which can measure angular velocities about three orthogonal axes. The ring gyroscope has a ring connected to the gyroscope main body by support-ligaments which are arranged with cyclic symmetry. The natural modes of its vibration can be distinguished into the in-plane motion and the out-of-plane motion which are coupled by the gyro-effect due to the rotation of the gyroscope main body. The equations of motion, the response to angular velocities, and the relationships between the natural modes of vibration are derived and compared with the previous studies for the design of a micro three-axis ring gyroscope.

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Dynamics of a Micro Three-axis Ring Gyroscope (마이크로 3축 링 자이로스코프의 동역학)

  • Kim, Chang-Boo;Choi, Sang-Hyun
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.12 no.12
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    • pp.1001-1009
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    • 2002
  • In this paper, we analyse and present mechanical dynamic characteristics of a micro-machined vibrating silicon ring gyroscope which can measure angular velocities about three orthogonal axes. The ring gyroscope has a ring connected to the gyroscope main body by support-ligaments which are arranged with cyclic symmetry. The natural modes of its vibration can be distinguished into the in-plane motion and the out-of-plane motion which are coupled by the gyro-effect due to the rotation of the gyroscope main body. The equations of motion, the response to angular velocities, and the relationships between the natural modes of vibration are derived and compared with the previous studies for the design of a micro three-axis ring gyroscope.

Free In-plane Vibration of a Clamped Circular Plate (고정된 원형 플레이트의 평면내 자유진동)

  • Park, Chan-Il
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2005.05a
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    • pp.836-839
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    • 2005
  • The in-plane vibration response of a clamped circular plate should be predicted in many applications. Up to now, papers on the in-plane vibration of rectangular plate are published. However, analytical derivation on the in-plane vibration of the clamped circular plate is not carried out. Therefore, the in-plane vibration of the clamped circular plate is the concern of this paper. In order to derive the equations of motion for the clamped circular plate in the cylindrical coordinate, the kinetic energy and potential energy for the in-plane behavior are obtained by us ing the stress-strain-displacement expressions. Application of Hamilton's principle leads to two sets of differential equations. These displacement equations were highly coupled. It is possible to obtain a simpler set of equations by introducing Helmholtz decomposition. Substituting them into the coupled differential equations, we obtain the uncoupled equations of motion. In order to solve them, we assume that the solutions are harmonic. Then, they lead to the wave equations. Using the separation of variable, we obtain the general solutions for the equations. Based on the solutions, the displacements for r and $\theta$ direction are assumed. Finally we obtain the frequency equation for the clamped circular plate by the application of boundary conditions. The derived equation is compared with the finite element analysis for validation by using the some numerical examples.

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Dynamics of a Micro Three-axis Ring Gyroscope Considering Electrode Effects (전극 효과를 고려한 마이크로 3축 링 자이로스코프의 동역학)

  • 김창부;강태민
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.14 no.1
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    • pp.64-72
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    • 2004
  • In this paper. we analyse and present electro-mechanical dynamic characteristics of a micro-machined vibrating silicon ring gyroscope which can measure angular velocities about three orthogonal axes. The ring gyroscope has a ring connected to the gyroscope main body by support-ligaments which are arranged with cyclic symmetry. The natural modes of its vibration can be distinguished into the in-plane motion and the out-of-plane motion which are coupled by the gyro-effect due to the rotation of the gyroscope main body. The motions of the ring are electro-statically derived. sensed and balanced by electrodes. The equations of motion are formulated. The measuring method of angular velocities by force-to-rebalance is presented. The dynamic characteristics of a ring gyroscope are calculated and compared.

Dynamics of a Micro Three-Axis Ring Gyroscope Considering Electrode Effects (전극 효과를 고려한 마이크로 3축 링 자이로스코프의 동역학)

  • 강태민;김창부
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2003.11a
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    • pp.970-976
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    • 2003
  • In this paper, we analyse and present electro-mechanical dynamic characteristics of a micro-machined vibrating silicon ring gyroscope which can measure angular velocities about three orthogonal axes. The ring gyroscope has a ring connected to the gyroscope main body by support-ligaments which are arranged with cyclic symmetry. The natural modes of its vibration can be distinguished into the in-plane motion and the out-of-plane motion which are coupled by the gyro-effect due to the notation of the gyroscope main body. The motions of the ring are electro-statically derived, sensed and balanced by electrodes. The equations of motion are formulated. The scheme of angular velocities sensing by force-to-rebalance method is presented. The dynamic characteristics of a ring gyroscope are calculated and compared.

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Dynamics of a Micro Three-Axis Ring Gyroscope (마이크로 3축 링 자이로스코프의 동역학)

  • Park, Sang-Hyun;Kim, Chang-Boo
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2002.11a
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    • pp.312.1-312
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    • 2002
  • In this paper, we analyse and present mechanical dynamic characteristics of a micro-machined vibrating silicon ring gyroscope which can measure rates of turn about three orthogonal axes. The ring gyroscope has a ring connected to the gyroscope main body by support-ligaments which are arranged with cyclic symmetry. The natural modes of its vibration can be distinguished into the in-plane motion and the out-of-plane motion which are coupled by the gyro-effect due to the rotation of the gyroscope main body. (omitted)

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Nonlinear Vibration Analysis of Rotating Ring (회전하는 링의 비선형 진동해석)

  • Kim, S.K.;Lee, S.I.;Chung, J.
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2000.11a
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    • pp.553-557
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    • 2000
  • Nonlinear Vibrations of a flexible circular ring is studied in this paper. Based upon the von Karman strain theory, the nonlinear governing equations are derived, in which the in-plane bending and extension displacements as well as the out-of-plane bending displacement are fully coupled. After discretizing the governing equations by the Galerkin approximation method, we obtain the linearlized equation by using the pertubation method. The analysis results from the linearlized equations show that the in-plane displacement has effects on the natural frequencies of the out-of-plane displacement.

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