Existence of Periodic Solution for Equation of Motion of Simple Beams With Harmonically Variable Length

1995 ◽  
Author(s):  
Ebrahim Esmailzadeh ◽  
Gholamreza Nakhaie-Jazar ◽  
Bahman Mehri
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Nonlinear Function ◽  
Axial Direction ◽  
Equation Of Motion ◽  
The Other ◽  
Sufficient Condition ◽  
Vibrating String ◽  
The Stability ◽  
Special Case

Abstract The transverse vibrating motion of a simple beam with one end fixed while driven harmonically along its axial direction from the other end is investigated. For a special case of zero value for the rigidity of the beam, the system reduces to that of a vibrating string with the corresponding equation of its motion. The sufficient condition for the periodic solution of the beam is then derived by means of the Green’s function and Schauder’s fixed point theorem. The criteria for the stability of the system is well defined and the condition for which the performance of the beam behaves as a nonlinear function is stated.

Existence of Periodic Solution for Beams With Harmonically Variable Length

1997 ◽  
Vol 119 (3) ◽  
pp. 485-488 ◽  
Author(s):  
E. Esmailzadeh ◽  
G. Nakhaie-Jazar ◽  
B. Mehri
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Nonlinear Function ◽  
Longitudinal Axis ◽  
Equation Of Motion ◽  
The Other ◽  
Sufficient Condition ◽  
Vibrating String ◽  
The Stability ◽  
Special Case

The transverse oscillatory motion of a simple beam with one end fixed while driven harmonically at the other end along its longitudinal axis is investigated. For a special case of zero value for the rigidity of beam, the problem reduces to that of a vibrating string with its corresponding equation of motion. The sufficient condition for the periodic solution of the beam was determined using the Green’s function and Schauder’s fixed point theorem. The criterion for the stability of the system is well defined and the condition for which the performance of the beam behaves as a nonlinear function is stated.

Asymptotic Behavior of Periodic Cohen-Grossberg Neural Networks with Delays

2009 ◽  
Vol 21 (12) ◽  
pp. 3444-3459 ◽  
Author(s):  
Wei Lin
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Lyapunov Method ◽  
Autonomous Systems ◽  
Neural Systems ◽  
Stability Criteria ◽  
Volterra System ◽  
Numerical Examples ◽  
The Stability ◽  
Special Case

Without assuming the positivity of the amplification functions, we prove some M-matrix criteria for the [Formula: see text]-global asymptotic stability of periodic Cohen-Grossberg neural networks with delays. By an extension of the Lyapunov method, we are able to include neural systems with multiple nonnegative periodic solutions and nonexponential convergence rate in our model and also include the Lotka-Volterra system, an important prototype of competitive neural networks, as a special case. The stability criteria for autonomous systems then follow as a corollary. Two numerical examples are provided to show that the limiting equilibrium or periodic solution need not be positive.

The hydromagnetic Kelvin—Helmholtz problem in a Hall plasma

1971 ◽  
Vol 5 (2) ◽  
pp. 275-288 ◽  
Author(s):  
J. F. McKenzie
Keyword(s):  
Sound Speed ◽  
Shear Plane ◽  
Incompressible Fluids ◽  
The Other ◽  
Cold Fluid ◽  
Helmholtz Problem ◽  
Hall Plasma ◽  
The Stability ◽  
Special Case

The hydromagnetic analogue of the Kelvin–Helmholtz problem is extended to include the effects of the Hall term. In contrast to other results in the literature it is shown that, in the case of incompressible fluids, the stability of a shear plane is unaffected by the introduction of the Hall term. The special case of a hot, uninagnetized fluid on one side of the interface and a cold, magnetized fluid on the other is studied in some detail. In this case it is shown that the presence of the Hall term can have either a stabilizing or a destabilizing effect, depending upon whether the sound speed in the hot fluid is very much greater than the Alfvén speed in the cold fluid or vice versa.

scholarly journals Global Stability and Oscillation of a Discrete Annual Plants Model

2010 ◽  
Vol 2010 ◽  
pp. 1-18
Author(s):  
S. H. Saker
Keyword(s):  
Fixed Point ◽  
Global Stability ◽  
Numerical Simulations ◽  
Positive Solutions ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Annual Plants ◽  
Discrete Delay ◽  
The Stability ◽  
Positive Fixed Point

The objective of this paper is to systematically study the stability and oscillation of the discrete delay annual plants model. In particular, we establish some sufficient conditions for global stability of the unique positive fixed point and establish an explicit sufficient condition for oscillation of the positive solutions about the fixed point. Some illustrative examples and numerical simulations are included to demonstrate the validity and applicability of the results.

On one-pass CPS transformations

2007 ◽  
Vol 17 (6) ◽  
pp. 793-812 ◽  
Author(s):  
OLIVIER DANVY ◽  
KEVIN MILLIKIN ◽  
LASSE R. NIELSEN
Keyword(s):  
Fixed Point ◽  
Normal Form ◽  
Lambda Calculus ◽  
Higher Order ◽  
The Other ◽  
Left Inverse ◽  
Post Processing ◽  
Transformation Time ◽  
Special Case ◽  
Implementation Technique

AbstractWe bridge two distinct approaches to one-pass CPS transformations, i.e, CPS transformations that reduce administrative redexes at transformation time instead of in a post-processing phase. One approach is compositional and higher-order, and is independently due to Appel, Danvy and Filinski, and Wand, building on Plotkin's seminal work. The other is non-compositional and based on a reduction semantics for the lambda-calculus, and is due to Sabry and Felleisen. To relate the two approaches, we use three tools: Reynolds's defunctionalization and its left inverse, refunctionalization; a special case of fold–unfold fusion due to Ohori and Sasano, fixed-point promotion; and an implementation technique for reduction semantics due to Danvy and Nielsen, refocusing. This work is directly applicable to transforming programs into monadic normal form.

scholarly journals Positive Almost Periodic Solution on a Nonlinear Differential Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Ni Hua ◽  
Tian Li-xin ◽  
Liu Xun
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Nonlinear Equation ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Positive Almost Periodic Solution ◽  
The Stability

We study the following nonlinear equationdx(t)/dt=x(t)[a(t)-b(t)xα(t)-f(t,x(t))]+g(t), by using fixed point theorem, the sufficient conditions of the existence of a unique positive almost periodic solution for above system are obtained, by using the theories of stability, the sufficient conditions which guarantee the stability of the unique positive almost periodic solution are derived.

scholarly journals On One-Pass CPS Transformations

2007 ◽  
Vol 14 (6) ◽  
Author(s):  
Olivier Danvy ◽  
Kevin Millikin ◽  
Lasse R. Nielsen
Keyword(s):  
Fixed Point ◽  
Normal Form ◽  
Lambda Calculus ◽  
Higher Order ◽  
The Other ◽  
Left Inverse ◽  
Post Processing ◽  
Transformation Time ◽  
Special Case ◽  
Implementation Technique

We bridge two distinct approaches to one-pass CPS transformations, i.e., CPS transformations that reduce administrative redexes at transformation time instead of in a post-processing phase. One approach is compositional and higher-order, and is independently due to Appel, Danvy and Filinski, and Wand, building on Plotkin's seminal work. The other is non-compositional and based on a reduction semantics for the lambda-calculus, and is due to Sabry and Felleisen. To relate the two approaches, we use three tools: Reynolds's defunctionalization and its left inverse, refunctionalization; a special case of fold-unfold fusion due to Ohori and Sasano, fixed-point promotion; and an implementation technique for reduction semantics due to Danvy and Nielsen, refocusing.<br /> <br />This work is directly applicable to transforming programs into monadic normal form.

The Stabilization of Switched Systems with Input Saturation

2014 ◽  
Vol 945-949 ◽  
pp. 2676-2679
Author(s):  
Li Jing ◽  
Li Liu
Keyword(s):  
Switched Systems ◽  
Convex Combination ◽  
Input Saturation ◽  
Switched System ◽  
New Method ◽  
Combination Method ◽  
Sufficient Condition ◽  
The Stability ◽  
Special Case ◽  
Convex Combination Method

The paper analyzed the stability of switched systems with input saturation. First it considered a special case: the switched system with only one subsystem. Using a new method to dispose saturation in the system, the paper gets the sufficient condition of stability of the system. Based on the result, the controller of the system is designed. Then common switched systems were studied. By convex combination method we obtain the sufficient conditon of stability of switched systems and propose a method to estimate the attration domain of the systems.

EXISTENCE OF A CUSP POINT ON A FOLD BIFURCATION CURVE AND STABILITY OF THE ASSOCIATED FIXED POINT: CASE OF AN n-DIMENSIONAL MAP

1999 ◽  
Vol 09 (05) ◽  
pp. 875-894 ◽  
Author(s):  
J. P. CARCASSÈS ◽  
H. KAWAKAMI
Keyword(s):  
Fixed Point ◽  
Center Manifold ◽  
Sufficient Condition ◽  
Bifurcation Curve ◽  
Cusp Point ◽  
Necessary And Sufficient Condition ◽  
Fold Bifurcation ◽  
Numerical Computing ◽  
The Stability ◽  
Necessary And Sufficient

Considering an n–dimensional map T, a necessary and sufficient condition for the existence of a cusp point on a fold bifurcation curve in a parameter plane of T is proposed. In the case of a nondegenerated cusp point, a necessary and sufficient condition for the stability of the associated nonhyperbolic fixed point is established. These conditions, obtained using the classical methods (center manifold, normal form), are expressed in an explicit algebraic well adapted for numerical computing.

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