Dynamic Stability of a Girder Under Traveling Load Mass Systems

1991 ◽  
Vol 113 (3) ◽  
pp. 467-471
Author(s):  
T. Aida ◽  
R. Green
Keyword(s):  
Dynamic Stability ◽  
Railway Bridge ◽  
Additional Mass ◽  
Parametrically Excited ◽  
Simply Supported ◽  
Excited Vibration ◽  
Unstable Vibration ◽  
Parametrically Excited Vibration ◽  
Unsprung Mass ◽  
Load Mass

When a multi-vehicle train passes over a railway bridge, it may be expected that a parametrically excited vibration occurs in the girders, due to the change in the additional mass distribution caused by the unsprung mass of the vehicles. An analytical method to determine the dynamic stability of thin-walled beams under a sequence of equidistant masses traveling at a constant speed is developed in this paper. In the numerical examples, it is shown that the magnitude of the unsprung mass of vehicles, the distance between them and the speed of the vehicles have a large effect on the parametrically excited unstable vibration of girders. The dynamic stability of a simply supported railway bridge is clarified using the above method.

Parametrically Excited Stability of Periodically Supported Beams Under Longitudinal Harmonic Excitations

2019 ◽  
Vol 19 (09) ◽  
pp. 1950095
Author(s):  
Z. G. Ying ◽  
Y. Q. Ni ◽  
L. Fan
Keyword(s):  
Fourier Series ◽  
Dynamic Stability ◽  
Mode Coupling ◽  
Parametrically Excited ◽  
Coupling Vibration ◽  
Excited Vibration ◽  
Harmonic Excitations ◽  
Multi Mode ◽  
Floquet Theorem ◽  
Parametrically Excited Vibration

A direct eigenvalue analysis approach for solving the stability problem of periodically supported beams with multi-mode coupling vibration under general harmonic excitations is developed based on the Floquet theorem, Fourier series and matrix eigenvalue analysis. The transverse periodic supports are considered for improving the parametrically excited stability of beams under longitudinal periodic excitations. The dynamic stability of parametrically excited vibration of the beam with transverse spaced supports under longitudinal harmonic excitations is studied. The partial differential equation of motion of the beam with spaced supports under harmonic excitations is given and converted into ordinary differential equations with time-varying periodic parameters using the Galerkin method, which describe the parametrically excited vibration of the beam with coupled multiple modes. The fundamental solution to the equations is expressed as the product of periodic and exponential components based on the Floquet theorem. The periodic component and periodic parameters are expanded into Fourier series, and the matrix eigenvalue equation is obtained which is used for directly determining the parametrically excited stability. The dynamic stability of parametrically excited vibration of the beam with spaced supports under harmonic excitations is illustrated by numerical results on unstable regions. The influence of the periodic supports and excitation parameters on the parametrically excited stability is explored. The parametrically excited stability of the beam with multi-mode coupling vibration can be improved by the periodic supports. The developed analysis method is applicable to more general period-parametric beams with multi-mode coupling vibration under various harmonic excitations.

PARAMETRICALLY EXCITED INSTABILITY OF A CABLE UNDER TWO SUPPORT MOTIONS

2006 ◽  
Vol 06 (01) ◽  
pp. 43-58 ◽  
Author(s):  
Z. G. YING ◽  
Y. Q. NI ◽  
J. M. KO
Keyword(s):  
Numerical Approach ◽  
Degree Of Freedom ◽  
Stay Cable ◽  
Parametrically Excited ◽  
Excited Vibration ◽  
Mode Vibration ◽  
The Galerkin Method ◽  
Support Motion ◽  
Parametrically Excited Vibration ◽  
General Period

A direct numerical approach for solving the instability problem of multi-degree-of-freedom dynamic systems with general period-parameter excitation is developed based on the Floquet theory, Fourier series and generalized eigenvalue analysis. The developed direct numerical approach to the instability is applied to an inclined stay cable with sag under periodic two-support-motion excitation. The partially differential equation for the parametrically excited vibration of the cable is derived by using the transformation of displacements and converted into ordinary differential equations according to the Galerkin method. The unstable regions for parametrically excited vibration of the damped cable system with multi-degree-of-freedom are obtained to illustrate its overall instability. The effects of each mode vibration and parameters of the cable on the unstable regions are analyzed. The developed direct numerical approach to the parametrically excited instability is applicable to more general periodic parameter-excited systems.

Nonlinear time-delay feedback controllability for vertical parametrically excited vibration of roll system in corrugated rolling mill

2020 ◽  
Vol 117 (2) ◽  
pp. 210
Author(s):  
Dongping He ◽  
Huidong Xu ◽  
Tao Wang ◽  
Zhongkai Ren
Keyword(s):  
Time Delay ◽  
Rolling Mill ◽  
Nonlinear Damping ◽  
Feedback Controller ◽  
Nonlinear Stiffness ◽  
Parametrically Excited ◽  
Excited Vibration ◽  
Roll System ◽  
Roller System ◽  
Parametrically Excited Vibration

This paper investigates vibration characteristics of the corrugated roll system and designs a time-delay feedback controller to control the parametrically excited vibration of system. The model of parametrically excited nonlinear vertical vibration of roller system is established by considering the nonlinear damping and nonlinear stiffness within corrugated interface of corrugated rolling mill. The approximate analytical solution and amplitude-frequency characteristic equations of principal resonance and sub-resonance of roller system are obtained by using the multiple-scale method. The influences of nonlinear stiffness coefficient, nonlinear damping coefficient, system damping coefficient and rolling force amplitude on vibration are further analyzed. The time-delay feedback controller is designed to eliminate the jump and hysteresis phenomenon of the roll system and numerical simulation results demonstrate the effectiveness of the controller. The analysis results provide some theoretical guidance for vibration suppression of roller system of corrugated rolling mill.

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