scholarly journals Chaotic dynamics in the forced nonlinear vibration of an axially accelerating viscoelastic beam

2013 ◽  
Vol 62 (20) ◽  
pp. 200502
Author(s):  
Ding Hu ◽  
Yan Qiao-Yun ◽  
Chen Li-Qun
Keyword(s):  
Nonlinear Vibration ◽  
Chaotic Dynamics ◽  
Viscoelastic Beam ◽  
Forced Nonlinear Vibration

scholarly journals Forced nonlinear vibration of shallow shell and application to technical diagnosis

2006 ◽  
Vol 28 (3) ◽  
pp. 189-196
Author(s):  
Le Ngoc Thach ◽  
Tran Van Lien
Keyword(s):  
Inverse Problems ◽  
Nonlinear Vibration ◽  
Shallow Shell ◽  
Theoretical Data ◽  
Direct And Inverse Problems ◽  
Technical Diagnosis ◽  
The Difference ◽  
Forced Nonlinear Vibration ◽  
External Loads ◽  
Diagnosis Criterion

This paper presents direct and inverse problems of forced nonlinear vibration of shallow shell. From that the method of establishment and solution of technical diagnosis for shallow shell under the vibrated load is proposed. The diagnosis criterion is the minimum of the difference between the square of experimental and theoretical data. The diagnosed parameters are the external loads and the reactions arose at the boundaries.

USING ENERGY-PHASE METHOD TO STUDY GLOBAL BIFURCATIONS AND SHILNIKOV TYPE MULTIPULSE CHAOTIC DYNAMICS FOR A NONLINEAR VIBRATION ABSORBER

2012 ◽  
Vol 22 (01) ◽  
pp. 1250001 ◽  
Author(s):  
S. B. LI ◽  
W. ZHANG ◽  
M. H. YAO
Keyword(s):  
Nonlinear Vibration ◽  
Chaotic Dynamics ◽  
Multiple Scales ◽  
Standard Form ◽  
Primary Resonance ◽  
Phase Method ◽  
Vibration Absorber ◽  
Global Bifurcations ◽  
Modulation Equation ◽  
Nonlinear Vibration Absorber

Global bifurcations and Shilnikov type multipulse chaotic dynamics for a nonlinear vibration absorber are investigated by using the energy-phase method for the first time. A two-degree-of-freedom model of a nonlinear vibration absorber is considered. After the nonlinear nonautonomous equations of this model are given, the method of multiple scales is used to derive four first-order nonlinear ordinary differential equations governing the modulation of the amplitudes and phases of the two interacting modes in the presence of 1:1 internal resonance and primary resonance. Using several coordinate transformations to transform the modulation equation into a standard form, we can apply the energy-phase method to show the existence of the multipulse chaotic dynamics by identifying Shilnikov-type multipulse orbits in the perturbed phase space. We are able to obtain the explicit restriction on the damping, forcing excitation and the detuning parameters, under which the multipulse chaotic dynamics is expected. These multipulse orbits represent the repeated departure from purely vertical oscillations for the nonlinear vibration absorber. Numerical simulations also indicate that there exist different forms of the multipulse chaotic responses and jumping phenomena for the nonlinear vibration absorber.

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