scholarly journals Equilibrium states and stability of pre-tensioned adhesive tapes

2014 ◽  
Vol 5 ◽  
pp. 1725-1731 ◽  
Author(s):  
Carmine Putignano ◽  
Luciano Afferrante ◽  
Luigi Mangialardi ◽  
Giuseppe Carbone
Keyword(s):  
Surface Energy ◽  
Stability Region ◽  
Initial Conditions ◽  
Critical Value ◽  
Unstable Region ◽  
Stability Behavior ◽  
Peeling Process ◽  
The Stability ◽  
Complete Detachment ◽  
Limiting Value

In the present paper we propose a generalization of the model developed in Afferrante, L.; Carbone, G.; Demelio, G.; Pugno, N. Tribol. Lett. 2013, 52, 439–447 to take into account the effect of the pre-tension in the tape. A detailed analysis of the peeling process shows the existence of two possible detachment regimes: one being stable and the other being unstable, depending on the initial configuration of the tape. In the stability region, as the peeling process advances, the peeling angle reaches a limiting value, which only depends on the geometry, on the elastic modulus of the tape and on the surface energy of adhesion. Vice versa, in the unstable region, depending on the initial conditions of the system, the tape can evolve towards a state of complete detachment or fail before reaching a state of equilibrium with complete adhesion. We find that the presence of pre-tension in the tape does not modify the stability behavior of the system, but significantly affects the pull-off force which can be sustained by the tape before complete detachment. Moreover, above a critical value of the pre-tension, which depends on the surface energy of adhesion, the tape will tend to spontaneously detach from the substrate. In this case, an external force is necessary to avoid spontaneous detachment and make the tape adhering to the substrate.

Dynamic and Stability Analysis of the Rotating Nanobeam in a Nonuniform Magnetic Field Considering the Surface Energy

2016 ◽  
Vol 08 (04) ◽  
pp. 1650048 ◽  
Author(s):  
M. Baghani ◽  
M. Mohammadi ◽  
A. Farajpour
Keyword(s):  
Magnetic Field ◽  
Stability Analysis ◽  
Angular Velocity ◽  
Surface Energy ◽  
Axial Load ◽  
Nonuniform Magnetic Field ◽  
Small Scale ◽  
Stability Behavior ◽  
Compressive Axial Load ◽  
The Stability

It is well-known that rotating nanobeams can have different dynamic and stability responses to various types of loadings. In this research, attention is focused on studying the effects of magnetic field, surface energy and compressive axial load on the dynamic and the stability behavior of the nanobeam. For this purpose, it is assumed that the rotating nanobeam is located in the nonuniform magnetic field and subjected to compressive axial load. The nonlocal elasticity theory and the Gurtin–Murdoch model are applied to consider the effects of inter atomic forces and surface energy effect on the vibration behavior of rotating nanobeam. The vibration frequencies and critical buckling loads of the nanobeam are computed by the differential quadrature method (DQM). Then, the numerical results are testified with those results are presented in the published works and a good correlation is obtained. Finally, the effects of angular velocity, magnetic field, boundary conditions, compressive axial load, small scale parameter and surface elastic constants on the dynamic and the stability behavior of the nanobeam are studied. The results show that the magnetic field, surface energy and the angular velocity have important roles in the dynamic and stability analysis of the nanobeams.

The chaotic dynamics of a quantum Cournot duopoly game with bounded rationality

2020 ◽  
Vol 18 (06) ◽  
pp. 2050029
Author(s):  
Xinli Zhang ◽  
Deshan Sun ◽  
Wei Jiang
Keyword(s):  
Quantum Entanglement ◽  
Stability Region ◽  
Chaotic Dynamics ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Largest Lyapunov Exponent ◽  
Cournot Duopoly ◽  
The Stability ◽  
The Impact ◽  
Rational Players

This paper analyzes the chaotic dynamics of a quantum Cournot duopoly game with bounded rational players by applying quantum game theory. We investigate the impact of quantum entanglement on the stability of the quantum Nash equilibrium points and chaotic dynamics behaviors of the system. The result shows that the stability region decreases with the quantum entanglement increasing. The adjustment speeds of bounded rational players can lead to chaotic behaviors, and quantum entanglement accelerates the bifurcation and chaos of the system. Numerical simulations demonstrate the chaotic features via stability region, bifurcation, largest Lyapunov exponent, strange attractors, sensitivity to initial conditions and fractal dimensions.

scholarly journals Competition and bistability of ordered undulations and undulation chaos in inclined layer convection

2008 ◽  
Vol 597 ◽  
pp. 261-282 ◽  
Author(s):  
KAREN E. DANIELS ◽  
OLIVER BRAUSCH ◽  
WERNER PESCH ◽  
EBERHARD BODENSCHATZ
Keyword(s):  
Rayleigh Number ◽  
Stability Region ◽  
Initial Conditions ◽  
Boussinesq Equations ◽  
Chaotic State ◽  
Correlation Lengths ◽  
Spectral Pattern ◽  
Inclined Layer ◽  
Theoretical Investigations ◽  
The Stability

Experimental and theoretical investigations of undulation patterns in high-pressure inclined layer gas convection at a Prandtl number near unity are reported. Particular focus is given to the competition between the spatiotemporal chaotic state of undulation chaos and stationary patterns of ordered undulations. In experiments, a competition and bistability between the two states is observed, with ordered undulations most prevalent at higher Rayleigh number. The spectral pattern entropy, spatial correlation lengths and defect statistics are used to characterize the competing states. The experiments are complemented by a theoretical analysis of the Oberbeck–Boussinesq equations. The stability region of the ordered undulations as a function of their wave vectors and the Rayleigh number is obtained with Galerkin techniques. In addition, direct numerical simulations are used to investigate the spatiotemporal dynamics. In the simulations, both ordered undulations and undulation chaos were observed dependent on initial conditions. Experiment and theory are found to agree well.

The influence of the Stokes and Archimedes forces on the stability of a two-phase flow

2003 ◽  
Vol 3 ◽  
pp. 266-270
Author(s):  
B.H. Khudjuyerov ◽  
I.A. Chuliev
Keyword(s):  
Spectral Method ◽  
Stability Region ◽  
Gas Flow ◽  
Two Phase Flow ◽  
Solid Phase ◽  
Stability Characteristic ◽  
Phase Flow ◽  
Two Phase ◽  
The Stability

The problem of the stability of a two-phase flow is considered. The solution of the stability equations is performed by the spectral method using polynomials of Chebyshev. A decrease in the stability region gas flow with the addition of particles of the solid phase. The analysis influence on the stability characteristic of Stokes and Archimedes forces.

Enlarging the region of stability in robust model predictive controller based on dual-mode control

2021 ◽  
pp. 014233122110123
Author(s):  
Fatemeh Khani ◽  
Mohammad Haeri
Keyword(s):  
Stability Region ◽  
Linear Matrix ◽  
Input State ◽  
Dual Mode ◽  
Model Predictive Controller ◽  
Mode Control ◽  
Robust Model ◽  
Output Constraints ◽  
Predictive Controller ◽  
The Stability

Industrial processes are inherently nonlinear with input, state, and output constraints. A proper control system should handle these challenging control problems over a large operating region. The robust model predictive controller (RMPC) could be an linear matrix inequality (LMI)-based method that estimates stability region of the closed-loop system as an ellipsoid. This presentation, however, restricts confident application of the controller on systems with large operating regions. In this paper, a dual-mode control strategy is employed to enlarge the stability region in first place and then, trajectory reversing method (TRM) is employed to approximate the stability region more accurately. Finally, the effectiveness of the proposed scheme is illustrated on a continuous stirred tank reactor (CSTR) process.

scholarly journals Stability of nonaxisymmetric ferrofluid flow in rotating cylinders with magnetic field

2005 ◽  
Vol 2005 (23) ◽  
pp. 3727-3737 ◽  
Author(s):  
Jitender Singh ◽  
Renu Bajaj
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Critical Value ◽  
Annular Space ◽  
Rotating Cylinders ◽  
The Stability

Effect of an axially applied magnetic field on the stability of a ferrofluid flow in an annular space between two coaxially rotating cylinders with nonaxisymmetric disturbances has been investigated numerically. The critical value of the ratioΩ∗of angular speeds of the two cylinders, at the onset of the first nonaxisymmetric mode of disturbance, has been observed to be affected by the applied magnetic field.

DRY TURBULENCE FROM A TIME-DELAYED CHUA'S CIRCUIT

1993 ◽  
Vol 03 (02) ◽  
pp. 645-668 ◽  
Author(s):  
A. N. SHARKOVSKY ◽  
YU. MAISTRENKO ◽  
PH. DEREGEL ◽  
L. O. CHUA
Keyword(s):  
Difference Equation ◽  
Stability Region ◽  
Nonlinear Difference Equation ◽  
Chua’S Circuit ◽  
Stability Boundaries ◽  
Chua's Circuit ◽  
Infinite Dimensional ◽  
Chaotic Region ◽  
The Stability ◽  
Left Portion

In this paper, we consider an infinite-dimensional extension of Chua's circuit (Fig. 1) obtained by replacing the left portion of the circuit composed of the capacitance C2 and the inductance L by a lossless transmission line as shown in Fig. 2. As we shall see, if the remaining capacitance C1 is equal to zero, the dynamics of this so-called time-delayed Chua's circuit can be reduced to that of a scalar nonlinear difference equation. After deriving the corresponding 1-D map, it will be possible to determine without any approximation the analytical equation of the stability boundaries of cycles of every period n. Since the stability region is nonempty for each n, this proves rigorously that the time-delayed Chua's circuit exhibits the "period-adding" phenomenon where every two consecutive cycles are separated by a chaotic region.

A PHYSICAL INTERPRETATION OF MELNIKOV’S METHOD

1992 ◽  
Vol 02 (01) ◽  
pp. 1-9 ◽  
Author(s):  
YOHANNES KETEMA
Keyword(s):  
Physical Interpretation ◽  
Poincaré Map ◽  
Initial Conditions ◽  
Homoclinic Orbits ◽  
Poincare Map ◽  
Stable And Unstable Manifolds ◽  
Melnikov's Method ◽  
Melnikov’S Method ◽  
Sensitive Dependence ◽  
The Stability

This paper is concerned with analyzing Melnikov’s method in terms of the flow generated by a vector field in contrast to the approach based on the Poincare map and giving a physical interpretation of the method. It is shown that the direct implication of a transverse crossing between the stable and unstable manifolds to a saddle point of the Poincare map is the existence of two distinct preserved homoclinic orbits of the continuous time system. The stability of these orbits and their role in the phenomenon of sensitive dependence on initial conditions is discussed and a physical example is given.

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