• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.24 no.1
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• pp.110-116
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• 2015

This study investigates the whirling stability of a rotating shaft-disk system under parametric excitation using periodically varying torque. The equations of motion were derived using a lumped-mass model, and the Floquet method was employed to find the effects of torque fluctuation, internal and external damping, and rotational speed on whirling stability. Results indicated that the effect of torque fluctuation was considerable on the instability around resonance, but minimal on supercritical instability. Stability diagrams were sensitive to the parametric excitation frequency; critical torque decreased upon increasing excitation frequency, with faster response convergence or divergence. In addition, internal and external damping had a considerable effect on unstable regions, and reduced the effects of the parametric excitation frequency on critical torque and speed. Results obtained from the Floquet approach were in good agreement with those obtained by numerical integration, except for some cases with Floquet multipliers very close to unity.

• International Journal of Naval Architecture and Ocean Engineering
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• v.11 no.2
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• pp.688-698
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• 2019

If heave motion in the platform causes horizontal parametric vibration of a Compliant Vertical Access Riser (CVAR), the riser may become unstable. A combination of riser parameters lies in the unstable region aggravates vibrational damage to the riser. Change of axial tensile stress in the riser combined with its natural frequency and mode shape change results in mode coupling. In accordance with the state transition matrices of the riser in the coupled and uncoupled states, the stable and unstable regions were obtained by Floquet theory, and the vibration response under different conditions was obtained. The parametric excitation of the CVAR is shown to occur mainly in first-order unstable regions. Mode coupling may cause parametric excitation in the least stable regions. Damping reduces the extent of unstable regions to a certain extent.

• Proceedings of the KIEE Conference
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• 1991.07a
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• pp.31-33
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• 1991

A passive power converter operating on the principle of parametric excitation, called Parametric transformer, is analyzed. The energy transfer from the input to the output is achieved through the double frequency variation of magnetic path reluctance to the input frequency without mutual flux coupling between two windings. Thus, output becomes available which is essentially independant of waveform of excitation. The mathmatical model of the device is developed and its solution is obtained. The outstanding characteristics of the device is explained from the analysis.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.2
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• pp.160-168
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• 2008

This paper presents the study on the stability of nonlinear oscillations of a thin cantilever beam subject to harmonic base excitation in vertical direction. Two partial differential governing equations under combined parametric and external excitations were derived and converted into two-degree-of-freedom ordinary differential Mathieu equations by using the Galerkin method. We used the method of multiple scales in order to analyze one-to-one combination resonance. From these, we could obtain the eigenvalue problem and analyze the stability of the system. From the thin cantilever experiment using foamax, we could observe the nonlinear modes of bending, twisting, sway, and snap-through buckling. In addition to qualitative information, the experiment using aluminum gave also the quantitative information for the stability of combination resonance of a thin cantilever beam under parametric excitation.

• Journal of Advanced Marine Engineering and Technology
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• v.16 no.5
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• pp.67-76
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• 1992

This paper describes the vibration characteristic of second-order nonlinear systems subjected to parametric excitation. Emphasis is put on the examination of the hydrodynamic nonlinear damping effect on limiting the response amplitudes of parametric vibration. Since the parametric vibration is described by the Mathieu equation, the Mathieu stability chart is examined in this paper. In addition, the steady-state solutions of the nonlinear Mathieu equation in the first instability region are obtained by using a perturbation technique and are compared with those by a numerical integration method. It is shown that the response amplitudes of parametric vibration are limited even in unstable conditions by hydrodynamic nonlinear damping force. The largest reponse amplitude of parametric vibration occurs in the first instability region of Mathieu stability chart. The parametric excitation induces the response of a dynamic system to be subharmonic, superharmonic or chaotic according to their dynamic conditions.

• International Journal of Aerospace System Engineering
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• v.2 no.2
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• pp.34-39
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• 2015

Experimental studies were conducted on the liquid sloshing characteristics in a spherical tank covered with a flexible membrane. A spherical acrylic tank with 145.2 mm in radius was used as a test tank, and it was half-filled with water. Silicon membranes with 0.2 mm thickness were used as a test membrane with plane or hemispherical types. The test tank was harmonically excited in a vertical direction by an electro-dynamic exciter. In this case, a parametric instability vibration comes up when the excitation frequency is twice the natural frequency. Parametric instability regions of natural modes were measured for three cases, i.e. liquid surface is free, covered with plane membrane and hemi-spherical membrane.

• Proceedings of the KIEE Conference
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• 1992.07b
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• pp.706-709
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• 1992

This paper deals with the operation of a parametric transformer through the normalization of system equations. Based on these equations, the effects of excitation voltage waveforms on the performances of the parametric transformer are analyzed.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.669-674
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• 2004

In this study, the analytical method to evaluate the response of rotor-bearing system subjected to base excitation was presented. The equations of motion contain speed dependent gyroscopic terms, base rotation dependent parametric terms and several forcing function terms which depend on linear accelerations, rotational accelerations and a combination of linear and rotational combination. The study of rotor-bearing system excited by its base motion is not only able to predict the rotational performance, but provides the fundamental data for vibration isolation. In order to illustrate transient response, transient response analysis of a practical application sample were performed. The transient response was carried out for the given base excitation by using the state-space Newmark method that incorporates the average velocity concept.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11b
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• pp.863-868
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• 2002

Operational Modal Analysis also known as Ambient Modal Analysis has an increasing interest in mechanical engineering. Especially on big structures where the excitation and not less important the determination of the forces is most often a problem. In a structure like a wind turbine wing where the modes occur both close in frequency and hi-directional the ambient excitation has big advantages. In this paper modal parameters are identified from the wing by operational modal analysis. For the parameter identification both parametric and non-parametric techniques are used. Advantages and disadvantages are discussed and results from the different techniques are compared

• Structural Engineering and Mechanics
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• v.86 no.2
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• pp.221-235
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• 2023

To calculate the vibrations of a tout cable subjected to axial support excitations, a nonlinear relationship of cable force and the support displacement under static situations are employed to depict the quasi-static vibration of the cable. The dynamic components of quasi-static vibration are inputted as "direct loads" to cause the parametric vibrations on the cable. Both the governing equations of motion and deformation compatibility for parametric vibrations are then derived, which indicates the high coupling of cable parametric force and deformation. Numerical solutions, based on the finite difference method, are put forward for the parametric vibrations, which is validated by the finite element method under periodic axial support excitations. For the quasi-static response, the shorter cables are more sensitive to support excitations than longer ones at small cable force. The quasi-static cable force makes the greatest contribution to the total cable force, but the parametric cable force is responsible for the occurrence of cable loosening at large excitation amplitudes. Moreover, this study also revealed that the traditional approach, assuming a linear relationship between quasi-static cable force and axial support displacement, would result in some great error of the cable parametric responses.