• 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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.7 s.94
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• pp.1719-1730
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• 1993

This paper presents the theoretical natural frequencies of out-of-plane deformable ring based on the variables such as out-of-plane deflection, torsional rotation and shear rotation. Based on the same variables, a finite element eigen analysis is carried out by using the $C^0$-continuous, isoparametric element which has three nodes per element and three degrees-of-freedom at each node. Numerical experiments are peformed to find the integration scheme which produces accurate natural frequencies, natural modes and correct rigid body motion. The uniformly reduced integration and the selective reduced integration give more accurate numerical frequencies than the uniformly full integration, but the uniformly reduced integration produces incorrect rigid body motion while selective reduced integration does correct one. Therefore, the ring element based on the three variables which employes selective reduced integration is recommended to avoid spurious modes, to alleviate the error due to shear locking and to produce correct rigid body motion, simultaneously.

• 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)

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.9
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• pp.1905-1913
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• 2002

Using the finite element method, this study investigates the dynamic time responses of a flexible spinning disk of which axis of rotation is misaligned with the axis of symmetry. The misalignment between the axes of symmetry and rotation is one of the major vibration sources in optical disk drives such as CD-ROM, CD-R, CD-RW and DVD drives. Based upon the Kirchhoff plate theory and the von-Karman strain theory, three coupled equations of motion for the misaligned disk are obtained: two of the equations are for the in-plane motion while the other is for the out-of-plane motion. After transforming these equations into two weak forms for the in-plane and out-of-plane motions, the weak forms are discretized by using newly defined annular sector finite elements. Applying the generalized-$\alpha$ time integration method to the discretized equations, the time responses and the displacement distributions are computed and then the effects of the misalign ment on the responses and the distributions are analyzed. The computation results show that the misalignment has an influence on the magnitudes of the in-plane displacements and it results in the amplitude modulation or the beat phenomenon in the time responses of the out-of-plane displacement.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.10 s.103
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• pp.1186-1194
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• 2005

In this paper, we have systematically formulated the equations concerned to the in-plane and out-of-plane motions and deformations of a thick circular beam by using the kinetic and strain energies in order to analyse natural frequencies of a thick ring. The effects of variation of radius of curvature across the cross-section and also the effects of bending shear, extension and twist are considered. The equations of motion for natural vibration analysis of a ring are obtained utilizing the cyclic symmetry of vibration modes of the ring. The frequencies calculated using thick ring model and thin ring model are compared and discussed with the ones obtained from finite element analysis using the method of cyclic symmetry with 20-node hexahedral solid elements for rings with the different ratio of radial thickness to mean radius.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.597-600
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• 2004

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 are equally important. Complex eigenvalue 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. Nonlinear analysis is also performed to demonstrate various responses. Comparing the responses with experimental data has shown that the proposed model may qualitatively well represent a certain type of brake noise.

• Journal of the Society of Naval Architects of Korea
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• v.44 no.3 s.153
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• pp.219-227
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• 2007

A stereo-PIV (particle image velocimetry) technique is used to investigate the vortical structure of the wake behind a rotating propeller in the present study. A four bladed propeller is tested in a cavitaion tunnel without any wake screen. Hundreds of instantaneous velocity fields are phase-averaged to reveal the three dimensional spatial evolution of the flow behind the propeller. The results of conventional 2-D PIV are also compared with those of the stereo-PIV to understand the vortical structure of propeller wake deeply. The variations of radial and axial velocities in the 2-D PIV results seem to be affected by the out-of-plane motion. generating a little perspective error in the in-plane velocity components of the slipstream. The strong out-of-plane motion around the hub vortex also causes the perspective error to vary the axial velocity component a little at the near wake region. The out-of-plane velocity component had the maximum value of about 0.3U0 in the tip vortices and continued its magnitude in the wake region.

• Structural Engineering and Mechanics
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• v.61 no.1
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• pp.65-76
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• 2017

Prediction of the characteristics of both in-plane and out-of-plane elastic waves within conducting nanoplates in the presence of bidirectionally in-plane magnetic fields is of interest. Using Lorentz's formulas and nonlocal continuum theory of Eringen, the nonlocal elastic version of the equations of motion is obtained. The frequencies as well as the corresponding phase and group velocities pertinent to the in-plane and out-of-plane waves are analytically evaluated. The roles of the strength of in-plane magnetic field, wavenumber, wave direction, nanoplate's thickness, and small-scale parameter on characteristics of waves are discussed. The obtained results show that the in-plane frequencies commonly grow with the in-plane magnetic field. However, the transmissibility of the out-of-plane waves rigorously depends on the magnetic field strength, direction of the propagated transverse waves, small-scale parameter, and thickness of the nanoplate. The criterion for safe transferring of the out-of-plane waves through the conducting nanoplate immersed in a bidirectional magnetic field is also explained and discussed.

• Korean Journal of Applied Biomechanics
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• v.32 no.4
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• pp.147-152
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• 2022

Objective: The purpose of this study was to analyze the effects of club head and golf ball kinematics and body alignment according to the swing plane during golf driver swing. Method: Sixteen college golfers participated in this study. Kinematic data of the club head and golf ball were collected using golf swing analysis system (Trackman Ver. 3e). The body alignment variables were collected using 8 motion capture system. An Independent samples t-test was used for comparison between the Out-to-In group and In-to-Out group, and the statistical significance level was set at .05. Results: For the club head related variables, club path and club face angle showed higher values in Out-to-In swing plane than In-to-Out swing plane. For the kinematic variables of the golf ball, the total distance showed a higher value in the In-to-Out swing plane than that of the Out-to-In swing plane. For the body alignment, the In-to-Out swing plane showed higher values than the Out-to-In swing plane for the pelvis rotation angle and trunk rotation angle. Conclusion: This study suggest that it would be more effective to use the In-to-Out swing plane for increasing the total distance during the golf driver swing.

• Journal of Mechanical Science and Technology
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• v.19 no.spc1
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• pp.305-311
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• 2005

This research presents a three-dimensional modeling technique for a flexible sheet. A relative coordinate formulation is used to represent the kinematics of the sheet. The three-dimensional flexible sheet is modeled by multi-rigid bodies interconnected by out-of-plane joints and plate force elements. A parent node is designated as a master body and is connected to the ground by a floating joint to cover the rigid motion of the flexible sheet in space. Since the in-plane deformation of a sheet such as a paper and a film is relatively small, compared to out-of-plane deformation, only the out-of-plane deformation is accounted for in this research. The recursive formulation has been adopted to solve the equations of motion efficiently. An example is presented to show the validity of the proposed method.