scholarly journals Forced Oscillations of a Horizontal Continuous Rotor with Geometric Nonlinearity. Internal Resonance Phenomena at Harmonic Resonances and at Subharmonic Resonances of Order 1/3.

1997 ◽  
Vol 63 (605) ◽  
pp. 10-15 ◽  
Author(s):  
Yukio ISHIDA ◽  
Imao NAGASAKA ◽  
Seongwoo LEE
Keyword(s):  
Geometric Nonlinearity ◽  
Internal Resonance ◽  
Forced Oscillations ◽  
Resonance Phenomena ◽  
Subharmonic Resonances

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.

Forced Oscillations of a Continuous Asymmetrical Rotor With Geometric Nonlinearity (Major Critical Speed and Secondary Critical Speed)

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Imao Nagasaka ◽  
Yukio Ishida ◽  
Jun Liu
Keyword(s):  
Geometric Nonlinearity ◽  
Internal Resonance ◽  
Critical Speed ◽  
Longitudinal Direction ◽  
Lateral Force ◽  
Forced Oscillations ◽  
Almost Periodic ◽  
Flexible Rotor ◽  
Double Row ◽  
Stiffening Effect

Forced oscillations in the vicinities of both the major and the secondary critical speeds of a continuous asymmetrical rotor with the geometric nonlinearity are discussed. When the self-aligning double-row ball bearings support the slender flexible rotor at both ends, the geometric nonlinearity appears due to the stiffening effect in elongation of the shaft if the movements of the bearings in the longitudinal direction are restricted. The nonlinearity is symmetric when the rotor is supported vertically, and is asymmetric when it is supported horizontally. Because the rotor is slender, the natural frequency pfn of a forward whirling mode and pbn of a backward whirling mode have the relation of internal resonance pfn:pbn=1:(−1). Due to the influence of the internal resonance, various phenomena occur, such as Hopf bifurcation, an almost periodic motion, the appearance of new branches, and the diminish of unstable region. These phenomena were clarified theoretically and experimentally. Moreover, this paper focuses on the influences of the nonlinearity, the unbalance, the damping, and the lateral force on the vibration characteristics.

scholarly journals Influence of hinged device parameters on negative resonance oscillations during the operation of machine-tractor unit in transport mode

2020 ◽  
pp. 129-136
Author(s):  
V. M. Тretyak ◽  
V. V. Sheban ◽  
R. V. Oliadnichuk ◽  
O. F. Govorov ◽  
R. V. Melnik
Keyword(s):  
Oscillation Theory ◽  
Forced Oscillations ◽  
Structural Elements ◽  
Supporting Surface ◽  
Analytical Geometry ◽  
Transport Mode ◽  
Resonance Phenomena ◽  
Instantaneous Center ◽  
Strain Gauge Measurements ◽  
Kinematic Diagram

Annotation Purpose. Reducing the influence of resonance phenomena on the structural elements of a tractor of the KIY 14102 type when driving with an attached implement in transport mode. Methods. To solve this problem means of graph-analytical constructions, analytical geometry, oscillation theory and theoretical mechanics were used. Results. On the basis of the graphic-analytical analysis of the kinematic diagram of the tractor attachment of the KIY 14102 type, it was found that the position of the instantaneous center of its rotation significantly depends on the change in the angle between the tractor frame and the levers, which are united by the CA-1 automatic connection device. The frequency range of forced oscillations of the tractor frame, which occur when driving in a certain speed range, can coincide with the relative natural frequency of the tractors, which leads to resonance phenomena. Resonant longitudinal-angular vibrations of the tractor frame reduce the normal reactions of the steered wheels with the supporting surface, which worsens controllability. Changing the frequency of the natural resonance of the elements connecting the tractor with the implement can be done by changing the kinematic stiffness of the mounted system. Conclusions 1. The kinematic diagram of the hinged device of tractors significantly affects the dependence of the position of the instantaneous center of rotation of the hinged device relative to the mass of the implement that is aggregated. 2. The existing parameters of the mounted systems of tractors of the KIY 14102 type can lead to the occurrence of resonance phenomena when driving in transport mode on unpaved field roads, which negatively affects the controllability of the MTA. 3. Reducing the resonant frequency of natural vibrations of the attachment system with the tool, by reducing the kinematic stiffness, improves the dynamics of the interaction of the elements of the machine-tractor unit with each other and with the supporting surface. Keywords: machine-tractor unit, clutch system, tests, dynamic loads, strain gauge measurements, air pressure in tires.

Internal Resonance Phenomena of the Jeffcott Rotor With Nonlinear Spring Characteristics

2004 ◽  
Vol 126 (4) ◽  
pp. 476-484 ◽  
Author(s):  
Yukio Ishida ◽  
Tsuyoshi Inoue
Keyword(s):  
Internal Resonance ◽  
Critical Speed ◽  
Nonlinear Phenomena ◽  
Nonlinear Analyses ◽  
Rotor Systems ◽  
Gyroscopic Moment ◽  
Resonance Phenomena ◽  
Jeffcott Rotor ◽  
The One ◽  
Two Degree Of Freedom

The Jeffcott rotor is a two-degree-of-freedom linear model with a disk at the midspan of a massless elastic shaft. This model, executing lateral whirling motions, has been widely used in the linear analyses of rotor vibrations. In the Jeffcott rotor, the natural frequency of a forward-whirling mode pf>0 and that of a backward-whirling mode pb<0 have the relation of internal resonance pf:pb=1:−1. Recently, many researchers analyzed nonlinear phenomena by using the Jeffcott rotor with nonlinear elements. However, they did not take this internal resonance relationship into account. Furthermore in many practical rotating machines, the effect of gyroscopic moments are relatively small. Therefore, the one-to-one internal resonance relationship holds approximately between forward and backward natural frequencies in such machinery. In this paper, nonlinear phenomena in the vicinity of the major critical speed and the rotational speeds of twice and three times the major critical speed are investigated in the Jeffcott rotor and rotor systems with a small gyroscopic moment. The influences of internal resonance on the nonlinear resonances are studied in detail. The following were clarified theoretically and experimentally: (a) the shape of resonance curves becomes far more complex than that of a single resonance; (b) almost periodic motions occur; (c) these phenomena are influenced remarkably by the asymmetrical nonlinearity and gyroscopic moment; and (d) the internal resonance phenomena are strongly influenced by the degree of the discrepancies among critical speeds. The results teach us that the usage of the Jeffcott rotor in nonlinear analyses of rotor systems may induce incorrect results.

Internal Resonance Phenomena of an Asymmetrical Rotating Shaft

2005 ◽  
Vol 11 (9) ◽  
pp. 1173-1193 ◽  
Author(s):  
Yukio Ishida ◽  
Tsuyoshi Inoue
Keyword(s):  
Internal Resonance ◽  
Critical Speed ◽  
Nonlinear Phenomena ◽  
Resonance Case ◽  
Rotating Shaft ◽  
Disk System ◽  
Resonance Phenomena ◽  
Previously Treated ◽  
Unstable Vibration ◽  
Asymmetrical Rotating Shaft

In general, asymmetrical shaft-disk systems have been investigated where unstable vibrations may occur. Most studies have treated a single resonance case for the linear system, and we have previously treated a single resonance case for the nonlinear system. However, when natural frequencies have a simple integer ratio relation in a nonlinear asymmetrical shaft-disk system, an internal resonance may occur and the vibration phenomena change remarkably compared to the characteristics of a single resonance case (the case without internal resonance). In this study, the internal resonance phenomena of an asymmetrical shaft are investigated theoretically and experimentally in the vicinities of the major critical speed, and twice and three times the major critical speed. We clarify that the shape of the resonance curves changes, almost periodic motions occur, and, especially, the occurrence of unstable vibration at the rotational speed of twice the major critical speed is extremely affected by the internal resonance. Further, we show the change of nonlinear phenomena between the systems with and without internal resonance.

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