Principal resonance in transverse nonlinear parametric vibration of an axially accelerating viscoelastic string

2004 ◽  
Vol 20 (3) ◽  
pp. 307-316 ◽  
Author(s):  
Chen Liqun ◽  
Jean W. Zu ◽  
Wu Jun
Keyword(s):  
Parametric Vibration ◽  
Principal Resonance ◽  
Nonlinear Parametric Vibration

scholarly journals Analytical Analysis on Nonlinear Parametric Vibration of an Axially Moving String with Fractional Viscoelastic Damping

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Ying Li ◽  
Ye Tang
Keyword(s):  
Steady State ◽  
Viscoelastic Model ◽  
Material Model ◽  
Parametric Vibration ◽  
Axially Moving String ◽  
Stiffness Constant ◽  
Nonlinear Parametric Vibration ◽  
Steady State Responses ◽  
Axially Moving ◽  
State Responses

The nonlinear parametric vibration of an axially moving string made by rubber-like materials is studied in the paper. The fractional viscoelastic model is used to describe the damping of the string. Then, a new nonlinear fractional mathematical model governing transverse motion of the string is derived based on Newton’s second law, the Euler beam theory, and the Lagrangian strain. Taking into consideration the fractional calculus law of Riemann-Liouville form, the principal parametric resonance is analytically investigated via applying the direct multiscale method. Numerical results are presented to show the influences of the fractional order, the stiffness constant, the viscosity coefficient, and the axial-speed fluctuation amplitude on steady-state responses. It is noticeable that the amplitudes and existing intervals of steady-state responses predicted by Kirchhoff’s fractional material model are much larger than those predicted by Mote’s fractional material model.

scholarly journals Study on nonlinear parametric vibration of footbridge considering time-lag effect

2019 ◽  
Vol 490 ◽  
pp. 032016
Author(s):  
De-yuan Deng ◽  
Guo-rui Chen ◽  
Zhou Chen ◽  
Xiao-qing Zhang ◽  
Jian-xin Lu
Keyword(s):  
Time Lag ◽  
Parametric Vibration ◽  
Lag Effect ◽  
Nonlinear Parametric Vibration
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