Dynamic stability of a lightly damped column trapped by a harmonically slowly varying explicitly time dependent load

2007 ◽  
Vol 8 (1) ◽  
Author(s):  
A M Ette
Keyword(s):  
Dynamic Stability ◽  
Time Dependent

Analytical Treatment of In-Plane Parametrically Excited Undamped Vibrations of Simply Supported Parabolic Arches

2003 ◽  
Vol 125 (1) ◽  
pp. 73-79 ◽  
Author(s):  
Dimitris S. Sophianopoulos ◽  
George T. Michaltsos
Keyword(s):  
Differential Equations ◽  
Free Vibration ◽  
Dynamic Stability ◽  
Parametric Excitation ◽  
Stability Problem ◽  
Axial Loading ◽  
Time Dependent ◽  
Analytical Treatment ◽  
Simply Supported ◽  
Forced Motion

The present work offers a simple and efficient analytical treatment of the in-plane undamped vibrations of simply supported parabolic arches under parametric excitation. After thoroughly dealing with the free vibration characteristics of the structure dealt with, the differential equations of the forced motion caused by a time dependent axial loading of the form P=P0+Pt cos θt are reduced to a set of Mathieu-Hill type equations. These may be thereafter tackled and the dynamic stability problem comprehensively discussed. An illustrative example based on Bolotin’s approach produces results validating the proposed method.

DYNAMIC STABILITY OF CABLE-STAYED BRIDGE PYLONS

2008 ◽  
Vol 08 (04) ◽  
pp. 627-643 ◽  
Author(s):  
G. T. MICHALTSOS ◽  
I. G. RAFTOYIANNIS ◽  
T. G. KONSTANTAKOPOULOS
Keyword(s):  
Dynamic Stability ◽  
Dynamic Load ◽  
Solution Method ◽  
Bridge Deck ◽  
Nonlinear Problems ◽  
Time Dependent ◽  
Metal Structures ◽  
Cable Stayed Bridge ◽  
The Stability ◽  
Cable Stayed Bridges

This paper deals with the stability of the pylons of a cable-stayed bridge under the action of time-dependent loads, due to the vibration of the bridge deck. The stability of such problems of cable-stayed bridges is solved by a technique developed in the Laboratory of Metal Structures and Steel Bridges, of National Technical University of Athens (NTUA), as well as Bolotin's technique for the solution of nonlinear problems of dynamic stability. Three cases are studied: pylons with damping, pylons under forced vibration, and pylons subjected to an arbitrary external dynamic load. Useful relations are established by the aforementioned solution method, examples for a variety of pylons are presented, and interesting results regarding the stability of each case are given in diagrams.

scholarly journals Dynamic Electromechanical Response of a Viscoelastic Dielectric Elastomer under Cycle Electric Loads

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Junjie Sheng ◽  
Yuqing Zhang
Keyword(s):  
Dynamic Response ◽  
Dynamic Stability ◽  
Relaxation Times ◽  
Excitation Frequency ◽  
Dielectric Elastomer ◽  
Time Dependent ◽  
Electric Load ◽  
Single Cycle ◽  
Set Up ◽  
Electric Loads

Dielectric elastomer (DE) is able to produce large electromechanical deformation which is time-dependent due to the viscoelasticity. In the current study, a thermodynamic model is set up to characterize the influence of viscoelasticity on the electromechanical and dynamic response of a viscoelastic DE. The time-dependent dynamic deformation, the hysteresis, and the dynamic stability undergoing viscoelastic dissipative processes are investigated. The results show that the electromechanical stability has strong frequency dependence; the viscoelastic DE can attain a larger stretch in the dynamic response than the quasistatic actuation. Furthermore, with the decreasing frequency of the applied electric load, the viscoelastic DE system will present dynamic stability evolution from an aperiodic motion to the quasiperiodic motion. The DE system may also experience a stability evolution from a single cycle motion to multicycle motion with the increasing relaxation times. The value and variation trend of the amplitude of the stretch are highly dependent on the excitation frequency and the relaxation time.

Aero/Hydrodynamic Stability of Elastically Supported Plates in Narrow Channels With Upstream Barriers Preventing Flow Redistribution

1985 ◽  
Vol 107 (3) ◽  
pp. 319-328 ◽  
Author(s):  
W. D. Mark
Keyword(s):  
Pressure Distribution ◽  
Dynamic Stability ◽  
Equations Of Motion ◽  
Sufficient Conditions ◽  
Narrow Channel ◽  
Small Time ◽  
Time Dependent ◽  
Fluid System ◽  
Narrow Channels ◽  
Elastically Supported

The dynamic stability of an elastically supported finite rigid plate centered in a straight narrow channel with incompressible flow on both sides of the plate and an upstream barrier preventing flow redistribution is analyzed. An integral equation for the pressure in a narrow channel having arbitrary small time-dependent boundary displacements is formulated and solved for the pressure distribution in terms of the boundary motion. The resulting expression for the time-dependent pressure distribution is combined with the plate differential equations of motion to yield the homogeneous equations of motion of the plate–fluid autonomous system. The Lie´nard–Chipart stability criterion is applied to the coefficients of the plate–fluid system equations to yield necessary and sufficient conditions for the dynamic stability of the plate–fluid system. The resulting stability requirements are expressed as algebraic inequalities involving dimensionless plate–fluid system parameters.

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