scholarly journals Bifurcation Analysis of a Four-Dimensional System of Two Symmetric Coupled Nonlinear Oscillators with Clearance

2022 ◽  
Vol 2160 (1) ◽  
pp. 012072
Author(s):  
Ziyu Guo ◽  
Jing Li ◽  
Shaotao Zhu ◽  
Hui Geng
Keyword(s):  
Approximate Solution ◽  
Nonlinear Vibration ◽  
Bifurcation Analysis ◽  
Dynamic Behaviour ◽  
Averaging Method ◽  
Singularity Theory ◽  
Nonlinear Oscillators ◽  
Dynamical Analysis ◽  
Dimensional System ◽  
Coupled Nonlinear Oscillators

Abstract The research gradually highlights vibration and dynamical analysis of symmetric coupled nonlinear oscillators model with clearance. The aim of this paper is the bifurcation analysis of the symmetric coupled nonlinear oscillators modeled by a four-dimensional nonsmooth system. The approximate solution of this system is obtained with aid of averaging method and Krylov-Bogoliubov (KB) transformation presented by new notations of matrices. The bifurcation function is derived to investigate its dynamic behaviour by singularity theory. The results obtained provide guidance for the nonlinear vibration of symmetric coupled nonlinear oscillators model with clearance.

Experimental observations of nonlinear vibration localization in a cyclic chain of weakly coupled nonlinear oscillators

2021 ◽  
Vol 497 ◽  
pp. 115952
Author(s):  
B. Niedergesäß ◽  
A. Papangelo ◽  
A. Grolet ◽  
A. Vizzaccaro ◽  
F. Fontanela ◽  
...  
Keyword(s):  
Nonlinear Vibration ◽  
Nonlinear Oscillators ◽  
Vibration Localization ◽  
Weakly Coupled ◽  
Coupled Nonlinear Oscillators

scholarly journals Nonlinear vibration localisation in a symmetric system of two coupled beams

2020 ◽  
Author(s):  
Filipe Fontanela ◽  
Alessandra Vizzaccaro ◽  
Jeanne Auvray ◽  
Björn Niedergesäß ◽  
Aurélien Grolet ◽  
...  
Keyword(s):  
Experimental Investigation ◽  
Nonlinear Vibration ◽  
Piecewise Linear ◽  
Nonlinear Oscillators ◽  
Symmetric System ◽  
Weakly Coupled ◽  
Coupled Nonlinear Oscillators ◽  
Coupled Beams ◽  
Two Degree Of Freedom ◽  
Piecewise Linear Stiffness

Abstract We report nonlinear vibration localisation in a system of two symmetric weakly coupled nonlinear oscillators. A two degree-of-freedom model with piecewise linear stiffness shows bifurcations to localised solutions. An experimental investigation employing two weakly coupled beams touching against stoppers for large vibration amplitudes confirms the nonlinear localisation.

Dynamical Analysis and Realization of an Adaptive Isolator

2017 ◽  
Vol 85 (1) ◽  
Author(s):  
Sun Xiuting ◽  
Shu Zhang ◽  
Jian Xu ◽  
Feng Wang
Keyword(s):  
Nonlinear Vibration ◽  
Structural Property ◽  
Vibration Isolation ◽  
Structural Parameters ◽  
Singularity Theory ◽  
Dynamical Analysis ◽  
Damping Properties ◽  
Isolation System ◽  
State Band ◽  
Stiffness And Damping

An adaptive vibration isolation system is proposed in this paper to combine the advantages of both linear and nonlinear isolators. Because of the proposed structural piecewise characteristics for different levels of response, the stiffness and damping properties could be designed according to the vibration performances. The adaptive stiffness and damping properties are achieved by the joined utilization of symmetrical precompression triangle-like structure (TLS) and column frame with cam. In order to design the control mechanism with optimum structural parameters, nonlinear vibration performances are analyzed by using averaging method and singularity theory. The parameter plane is divided into transition sets, and then the optimization criterions for structural design are provided according to multiple nonlinear vibration performances including frequency band for effective isolation, multisteady state band and resonance peak, etc. The experiment is carried out to verify the theoretical selection of desirable parameters and indicates the advantages and improvement of vibration isolation/suppression brought by the structural property adaptation. This study provides a novel method of achieving structural property adaptation for the improvement of isolation effectiveness, which shows the intelligent realization by passive components.

scholarly journals Experimental Observation of the Amplitude Death Effect in Two Coupled Nonlinear Oscillators

2000 ◽  
Vol 84 (23) ◽  
pp. 5312-5315 ◽  
Author(s):  
R. Herrero ◽  
M. Figueras ◽  
J. Rius ◽  
F. Pi ◽  
G. Orriols
Keyword(s):  
Experimental Observation ◽  
Nonlinear Oscillators ◽  
Amplitude Death ◽  
Coupled Nonlinear Oscillators

Bifurcations of a Nonlinear Two-Degree-of-Freedom System Under Narrow-Band Stochastic Excitation

1992 ◽  
Vol 114 (1) ◽  
pp. 24-31
Author(s):  
R. Lin ◽  
K. Huseyin ◽  
C. W. S. To
Keyword(s):  
Relaxation Time ◽  
Correlation Time ◽  
Averaging Method ◽  
Narrow Band ◽  
Singularity Theory ◽  
Random Parameter ◽  
Degree Of Freedom ◽  
Stochastic Excitation ◽  
Static Approach ◽  
Two Degree Of Freedom

In this paper, bifurcations of a nonlinear two-degree-of-freedom system subjected to a narrow-band stochastic excitation are investigated. Under the assumption that the correlation time greatly exceeds the relaxation time, a quasi-static approach combined with averaging method is adopted to obtain the bifurcation equations, and the singularity theory is applied to analyze the bifurcations. It is demonstrated that bifurcation patterns jump from one to another due to the influence of a random parameter. The probabilities of the jumping bifurcation patterns are given.

Brownian Motion of Coupled Nonlinear Oscillators: Thermalized Solitons and Nonlinear Response to External Forces

1978 ◽  
Vol 40 (4) ◽  
pp. 206-210 ◽  
Author(s):  
S. E. Trullinger ◽  
M. D. Miller ◽  
R. A. Guyer ◽  
A. R. Bishop ◽  
F. Palmer ◽  
...  
Keyword(s):  
Brownian Motion ◽  
Nonlinear Response ◽  
Nonlinear Oscillators ◽  
Coupled Nonlinear Oscillators ◽  
External Forces
Sign in / Sign up

Export Citation Format

Share Document