scholarly journals STABILITY ANALYSIS OF A NONLOCAL FRACTIONAL IMPULSIVE COUPLED EVOLUTION DIFFERENTIAL EQUATION

2020 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Manzoor Ahmad ◽  
◽  
Akbar Zada ◽  
Wei Dong ◽  
Jiafa Xu ◽  
...  
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Evolution Differential Equation

Numerical Integration Method for Stability Analysis of Milling With Variable Spindle Speeds

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Ye Ding ◽  
Jinbo Niu ◽  
LiMin Zhu ◽  
Han Ding
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Numerical Integration ◽  
Integration Method ◽  
Transcendental Equation ◽  
Spindle Speed ◽  
Machining Parameters ◽  
Numerical Integration Method ◽  
Stability Diagrams ◽  
Time Period

A semi-analytical method is presented in this paper for stability analysis of milling with a variable spindle speed (VSS), periodically modulated around a nominal spindle speed. Taking the regenerative effect into account, the dynamics of the VSS milling is governed by a delay-differential equation (DDE) with time-periodic coefficients and a time-varying delay. By reformulating the original DDE in an integral-equation form, one time period is divided into a series of subintervals. With the aid of numerical integrations, the transition matrix over one time period is then obtained to determine the milling stability by using Floquet theory. On this basis, the stability lobes consisting of critical machining parameters can be calculated. Unlike the constant spindle speed (CSS) milling, the time delay for the VSS is determined by an integral transcendental equation which is accurately calculated with an ordinary differential equation (ODE) based method instead of the formerly adopted approximation expressions. The proposed numerical integration method is verified with high computational efficiency and accuracy by comparing with other methods via a two-degree-of-freedom milling example. With the proposed method, this paper details the influence of modulation parameters on stability diagrams for the VSS milling.

THE STABILITY ANALYSIS OF HEAT TRANSFER IN SATURATED LIQUID FILM OF THE SPECIAL MATERIALS

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1547-1550
Author(s):  
YOULIANG CHENG ◽  
XIN LI ◽  
ZHONGYAO FAN ◽  
BOFEN YING
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Surface Tension ◽  
Stability Analysis ◽  
Liquid Film ◽  
Nonlinear Relationship ◽  
Saturated Liquid ◽  
Nonlinear Surface ◽  
Isothermal Wall ◽  
The Stability

Representing surface tension by nonlinear relationship on temperature, the boundary value problem of linear stability differential equation on small perturbation is derived. Under the condition of the isothermal wall the effects of nonlinear surface tension on stability of heat transfer in saturated liquid film of different liquid low boiling point gases are investigated as wall temperature is varied.

The Out-of-Plane Stability Analysis of Crane Jib with Two Symmetric Drawbars

2013 ◽  
Vol 446-447 ◽  
pp. 469-473
Author(s):  
Nian Li Lu ◽  
Ce Chen ◽  
Shi Ming Liu
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Boundary Conditions ◽  
Characteristic Equation ◽  
Critical Condition ◽  
Design Rules ◽  
Special Cases ◽  
Out Of Plane

The out-of-plane stability of the crane jib with two symmetric drawbars is studied. Differential equation with two non-conservative forces caused by the two symmetric drawbars is established in critical condition. According to the boundary conditions and proper parameter processing, the out-of-plane characteristic equation is obtained for the crane jib. Comparison with the ANSYS results verified the correctness of the method. And special cases are given to show the consistency of the method used in this paper and that with one drawbar given by the Chinese Design Rules for crane (GB3811-2008). The contribution of the angle between two symmetric drawbars to the out-of-plane stability of the crane jib is also discussed. The results show that, the crane jib with two symmetric drawbars has higher out-of-plane stability than that with one drawbar, and the increase of the angle between the two symmetric drawbars will lead to the significant increase of the out-of-plane stability of the crane jib.

Nonlinear Effects on Coexistence Phenomenon in Parametric Excitation

2002 ◽  
Author(s):  
Leslie Ng ◽  
Richard Rand
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Stability Analysis ◽  
Linear Stability Analysis ◽  
Perturbation Methods ◽  
Nonlinear Effects ◽  
Free Vibrations ◽  
The Stability ◽  
Parameter Values ◽  
Two Degree Of Freedom

We investigate the effect of nonlinearites on a parametrically excited ordinary differential equation whose linearization exhibits the phenomena of coexistence. The differential equation studied governs the stability mode of vibration in an unforced conservative two degree of freedom system used to model the free vibrations of a thin elastica. Using perturbation methods, we show that at parameter values corresponding to coexistence, nonlinear terms can cause the origin to become nonlinearly unstable, even though linear stability analysis predicts the origin to be stable. We also investigate the bifurcations associated with this instability.

Lyapunov-Based Sufficient Conditions for Nonlinear Impulsive Systems

2011 ◽  
Vol 219-220 ◽  
pp. 508-512
Author(s):  
Yong Liang Gao ◽  
Xiao Wu Mu
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Lyapunov Function ◽  
Sufficient Conditions ◽  
Invariant Set ◽  
Positive Definite ◽  
Impulsive Systems ◽  
Stability Theorems ◽  
Sufficient Conditions For Convergence ◽  
The Stability

This paper focuses on the stability analysis and invariant set stability theorems for nonlinear impulsive systems. A set of Lyapunov-based sufficient conditions are established for these convergent properties. These results do not require the Lyapunov function to be positive definite. Inequalities relating the righthandside of the differential equation and the Lyapunov function derivative are involved for these results. These inequalities make it possible to deduce properties of the functions and thus leads to sufficient conditions for convergence and stability.

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