Resonant Dynamics and Saturation in a Coupled System With Quadratic Nonlinearities

2004 ◽  
Author(s):  
Reddy Mankala ◽  
D. Dane Quinn
Keyword(s):  
Angular Velocity ◽  
Normal Modes ◽  
Coupled System ◽  
Angular Speed ◽  
Degree Of Freedom ◽  
Weakly Coupled System ◽  
Quadratic Nonlinearities ◽  
Resonant Dynamics ◽  
Three Degree Of Freedom ◽  
Dynamic Resonance

This work examines the behavior of a three-degree-of-freedom weakly coupled system. The system is composed of two components. The first is a two degree-of-freedom translational system that possesses an internal 2 : 1 resonance between the linear normal modes, which are coupled through quadratic nonlinearities. Under external forcing this component exhibits the saturation phenomena. The second is a rotational mass with a small imbalance, supported by the translational component. The angular speed of the rotor is not fixed, rather, the rotor is subject to a small torque and therefore its angular velocity slowly varies in time. A dynamic resonance occurs when the angular velocity of the rotor evolves to a neighborhood of one of the frequencies of the linear normal modes. Each of these resonances has been independently investigated previously in the literature. This work uncovers how the behavior of the dynamic resonance is modified by the mode coupling introduced by the 2 : 1 internal resonance and describes how the amplitudes of the linear normal modes are dependent on the properties of the dynamic resonance.

Instabilities Arising From the Frictional Interaction of a Pin-Disk System Resulting in Noise Generation

1976 ◽  
Vol 98 (1) ◽  
pp. 81-86 ◽  
Author(s):  
S. W. E. Earles ◽  
C. K. Lee
Keyword(s):  
Angular Speed ◽  
Degree Of Freedom ◽  
Noise Generation ◽  
Disk System ◽  
Single Degree Of Freedom ◽  
Disk Brake ◽  
Thin Steel ◽  
Three Degree Of Freedom ◽  
Squeal Noise ◽  
Experimental Rig

A steel pin, supported on a flexible cantilever, is pressed against a thin steel disk which rotates at a uniform angular speed. The orientation of the pin’s central axis to the plane of the disk, the bending and torsional stiffnesses of the pin support, the stiffness of the disk, and the line of action of the resultant interactive force are all shown to affect the self-induced coupled frequencies and modes generated. The analysis of the experimental arrangement in terms of a three-degree-of-freedom pin subsystem and a single-degree-of-freedom disk element suggests that the system is unstable for certain combinations of the variables. The instabilities are shown to belong to a class of “geometrically induced” or “kinematic constraint” instability. The region of squeal-noise generation within the experimental rig is shown to correspond to the oscillatory unstable region predicted theoretically. The noise generated is similar to disk-brake squeal, and so the work furthers the understanding of this practical problem.

scholarly journals Nonlinear Normal Modes in a Three-Degree-of-Freedom Vibration Isolating System with Internal Resonance.

2002 ◽  
Vol 68 (671) ◽  
pp. 1950-1958
Author(s):  
Tetsuro TOKOYODA ◽  
Noriaki YAMASHITA ◽  
Hiroyuki OISHI ◽  
Takeshi YAMAMOTO ◽  
Masatsugu YOSHIZAWA
Keyword(s):  
Internal Resonance ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Degree Of Freedom ◽  
Nonlinear Normal ◽  
Three Degree Of Freedom

Non-Ideal System With Quadratic Nonlinearities Containing a Two-to-One Internal Resonance

2016 ◽  
Author(s):  
Rodrigo T. Rocha ◽  
Jose M. Balthazar ◽  
D. Dane Quinn ◽  
Angelo M. Tusset ◽  
Jorge L. P. Felix
Keyword(s):  
Internal Resonance ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Excitation Frequency ◽  
Coupled System ◽  
Dynamical Behaviour ◽  
Main System ◽  
Weakly Coupled System ◽  
Ideal System ◽  
Quadratic Nonlinearities

The dynamical behaviour of a non-ideal three-degrees-of-freedom weakly coupled system associated with the quadratic nonlinearities in the equations of motion is investigated. The main system consists of two nonlinear mechanical oscillators coupling with quadratic nonlinearities and in which possess a 2:1 internal resonance between their translational movements. Under these conditions, we analyzed the response when a DC unbalanced motor with limited power supply (non-ideal system) excites the main system. When the excitation frequency is near to second natural frequency of the main system, saturation and jump phenomena are presented. Then, this work will analyze some torques of the motor, which causes the phenomena, and due to high amplitudes of motion will be possible to look for a way to harvest energy in a future work.

Nonlinear Normal Modes for Multi-Degree-of-Freedom Nonlinear Vibration Isolation System

2006 ◽  
Author(s):  
Xiang Yu ◽  
Shi-Jian Zhu ◽  
Shu-Yong Liu
Keyword(s):  
Nonlinear Vibration ◽  
Vibration Isolation ◽  
Equations Of Motion ◽  
Normal Modes ◽  
Coupled System ◽  
Degree Of Freedom ◽  
Isolation System ◽  
Vibration Isolation System ◽  
Invariant Surfaces ◽  
Nonlinear Normal

Nonlinear vibration isolation system (VIS) plays an important role for improving the capability of hydroacoustic stealth of naval vessels. In engineering, Nonlinear VIS is generally a multi-degree-of-freedom system and its mathematical model is a set of coupled differential equations. Nonlinear normal mode (NNM) is an effective tool for decoupling and analyzing the dynamics of this coupled system. In this paper, taking the flexibility of the base into consideration, the equations of motion of an on-board VIS with quadric and cubic nonlinearities is formulated. The NNMs of this multi-degree-of-freedom nonlinear VIS are constructed by using the invariant manifold approach. The invariant surfaces of the NNMs and the decoupled oscillators are presented.

scholarly journals Nonliner Normal Modes in a Three-Degree-of-Freedom Vibration Isolating System : Application of Qualitative Nonlinear Analysis

2003 ◽  
Vol 2003.9 (0) ◽  
pp. 277-278
Author(s):  
Masakazu NAKAMURA ◽  
Takeshi YAMAMOTO ◽  
Tetsuro TOKOYODA ◽  
Hiroshi YABUNO ◽  
Makatsugu YOSHIZAWA
Keyword(s):  
Nonlinear Analysis ◽  
System Application ◽  
Normal Modes ◽  
Degree Of Freedom ◽  
Three Degree Of Freedom
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