Stability of Cylindrical Shells Under Moving Loads by the Direct Method of Liapunov

1967 ◽  
Vol 34 (4) ◽  
pp. 991-998 ◽  
Author(s):  
G. A. Hegemier
Keyword(s):  
Constant Velocity ◽  
Local Stability ◽  
Shell Theory ◽  
Circular Cylindrical Shell ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Functional Space ◽  
Moving Loads ◽  
The Stability ◽  
Shell Axis

The stability of a long, thin, elastic circular cylindrical shell subjected to axial compression and an axisymmetric load moving with constant velocity along the shell axis is studied. With the aid of the direct method of Liapunov, and employing a nonlinear Donnell-type shell theory, sufficient conditions for local stability of the axisymmetric response are established in a functional space whose metric is defined in an average sense. Numerical results, which are presented for the case of a moving decayed step load, reveal that the sufficient conditions for stability developed here and the sufficient conditions for instability obtained in a previous paper lead to the actual stability transition boundary.

Dynamic Stability of Isotropic or Composite-Material Cylindrical Shells Containing Swirling Fluid Flow

1977 ◽  
Vol 44 (1) ◽  
pp. 112-116 ◽  
Author(s):  
T. L. C. Chen ◽  
C. W. Bert
Keyword(s):  
Shell Theory ◽  
Swirling Flow ◽  
Circular Cylindrical Shell ◽  
Critical Flow ◽  
Fluid System ◽  
Critical Flow Velocity ◽  
Rotating Speed ◽  
Fluid Forces ◽  
Shell Motion ◽  
The Stability

A linear stability analysis is presented for a thin-walled, circular cylindrical shell of orthotropic material conveying a swirling flow. Shell motion is modeled by using the dynamic orthotropic version of the Sanders shell theory and fluid forces are described by inviscid, incompressible flow theory. The critical flow velocities are determined for piping made of composite and isotropic materials conveying swirling water. Fluid rotation strongly degrades the stability of the shell/fluid system, i.e. increasing the fluid rotating speed severely decreases the critical flow velocity.

Stability Conditions for a Class of Distributed-Parameter Systems

1966 ◽  
Vol 88 (2) ◽  
pp. 475-479 ◽  
Author(s):  
R. E. Blodgett
Keyword(s):  
Equilibrium State ◽  
Local Stability ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Chemical Reactor ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Stability Conditions ◽  
Stability And Instability ◽  
Liapunov's Direct Method

The purpose of this paper is to obtain stability conditions for a class of nonlinear distributed-parameter systems by using a generalization of Liapunov’s direct method. Sufficient conditions for local stability and instability of the equilibrium state are derived. An application is given in which conditions are obtained for stability of a chemical-reactor process.

scholarly journals Stability of reaction–diffusion systems with stochastic switching

2019 ◽  
Vol 24 (3) ◽  
pp. 315-331 ◽  
Author(s):  
Lijun Pan ◽  
Jinde Cao ◽  
Ahmed Alsaedi
Keyword(s):  
Direct Method ◽  
Markov Switching ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Fubini Theorem ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Stochastic Switching ◽  
The Stability ◽  
Independent And Identically Distributed

In this paper, we investigate the stability for reaction systems with stochastic switching. Two types of switched models are considered: (i) Markov switching and (ii) independent and identically distributed switching. By means of the ergodic property of Markov chain, Dynkin formula and Fubini theorem, together with the Lyapunov direct method, some sufficient conditions are obtained to ensure that the zero solution of reaction–diffusion systems with Markov switching is almost surely exponential stable or exponentially stable in the mean square. By using Theorem 7.3 in [R. Durrett, Probability: Theory and Examples, Duxbury Press, Belmont, CA, 2005], we also investigate the stability of reaction–diffusion systems with independent and identically distributed switching. Meanwhile, an example with simulations is provided to certify that the stochastic switching plays an essential role in the stability of systems.

Stability Theory in the Sense of Lyapunov — Basic Approach: Discrete Singular Time Delayed System

Volume 1 ◽  
2004 ◽  
Author(s):  
D. Lj. Debeljkovic ◽  
S. A. Milinkovic ◽  
S. B. Stojanovic ◽  
M. B. Jovanovic
Keyword(s):  
Stability Theory ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Discrete Delay ◽  
Basic Approach ◽  
Delayed System ◽  
The Stability ◽  
Working Out ◽  
Singular Time

This paper gives sufficient conditions for the stability of linear singular discrete delay systems of the form Ex(k+1) = Aox(k)+A1x((k-1). These new, delay-independent conditions are derived using approach based on Lyapunov’s direct method. A numerical example has been working out to show the applicability of results derived. To the best knowledge of the authors, such result have not yet been reported.

scholarly journals Delay Induced Hopf Bifurcation of an Epidemic Model with Graded Infection Rates for Internet Worms

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Tao Zhao ◽  
Dianjie Bi
Keyword(s):  
Hopf Bifurcation ◽  
Local Stability ◽  
Sufficient Conditions ◽  
Propagation Model ◽  
Infection Rates ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Internet Worms ◽  
Form Theory ◽  
The Stability

A delayed SEIQRS worm propagation model with different infection rates for the exposed computers and the infectious computers is investigated in this paper. The results are given in terms of the local stability and Hopf bifurcation. Sufficient conditions for the local stability and the existence of Hopf bifurcation are obtained by using eigenvalue method and choosing the delay as the bifurcation parameter. In particular, the direction and the stability of the Hopf bifurcation are investigated by means of the normal form theory and center manifold theorem. Finally, a numerical example is also presented to support the obtained theoretical results.

A Procedure for Investigating the Liapunov Stability of Nonautonomous Linear Second-Order Systems

1973 ◽  
Vol 40 (4) ◽  
pp. 1103-1106 ◽  
Author(s):  
S. E. Jones ◽  
T. R. Robe
Keyword(s):  
Differential Equation ◽  
Ad Hoc ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Liapunov Function ◽  
Null Solution ◽  
Liapunov Stability ◽  
The Stability ◽  
Second Order Systems ◽  
Liapunov's Direct Method

Utilizing Liapunov’s direct method a procedure is presented which generates sufficient conditions for the stability of the null solution of the nonautonomous differential equation x¨ + b(t)x˙ + a(t)x = 0. This procedure systematically leads to the construction of a Liapunov function for a given differential equation and thus eliminates the normally ad hoc nature of the direct method. Four examples illustrating the procedure are discussed.

Response of Cylindrical Shells to Moving Loads

1964 ◽  
Vol 31 (1) ◽  
pp. 105-111 ◽  
Author(s):  
J. P. Jones ◽  
P. G. Bhuta
Keyword(s):  
Cylindrical Shell ◽  
Constant Velocity ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Moving Loads ◽  
Coupling Effects ◽  
Influence Coefficients ◽  
Pressure Pulses

The response of a circular cylindrical shell subjected to a moving ring load with a constant velocity has been examined in detail when both longitudinal and transverse coupling effects are included. It is found that the correction in the bending resonance velocity resulting from the inclusion of longitudinal coupling effects is small. The results of the analysis may be used as influence coefficients to determine, by means of Duhamel integrals, the displacements and stresses produced by varying pressure pulses.

scholarly journals Instability of Cylindrical Shells Subjected to Axisymmetric Moving Loads

1966 ◽  
Vol 33 (2) ◽  
pp. 289-296 ◽  
Author(s):  
G. A. Hegemier
Keyword(s):  
Cylindrical Shell ◽  
Constant Velocity ◽  
Broad Class ◽  
Infinite Length ◽  
Functional Difference ◽  
Moving Loads ◽  
Loading Function ◽  
Double Laplace Transform ◽  
Special Cases ◽  
The Stability

Using a Donnell-type nonlinear theory and the stability in the small concept of Poincare´, the instability of an infinite-length cylindrical shell subjected to a broad class of axisymmetric loads moving with constant velocity is studied. Special cases of the general loading function include the moving-ring, step, and decayed-step loads. The analysis is carried out with a double Laplace transform, functional-difference technique. Numerical results are presented for the case of the moving-ring load.

scholarly journals Hopf Bifurcation of a Predator-Prey System with Delays and Stage Structure for the Prey

2012 ◽  
Vol 2012 ◽  
pp. 1-28 ◽  
Author(s):  
Zizhen Zhang ◽  
Huizhong Yang
Keyword(s):  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Local Stability ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Positive Equilibrium ◽  
Predator Prey ◽  
Center Manifold Theorem ◽  
Prey System ◽  
The Stability

This paper is concerned with a Holling type III predator-prey system with stage structure for the prey population and two time delays. The main result is given in terms of local stability and bifurcation. By choosing the time delay as a bifurcation parameter, sufficient conditions for the local stability of the positive equilibrium and the existence of periodic solutions via Hopf bifurcation with respect to both delays are obtained. In particular, explicit formulas that can determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are established by using the normal form method and center manifold theorem. Finally, numerical simulations supporting the theoretical analysis are also included.

scholarly journals Stability and Hopf Bifurcation of a Predator-Prey Model with Distributed Delays and Competition Term

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Lv-Zhou Zheng
Keyword(s):  
Hopf Bifurcation ◽  
Local Stability ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Positive Equilibrium ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Positive Equilibrium Point ◽  
The Stability

A class of predator-prey system with distributed delays and competition term is considered. By considering the time delay as bifurcation parameter, we analyze the stability and the Hopf bifurcation of the predator-prey system. According to the theorem of Hopf bifurcation, some sufficient conditions are obtained for the local stability of the positive equilibrium point.

Sign in / Sign up

Export Citation Format

Share Document