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.

Global Analyses of Multi-Degree-of-Freedom Nonlinear Vibration Isolation System

2007 ◽  
Author(s):  
Xiang Yu ◽  
Shijian Zhu ◽  
Shuyong Liu
Keyword(s):  
Nonlinear Vibration ◽  
Vibration Isolation ◽  
Complex Dynamics ◽  
Equations Of Motion ◽  
Mapping Method ◽  
Degree Of Freedom ◽  
High Dimensional ◽  
Isolation System ◽  
Vibration Isolation System ◽  
A Cell

The abundant and complex dynamics of high-dimensional nonlinear systems have drawn increasing attentions in recent years, but further analyses have been confined because of the inefficiency of some analytic methods for high-dimensional systems. This paper focuses on the bifurcation and global analyses of a multi-degree-of-freedom nonlinear vibration isolation system using numerical methods. Firstly, the equations of motion of the multi-degree-of-freedom nonlinear vibration isolation system for onboard machine are formulated. Then, exhaustive bifurcation analyses are carried out and six branches are illustrated in the bifurcation diagrams revealing that several different types of stable motions may coexist in certain parameter regimes. A cell mapping method is modified to analyze the global characteristics including the locations and basins of the coexistent attractors of the multi-degree-of-freedom nonlinear vibration isolation system.

Dynamic Analysis of Nonlinear Vibration Isolation System Based on Flexible Foundation

2014 ◽  
Vol 1030-1032 ◽  
pp. 766-769
Author(s):  
Shu Ying Li ◽  
Rui Huo ◽  
Xing Ke Cui ◽  
Cui Ping Liu ◽  
Dao Kun Zhang
Keyword(s):  
Nonlinear Vibration ◽  
Power Flow ◽  
Vibration Isolation ◽  
Low Frequency ◽  
Coupled System ◽  
Optimized Design ◽  
Isolation System ◽  
Vibration Isolation System ◽  
Vibration Isolators ◽  
Flexible Foundation

In this paper,a general dynamic model of the isolation coupled system which is composed of isolation object,nonlinear vibration isolation support,and flexible foundation is established,calculated method of applying vibration power flow to analyze isolation effectiveness is studied.Further more,as an calculation example,a air spring vibration isolation system of HS-700 engines is numerically simulated.Designs several low-frequency nonlinear vibration isolators and analyzes its vibration isolation effect.It discusses the effect of the vibration isolator parameters on the transmitted power flow of the system.The results provide a theoretical basis for the optimized design of nonlinear vibration isolation system.

Dynamic Analysis of Multi-Supported Nonlinear Vibration Isolation System Mounted on Flexible Foundation

2013 ◽  
Vol 419 ◽  
pp. 223-227 ◽  
Author(s):  
Rui Huo ◽  
Hui Yu ◽  
Yan Feng Guan
Keyword(s):  
Numerical Solution ◽  
Nonlinear Vibration ◽  
Power Flow ◽  
Vibration Isolation ◽  
Engineering Application ◽  
System Dynamic ◽  
Dynamic Equations ◽  
Isolation System ◽  
Vibration Isolation System ◽  
Flexible Foundation

In view of its prototype in engineering application, a theoretical model of multi-supported nonlinear vibration isolation system installed on flexible foundation is studied, including derivation of system dynamic equations and analysis of system dynamic characteristics. For effectiveness evaluation of nonlinear vibration isolation systems, a generalized time-averaged power is proposed as an extension of classical theory of vibratory power flow, and a numerical solution method of time-averaged power is probed accompanying with the numerical solution of nonlinear dynamic equations. In a further concrete calculation example, an air spring vibration isolation system of a small UAV engine is numerically simulated based on Runge-Kutta method, and dynamic behavior and power flow transmission characteristics influenced by system parameters are investigated.

Fuzzy control of a semi-active multiple degree-of-freedom vibration isolation system

2013 ◽  
Vol 21 (8) ◽  
pp. 1608-1621 ◽  
Author(s):  
Chunsheng Song ◽  
Zude Zhou ◽  
Shengquan Xie ◽  
Yefa Hu ◽  
Jinguang Zhang ◽  
...  
Keyword(s):  
Fuzzy Control ◽  
Vibration Isolation ◽  
Degree Of Freedom ◽  
Isolation System ◽  
Vibration Isolation System

Passage Through Resonance in a Vibration Isolation System (Effects of Rate of Increasing the Voltage Applied to D.C. Motor)

2007 ◽  
Author(s):  
Tomohiko Tange ◽  
Ryo Kawana ◽  
Tetsuro Tokoyoda ◽  
Masatsugu Yoshizawa ◽  
Toshihiko Sugiura
Keyword(s):  
Rigid Body ◽  
Internal Resonance ◽  
Vibration Isolation ◽  
Transient Behavior ◽  
Degree Of Freedom ◽  
Isolation System ◽  
Vibration Isolation System ◽  
Rotational Vibration ◽  
Three Degree Of Freedom ◽  
Driving Torque

This paper deals with transient nonlinear vibration of a rigid body suspended on a foundation by elastic springs and constrained in a plane. In such a three degree-of-freedom vibration isolation system, we assume that ‘2-1-1’ internal resonance exists between the vertical and horizontal vibrations of the rigid body and the rotational vibration about its center of gravity. Our main purpose is to examine theoretically the transient behavior passing through resonance under the condition that the D.C. motor directly drives the unbalanced rotor. Numerical simulation was carried out to clarify effects of rate of increasing V(t) on the peak amplitude of the vibration of the rigid body and on the driving torque of the D.C. motor. Moreover, experiment was conducted with a physical model of a three degree-of-freedom vibration isolation system, and the transient behavior passing through resonance was observed and compared with theoretical results in a typical case with internal resonance.

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