Three-Dimensional Face Stability Analysis of Circular Tunnels by Numerical Simulations

Introduction: In this work, the projective synchronization of two identical three dimensional chaotic system with quadratic and quartic non linearities was considered as well as the equilibrium and stability analysis of the system. The projective synchronization with same and different scaling factor was carried out for this category of system to show its feasibility in order to establish that no matter the type and number of nonlinearities, projective synchronization can be achieved. Numerical simulations was done to verify the above. In all kinds of chaos synchronization, projective synchronization (PS), characterized by a scaling factor that two systems synchronize proportionally, is one of the most interesting problems. It was first reported by Mainieri et al [1] , where it was stated that the two identical systems (master and slave) could be synchronized up to a scaling factor, . They further stated that the scaling factor was dependent on the chaotic evolution and initial conditions so that the ultimate state of projective synchronization was unpredictable. Aims: Is to achieve projective synchronization of two identical three Dimensional chaotic system with quadratic and quartic nonlinearities synchronizing to a scaling factor and also present the equilibrium and stability analysis of the system. This is to establish that projective synchronization can be achieved for varied systems with varied nonlinearities. Materials and Methods: We employed the adaptive synchronization technique to achieve projective synchronization of the system (master and slave) with different scaling factors, and the fourth order RungeKutta algorithm is used for numerical solutions. Results: In this work, the projective synchronization of two identical three dimensional systems with quadratic and quartic nonlinearities was achieved with the same and different scaling factor, . The equilibrium and stability analysis of the system was also presented. Numerical simulations was done to verify the above. Conclusion: The investigated projective synchronization behaviour of two identical three-dimensional system with two nonlinearities (quadratic and quartic) was achieved for cases where the scaling factor is the same and when different. This shows that projective synchronization can be achieved for systems with varying nonlinearities even when the scaling factor is different and this suggests its use in communication using chaotic wave forms as carriers, perhaps with a view to securing communication.

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Bifurcations in shock-wave/laminar-boundary-layer interaction: global instability approach

Journal of Fluid Mechanics ◽

10.1017/s0022112007005095 ◽

2007 ◽

Vol 579 ◽

pp. 85-112 ◽

Cited By ~ 86

Author(s):

J.-CH. ROBINET

Keyword(s):

Boundary Layer ◽

Shock Wave ◽

Stability Analysis ◽

Numerical Simulations ◽

Laminar Boundary Layer ◽

Three Dimensional ◽

Oblique Shock Wave ◽

Global Instability ◽

Layer Interaction ◽

Boundary Layer Interaction

The principal objective of this paper is to study some unsteady characteristics of an interaction between an incident oblique shock wave impinging on a laminar boundary layer developing on a flat plate. More precisely, this paper shows that some unsteadiness, in particular the low-frequency unsteadiness, originates in a supercritical Hopf bifurcation related to the dynamics of the separated boundary layer. Various direct numerical simulations were carried out of a shock-wave/laminar-boundary-layer interaction (SWBLI). Three-dimensional unsteady Navier–Stokes equations are numerically solved with an implicit dual time stepping for the temporal algorithm and high-order AUSMPW+ scheme for the spatial discretization. A parametric study on the oblique shock-wave angle has been performed to characterize the unsteady behaviour onset. These numerical simulations have shown that starting from the incident shock angle and the spanwise extension, the flow becomes three-dimensional and unsteady. A linearized global stability analysis is carried out in order to specify and to find some characteristics observed in the direct numerical simulation. This stability analysis permits us to show that the physical origin generating the three-dimensional characters of the flow results from the existence of a three-dimensional stationary global instability.

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Quasi-three dimensional analysis of global instabilities: onset of vortex shedding behind a wavy cylinder

Journal of Fluid Mechanics ◽

10.1017/jfm.2011.102 ◽

2011 ◽

Vol 677 ◽

pp. 572-588 ◽

Cited By ~ 5

Author(s):

A. GARBARUK ◽

J. D. CROUCH

Keyword(s):

Stability Analysis ◽

Global Stability ◽

Numerical Simulations ◽

Vortex Shedding ◽

Eigenvalue Problems ◽

Landau Equation ◽

Three Dimensional ◽

Maximum Diameter ◽

Ginzburg Landau ◽

The Stability

In this paper the global-stability theory is extended to account for weak spanwise-flow variations using a quasi-three-dimensional framework. The analysis considers the onset of vortex shedding behind a circular cylinder with a spanwise-varying diameter. The quasi-three-dimensional approach models the fully three-dimensional flow structure as a series of two-dimensional eigenvalue problems representing the sectional-flow behaviour. The sectional results are coupled together using the Ginzburg–Landau equation, which models the diffusive coupling and provides the global response. The onset of global instability (and thus vortex shedding) is linked to both the sectional growth rates (characterized by the maximum-diameter location) and the spanwise extent of the zone of instability. Unsteady numerical simulations are used to guide the global-stability analysis and to assess the fidelity of the predictions. Results from the stability analysis are shown to be in good agreement with the numerical simulations, which are in close agreement with experiments.

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Analysis of Face Stability during Excavation of Double-O-Tube Shield Tunnel

The Scientific World JOURNAL ◽

10.1155/2013/781968 ◽

2013 ◽

Vol 2013 ◽

pp. 1-11 ◽

Cited By ~ 2

Author(s):

Yuyou Yang ◽

Qinghong Zhou ◽

Hongan Li ◽

Xuegang Huang ◽

Xiaoming Tu

Keyword(s):

Stability Analysis ◽

Failure Mechanism ◽

Three Dimensional ◽

Soil Mass ◽

Shield Tunnel ◽

Face Stability ◽

Supporting Pressure ◽

The Face ◽

Collapse Failure ◽

Kinematic Theorem

This paper focuses on the face stability analysis of Double-O-Tube shield tunnel. This kind of analysis is significant to ensure the safety of workers and reduce the influence on the surrounding environment. The key point of the stability analysis is to determine the supporting pressure applied to the face by the shield. A collapse failure will occur when the supporting pressure is not sufficient to prevent the movement of the soil mass towards the tunnel. A three-dimensional collapse failure mechanism was presented in this paper. Based on the mechanism of a single circular shield tunnel, the mechanism of Double-O-Tube shield tunnel was established by using the fact that both of the mechanisms are symmetrical. Then by means of the kinematic theorem of limit analysis, the numerical results were obtained, and a design chart was provided. The finite difference software FLAC3D was applied to investigate the face failure mechanism of DOT shield tunnel established in this paper; the critical supporting pressures of the collapse failure mechanism in different strata (sand and silt) were calculated. Through comparative analysis, the theoretical values were very close to the numerical values. This shows that the face failure mechanism of DOT shield tunnel is reasonable, and it can be applied to the sand and silt strata.

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