• Journal of KSNVE
• /
• v.9 no.1
• /
• pp.196-205
• /
• 1999

The existence. bifurcation. and the orbital stability of periodic motions, which is called nonlinear normal mode, in a nonlinear dual mass Hamiltonian system. which has 6th order homogeneous polynomial as a nonlinear term. are studied in this paper. By direct integration of the equations of motion. Poincare Map. which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space. is obtained. And via the Birkhoff-Gustavson canonical transformation, the analytic expression of the invariant curves in the Poincare Map is derived for small value of energy. It is found that the nonlinear system. which is considered in this paper. has 2 or 4 nonlinear normal modes depending on the value of nonlinear parameter. The Poincare Map clearly shows that the bifurcation modes are stable while the mode from which they bifurcated out changes from stable to unstable.

• Transactions of the Korean Society of Automotive Engineers
• /
• v.13 no.3
• /
• pp.41-47
• /
• 2005

This paper deals with a squeal noise in a brake system. It has been proved that the squeal noise is influenced by the angular misalignment of a disk, disk run-out, with the previously experimental study. In this study, a cause of the noise is examined by using FE analysis program(SAMCEF) and numerical analyses with a derived analytical equation of the disk based on the experimental results. The FE analyses and numerical results show that the squeal noise is due to the disk run-out as the experimental results and the frequency component of the noise equals to that of a disk's bending mode arising from the Hopf bifurcation.

• Proceedings of the KSME Conference
• /
• 2004.11a
• /
• pp.595-600
• /
• 2004

This paper deals with a cause analysis of a squeal noise in a brake system. It has been proved that the squeal noise is influenced by the angular misalignment of a disk, disk run-out, with the previously experimental study. In this study, a cause of the noise is examined by using FE analysis program(SAMCEF) and numerical analyses with a derived analytical equation of the disk based on the experimental results. The FE analyses and numerical results show that the squeal noise is due to the disk run-out as the experimental results and the frequency component of the noise equals to that of a disk's bending mode arising from the Hopf bifurcation.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2003.11a
• /
• pp.270-275
• /
• 2003

The nonlinear dynamic characteristic of a straight tube conveying fluid with constraints and an attached mass on the tube is examined in this study. An experimental apparatus composed of an elastomer tube conveying water which has an attached mass and constraints is made and comparisons are done between the theoretical results from non-linear equation of motion of piping system and experimental results. And the results show that the tube is destabilized as the mass of the attached mass increases, and stabilized as the position of the attached mass close to the fixed end. In case of a small end-mass, the system shows rich and different types of periodic solutions. For a constant end-mass, the system undergoes a series of bifurcations after the first Hopf bifurcation, as the flow velocity increases, which causes chaotic motion of the tube eventually.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.14 no.7
• /
• pp.561-568
• /
• 2004

The nonlinear dynamic characteristic of a straight tube conveying fluid with constraints and an attached mass on the tube is examined in this study An experimental apparatus with an elastomer tube conveying water which has an attached mass and constraints is made and comparisons are made between the theoretical results from the non-linear equation of motion of piping system and the experimental results. The comparisons show that the tube is destabilized as the magnitude of the attached mass increases, and stabilized as the position of the attached mass closes to the fixed end. In case of a small end-mass, the system shows complicated and different types of solutions. For a constant end-mass. the system undergoes a series of bifurcations after the first Hopf bifurcation, as the flow velocity increases. which causes chaotic motions of the tube eventually.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.25 no.4
• /
• pp.546-553
• /
• 2001

A Parametric study is numerically carried out for flow fields in a two-dimensional plane channel with thin obstacles(“baffles and blocks”) mounted symmetrically in the vertical direction and periodically in the streamwise direction. The aim of this investigation is to understand how various geometric conditions influence the critical characteristics and pressure drop. A range of BR(the ratio of baffle interval to channel height) between 1 and 5 is considered. Especially when BR is equal to 3, for which the critical Reynolds number turned out to be minimal, we add blocks in the center region in order to study their destabilizing effects on the flows. It is revealed that the critical Reynolds number is further decreased by the presence of the block.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2001.11b
• /
• pp.799-804
• /
• 2001

Nonlinear normal mode (NNM) vibration, in a nonlinear dual mass Hamiltonian system, which has 6th order homogeneous polynomial as a nonlinear term, is studied in this paper. The existence, bifurcation, and the orbital stability of periodic motions are to be studied in the phase space. In order to find the analytic expression of the invariant curves in the Poincare Map, which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space, Whittaker's Adelphic Integral, instead of the direct integration of the equations of motion or the Birkhotf-Gustavson (B-G) canonical transformation, is derived for small value of energy. It is revealed that the integral of motion by Adelphic Integral is essentially consistent with the one obtained from the B-G transformation method. The resulting expression of the invariant curves can be used for analyzing the behavior of NNM vibration in the Poincare Map.