Nonlinear Forced Oscillations Caused by Quartic Nonlinearity in a Rotating Shaft System

1990 ◽  
Vol 112 (3) ◽  
pp. 288-297 ◽  
Author(s):  
Y. Ishida ◽  
T. Ikeda ◽  
T. Yamamoto
Keyword(s):  
Polar Coordinates ◽  
Forced Oscillations ◽  
Ball Bearings ◽  
Rotating Shaft ◽  
Restoring Force ◽  
Double Row ◽  
Nonlinear Component ◽  
Shaft System ◽  
Nonlinear Components ◽  
Theoretical Results

This paper deals with nonlinear forced oscillations in a rotating shaft system which are caused by quartic nonlinearity in a restoring force. These oscillations are theoretically analyzed by paying attention to the nonlinear components represented by the polar coordinates. It is clarified which kind of nonlinear component has an influence on each oscillation. In experiments it was shown that, when the shaft was supported by double-row angular contact ball bearings, the restoring force had nonlinear spring characteristics involving quartic nonlinearity in addition to quadratic and cubic ones. Experimental results were compared with the theoretical results regarding the probability of occurrence and the shapes of the resonance curves.

Forced Oscillations of Rotating Shaft With Nonlinear Spring Characteristics and Internal Damping: Subharmonic Oscillation of Order 1/3 and Entrainment

1999 ◽  
Author(s):  
Yukio Ishida ◽  
Shin Murakami
Keyword(s):  
Critical Region ◽  
Critical Speed ◽  
Forced Oscillations ◽  
Ball Bearings ◽  
Internal Damping ◽  
Rotating Shaft ◽  
Nonlinear Spring ◽  
Subharmonic Oscillation

Abstract An elastic rotating shaft supported by ball bearings may have nonlinear spring characteristics due to clearance and internal damping due to friction between the shaft and the bearings. In such a system, self-excited oscillations appear in the post critical region and nonlinear forced oscillations appear at various resonance points. In this paper, a phenomenon in the neighborhood of the critical speed of the subharmonic oscillation of order 1/3 of a forward whirling mode is discussed. It is clarified that, similar to the case of the subharmonic oscillation of order 1/2 of a forward whirling mode, an entrainment phenomenon appears due to the interplay between self-excited oscillations and forced oscillations.

Forced Oscillations of a Continuous Rotor With Geometric Nonlinearity: Internal Resonance Phenomena at Harmonic and Subharmonic Resonances

1997 ◽  
Author(s):  
Yukio Ishida ◽  
Imao Nagasaka ◽  
Seongwoo Lee
Keyword(s):  
Geometric Nonlinearity ◽  
Internal Resonance ◽  
Forced Oscillations ◽  
Center Line ◽  
Rotating Shaft ◽  
Restoring Force ◽  
Resonance Phenomena ◽  
Geometric Stiffening ◽  
Resonance Curves ◽  
Subharmonic Resonances

Abstract Harmonic resonances and subharmonic resonances of order 1/2 and order 1/3 in a continuous rotating shaft with distributed mass are discussed. The restoring force of the shaft has geometric stiffening nonlinearity due to the extension of the shaft center line. It is supposed that a distributed bias force, such as the gravity, works. The possibility of their occurrences, the shapes of resonance curves, and internal resonance phenomena are investigated.

Simulation-based site amplification model for shallow bedrock sites in Korea

2021 ◽  
pp. 875529302098198
Author(s):  
Muhammad Aaqib ◽  
Duhee Park ◽  
Muhammad Bilal Adeel ◽  
Youssef M A Hashash ◽  
Okan Ilhan
Keyword(s):  
Linear Models ◽  
Site Response ◽  
Site Amplification ◽  
One Dimensional ◽  
Nonlinear Component ◽  
Nonlinear Site Response ◽  
Simulation Based ◽  
Linear And Nonlinear ◽  
Input Motion ◽  
Nonlinear Components

A new simulation-based site amplification model for shallow sites with thickness less than 30 m in Korea is developed. The site amplification model consists of linear and nonlinear components that are developed from one-dimensional linear and nonlinear site response analyses. A suite of measured shear wave velocity profiles is used to develop corresponding randomized profiles. A VS30 scaled linear amplification model and a model dependent on both VS30 and site period are developed. The proposed linear models compare well with the amplification equations developed for the western United States (WUS) at short periods but show a distinct curved bump between 0.1 and 0.5 s that corresponds to the range of site natural periods of shallow sites. The response at periods longer than 0.5 s is demonstrated to be lower than those of the WUS models. The functional form widely used in both WUS and central and eastern North America (CENA), for the nonlinear component of the site amplification model, is employed in this study. The slope of the proposed nonlinear component with respect to the input motion intensity is demonstrated to be higher than those of both the WUS and CENA models, particularly for soft sites with VS30 < 300 m/s and at periods shorter than 0.2 s. The nonlinear component deviates from the models for generic sites even at low ground motion intensities. The comparisons highlight the uniqueness of the amplification characteristics of shallow sites that a generic site amplification model is unable to capture.

Analysis of the rub-impact forces between a controlled nonlinear rotating shaft system and the electromagnet pole legs

2021 ◽  
Vol 93 ◽  
pp. 792-810
Author(s):  
N.A. Saeed ◽  
Emad Mahrous Awwad ◽  
Mohammed A. EL-meligy ◽  
Emad Abouel Nasr
Keyword(s):  
Rotating Shaft ◽  
Shaft System ◽  
Impact Forces
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