• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.12
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• pp.1314-1321
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• 2004

The non-linear responses of a slender rectangular cantilever beam subjected to lateral harmonic base-excitation are investigated by the 2-channel FFT analyzer. Both linear and nonlinear behaviors of the cantilever beam are compared with each other. Bending mode, torsional mode, and transverse mode are coupled in such a way that the energy transfer between them are observed. Especially, superharmonic, subharmonic, and chaotic motions which result from the unstable inertia terms in the transverse mode are analyzed by the FFT analyzer The aim is to give the explanations of the route to chaos, i.e., harmonic motion \longrightarrow superharmonic motion \longrightarrow subharmonic motion \longrightarrow chaos.

• Structural Engineering and Mechanics
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• v.42 no.5
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• pp.677-699
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• 2012

This article studies the secondary resonances of a clamped-clamped microresonator under combined electrostatic and piezoelectric actuations. The electrostatic actuation is induced by applying the AC-DC voltage between the microbeam and the electrode plate that lies at the opposite side of the microbeam. The piezoelectric actuation is induced by applying the DC voltage between upper and lower sides of piezoelectric layer. It is assumed that the neutral axis of bending is stretched when the microbeam is deflected. The drift effect of piezoelectric layer (the phenomenon where there is a slow increase of the free strain after the application of a DC field) is neglected. The equations of motion are solved by using the multiple scale perturbation method. The system possesses a subharmonic resonance of order one-half and a superharmonic resonance of order two. It is shown that using the DC piezoelectric actuation, the sensitivity of AC-DC electrostatically actuated microresonator under subharmonic and superharmonic resonances may be tuned. In addition, it is shown that the tuning domain of the microbeam under combined electrostatic and piezoelectric actuations at subharmonic and superharmonic conditions is larger than the tuning domain of microbeam under only the electrostatic actuation.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.690-695
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• 2005

Flexible circular cantilever beams when excited externally introduce a lot of dynamic characteristics. The non-linear elements that these flexible beams develop include non-linearity due to inertia terms, spring, and damping. They show different characteristics of motion from each other. In the modes of lower order, the non-linearity due to spring is prevalent, while the non-linearity due to inertia Is prevalent in the modes of higher order. To analyze these effects the non-linear phenomena are analyzed experimentally. When the response characteristics of non-linear vibration are analyzed using autospectrum, it is possible to analyze the subharmonic and superharmonic mot ion by comparison. The phase change is analyzed using the method of phase portrait and the non-linear characteristics of response characteristics that are developed in flexible structures can be predicted and applied to the stage of design.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.62-65
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• 2006

In this paper, nonlinear nonplanar vibration of a flexible rectangular cantilever beam is analyzed when one-to-one resonance occurs to the beam. The planar and nonplanar motions of the beam are analyzed in time and frequency domains. In frequency domain, FFT analyzer is used to perform autospectrum and cepstrum analyses for nonlinear response of the beam. In time domain, an oscilloscope is used to investigate the phase difference between the planar and nonplanar motions and to perform Torus analysis in the phase space. Through those analyzing process, the main frequencies of superharmonic, subharmonic, and super-subharmonic motions are investigated in the nonplanar motion due to one-to-one resonance. Analyzing the phase difference between the planar and nonplanar motions, it is observed that the phase difference varies in time.

• Journal of Mechanical Science and Technology
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• v.14 no.11
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• pp.1250-1256
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• 2000

Rubbing occurs when a rotor contacts with a stator during whirling motion of the rotor. Compared to full annular rub, partial rub against a nonrotating part is more common in practice. In this study, several partial rubbing phenomena of superharmonic and subharmonic vibrations and jump phenomenon are demonstrated experimentally for the cases of light and heavy rub for a flexible rotor. The orbit patterns of forward or backward whirling are also calculated using directional spectrum analysis. The occurrence if subharmonic vibration during heavy rub is demonstrated as one impact per two rotations both experimentally and numerically.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.567-571
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• 2005

The slender rectangular cantilever beam has vef interesting to study dynamic behaviors of the harmonic base excitation of a cantilever beam shows many nonlinear dynamics due to unstability , energy transfer and mode coupling. Nonlinear phenomenon shows superharmonic, subharmonic, super subharmonic and chaotic motions of the cantilever beam. Experimental observation and verification of these phenomenon carry much importance for the theoretical study as well as in it self. In the experimental cantilever beam, the chaotic motions of the beam appear as a pink noise signal in FFT analysis and as a torus structure in the oscilloscope analyzed to eventually give information of chaotic motions of the cantilever beam.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.77-82
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• 2004

There were many researches about the chatter vibration occur in the cutting process of machine tools. But there are in sufficient research parts ; the frequency about the chatter vibration and its characteristics and its nonlinear properties. This paper measured signals of vibration that occur before and immediately after and after the chatter vibration. This signals were analyzed through autospectrum obtained by the Fast Fourier Transform(FFT). And then, the nonlinear characteristis were analyzed by cepstrum analysis through FFT of autospectrun.

• Transactions of the Korean Society of Automotive Engineers
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• v.5 no.1
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• pp.69-78
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• 1997

Main sources of the vibration in gear driving system are transmission error and backlash. Transmission error is the difference of the rotation between driving and driven gear due to tooth deformation and profile error. Vibro-impacts induced by backlash between meshing gears lead to excessive vibration and noise in many geared rotation systems. Nonlinear dynamic characteristics of the gear driving system due to transmi- ssion error and backlash are investigated. Transmission error is calculated for spur gear. Nonlinear equation of motion for the gear driving system is developed with the calculated transmission error and backlash. Numerical analysis of the equation and the experimental results show the existence of meshing frequency, superharmonic compon- ents. Instability of the gear driving motion is found on the basis of Mathieu equation. Rattle vibration due to backlash is also discussed on the basis if nonlinear jump phenomenon.