Numerical results for the nonaxisymmetric problem of the stability of vertical mining excavations

1976 ◽  
Vol 12 (9) ◽  
pp. 973-975
Author(s):  
Zh. S. Akopyan
Keyword(s):  
Numerical Results ◽  
Nonaxisymmetric Problem ◽  
The Stability

scholarly journals On the Importance of the Influence of both Velocity and Aspect Ratios on the Occurrence of Bifurcation Phenomena within a Two-Sided Lid-Driven Enclosure

2015 ◽  
Vol 55 ◽  
pp. 160-172
Author(s):  
Fayçal Hammami ◽  
Nader Ben Cheikh ◽  
Brahim Ben Beya
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Numerical Results ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Left Wall ◽  
Driven Cavity ◽  
Aspect Ratios ◽  
The Stability ◽  
The Right

This paper deals with the numerical study of bifurcations in a two-sided lid driven cavity flow. The flow is generated by moving the upper wall to the right while moving the left wall downwards. Numerical simulations are performed by solving the unsteady two dimensional Navier-Stokes equations using the finite volume method and multigrid acceleration. In this problem, the ratio of the height to the width of the cavity are ranged from H/L = 0.25 to 1.5. The code for this cavity is presented using rectangular cavity with the grids 144 × 36, 144 × 72, 144 × 104, 144 × 136, 144 × 176 and 144 × 216. Numerous comparisons with the results available in the literature are given. Very good agreements are found between current numerical results and published numerical results. Various velocity ratios ranged in 0.01≤ α ≤ 0.99 at a fixed aspect ratios (A = 0.5, 0.75, 1.25 and 1.5) were considered. It is observed that the transition to the unsteady regime follows the classical scheme of a Hopf bifurcation. The stability analysis depending on the aspect ratio, velocity ratios α and the Reynolds number when transition phenomenon occurs is considered in this paper.

Stability of Horizontal Boundary Layers

2006 ◽  
Author(s):  
Jean-Yves Chemin ◽  
Benoit Desjardins ◽  
Isabelle Gallagher ◽  
Emmanuel Grenier
Keyword(s):  
Reynolds Number ◽  
Linear Stability ◽  
Mathematical Proof ◽  
Vertical Component ◽  
Ekman Layer ◽  
Numerical Results ◽  
Energy Estimates ◽  
Navier Stokes ◽  
The 1960S ◽  
The Stability

Let us now detail the stability properties of an Ekman layer introduced in Part I, page 11. First we will recall how to compute the critical Reynolds number. Then we will describe briefly what happens at larger Reynolds numbers. The first step in the study of the stability of the Ekman layer is to consider the linear stability of a pure Ekman spiral of the form where U∞ is the velocity away from the layer and ζ is the rescaled vertical component ζ = x3/√εν. The corresponding Reynolds number is Let us consider the Navier–Stokes–Coriolis equations, linearized around uE The problem is now to study the (linear) stability of the 0 solution of the system (LNSCε). If u=0 is stable we say that uE is linearly stable, if not we say that it is linearly unstable. Numerical results show that u=0 is stable if and only if Re<Rec where Rec can be evaluated numerically. Up to now there is no mathematical proof of this fact, and it is only possible to prove that 0 is linearly stable for Re<Re1 and unstable for Re>Re2 with Re1<Rec<Re2, Re1 being obtained by energy estimates and Re2 by a perturbative analysis of the case Re=∞. We would like to emphasize that the numerical results are very reliable and can be considered as definitive results, since as we will see below, the stability analysis can be reduced to the study of a system of ordinary differential equations posed on the half-space, with boundary conditions on both ends, a system which can be studied arbitrarily precisely, even on desktop computers (first computations were done in the 1960s by Lilly).

scholarly journals Dynamics of a Discretization Physiological Control System

2007 ◽  
Vol 2007 ◽  
pp. 1-16 ◽  
Author(s):  
Xiaohua Ding ◽  
Huan Su
Keyword(s):  
Control System ◽  
Discrete System ◽  
Numerical Results ◽  
Positive Equilibrium ◽  
Hopf Bifurcations ◽  
Physiological Control ◽  
Midpoint Rule ◽  
The Stability ◽  
Stability Of The Solution

We study the dynamics of solutions of discrete physiological control system obtained by Midpoint rule. It is shown that a sequence of Hopf bifurcations occurs at the positive equilibrium as the delay increases and we analyze the stability of the solution of the discrete system and calculate the direction of the Hopf bifurcations. The numerical results are presented.

Stability Analysis of Shear Deformable Trapezoidal Composite Plates

2019 ◽  
Vol 19 (08) ◽  
pp. 1971004 ◽  
Author(s):  
Amit Kumar ◽  
M. K. Singha ◽  
Vikrant Tiwari
Keyword(s):  
Numerical Technique ◽  
Composite Plates ◽  
Numerical Results ◽  
Shear Stresses ◽  
Quadrilateral Element ◽  
Buckling Resistance ◽  
Edge Based ◽  
The Stability ◽  
Shear Deformable ◽  
Transverse Shear Strains

The stability characteristics of shear deformable trapezoidal composite plates are studied here. Thestrain smoothing technique is employed to approximate the membrane strains and curvatures of the edge-based smoothing cells. The transverse shear strains within the Reissner–Mindlin quadrilateral element are obtained using the edge-consistent interpolation approach. At the beginning, the performance of the present numerical technique is examined for the buckling analysis of trapezoidal panels under in-plane compressive or shear stresses. Thereafter, new results on the buckling and postbuckling behaviors of trapezoidal composite plates are presented, for which comparable numerical results are rare in the literature. Representative numerical results are presented to highlight the interaction between the higher pre-buckling stresses and increased stiffness near the shorter edge with fiber orientation and loading direction on the buckling resistance of trapezoidal panels.

Development and Applicability of Multiscale Multiphysics Integrated Simulator for Tsunami

2019 ◽  
Vol 14 (2) ◽  
pp. 225-234 ◽  
Author(s):  
Taro Arikawa ◽  
Yu Chida ◽  
Katsumi Seki ◽  
Tomohiro Takagawa ◽  
Kenichiro Shimosako ◽  
...  
Keyword(s):  
Structural Analysis ◽  
Structural Damage ◽  
Numerical Results ◽  
Structural Deformation ◽  
Local Conditions ◽  
Physical Experiments ◽  
The Stability ◽  
Good Agreement

In this research, we develop a numerical fluid simulator coupled with a structural analysis. The purpose of this system is to efficiently calculate all stages of a tsunami from source to runup, including structural deformation. We also investigate the stability of breakwaters at Kamaishi port. The numerical results are compared with physical experiments, revealing good agreement. The system is applied to the local conditions at Kamaishi port to verify its applicability. Most of the breakwaters are washed away, which is similar to the actual reported damage, indicating that the proposed system can effectively reproduce tsunami structural damage.

scholarly journals Analysis of a New Fractional Model for Damped Bergers’ Equation

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 35-41 ◽  
Author(s):  
Jagdev Singh ◽  
Devendra Kumar ◽  
Maysaa Al Qurashi ◽  
Dumitru Baleanu
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Fractional Derivative ◽  
Numerical Solution ◽  
Numerical Results ◽  
Fractional Model ◽  
Applied Method ◽  
The Stability

AbstractIn this article, we present a fractional model of the damped Bergers’ equation associated with the Caputo-Fabrizio fractional derivative. The numerical solution is derived by using the concept of an iterative method. The stability of the applied method is proved by employing the postulate of fixed point. To demonstrate the effectiveness of the used fractional derivative and the iterative method, numerical results are given for distinct values of the order of the fractional derivative.

FINITE DIFFERENCE MODELING OF THE ULTRASONIC FIELD RADIATED BY CIRCULAR TRANSDUCERS

2004 ◽  
Vol 12 (04) ◽  
pp. 475-499 ◽  
Author(s):  
AHLEM ALIA ◽  
HAKIM DJELOUAH ◽  
NOUREDDINE BOUAOUA
Keyword(s):  
Ultrasonic Field ◽  
Ultrasonic Pulse ◽  
Absorbing Boundary Conditions ◽  
Numerical Results ◽  
Absorbing Boundary ◽  
Arrival Times ◽  
Solid Media ◽  
Spatio Temporal ◽  
The Stability ◽  
Response Method

In this paper, FD formulations in cylindrical coordinates are used to model the field radiated, by a circular source, in fluid and solid media. The stability of the used schemes is controlled by a proper choice of time and space steps. Absorbing boundary conditions are introduced to satisfy the assumption of a propagation in a half space medium. In order to minimize the CPU time, calculations are limited for regions disturbed by the propagating ultrasonic pulse then the calculus zone is incremented. Some numerical results are presented to illustrate the effect of the medium nature, source vibration profiles and eventually the presence of targets in the acoustic field. A spatio-temporal description of the diffraction phenomena is given. The radiated field is interpreted in terms of plane and edge waves. For solid media, this interpretation allows the determination of the arrival times which are compared with those numerically predicted. Numerical results corresponding to fluid media are compared to those obtained by the Impulse Response Method. The good agreement obtained justifies the choice of the FDM for the modeling of the wave propagation problems.

Stability and Vibrations of Geometrically Nonlinear Cylindrically Orthotropic Circular Plates

1984 ◽  
Vol 51 (2) ◽  
pp. 354-360 ◽  
Author(s):  
D. Shilkrut
Keyword(s):  
Stability Analysis ◽  
Qualitative Methods ◽  
Dynamic Method ◽  
Numerical Results ◽  
Geometrically Nonlinear ◽  
Circular Plates ◽  
Different Types ◽  
The Stability ◽  
Thermal Influence ◽  
Cylindrically Orthotropic

The stability analysis of axisymmetrical equilibrium states of geometrically nonlinear, orthotropic, circular plates that are deformed by multiparameter loading, including thermal influence, is presented. The dynamic method (method of small vibrations) is used to accomplish this purpose. The behavior of the plate in different cases is revealed. In particular, it is shown that two different types of snapping processes can occur. The values of frequencies of small eigenvibrations from various cases have been calculated. These investigations are realized by numerical and qualitative methods. Here only the numerical results are presented.

scholarly journals The stability of a trailing-line vortex in compressible flow

1994 ◽  
Vol 269 ◽  
pp. 323-351 ◽  
Author(s):  
Jillian A. K. Stott ◽  
Peter W. Duck
Keyword(s):  
Mach Number ◽  
Compressible Flow ◽  
Numerical Results ◽  
Line Vortex ◽  
Mach Numbers ◽  
The Stability ◽  
Vortex Axis ◽  
Very High ◽  
High Wavenumbers

We consider the inviscid stability of the Batchelor (1964) vortex in a compressible flow. The problem is tackled numerically and also asymptotically, in the limit of large (azimuthal and streamwise) wavenumbers, together with large Mach numbers. The nature of the solution passes through different regimes as the Mach number increases, relative to the wavenumbers. At very high wavenumbers and Mach numbers, the mode which is present in the incompressible case ceases to be unstable, whilst a new ‘centre mode’ forms, whose stability characteristics are determined primarily by conditions close to the vortex axis. We find that generally the flow becomes less unstable as the Mach number increases, and that the regime of instability appears generally confined to disturbances in a direction counter to the direction of the rotation of the swirl of the vortex.Throughout the paper comparison is made between our numerical results and results obtained from the various asymptotic theories.

scholarly journals Stability analysis of cylindrical shells subjected to complex loads

2001 ◽  
Vol 23 (4) ◽  
pp. 247-256
Author(s):  
Ngo Huong Nhu
Keyword(s):  
Cylindrical Shell ◽  
Stability Analysis ◽  
Composite Shell ◽  
Laminated Composite ◽  
Numerical Results ◽  
Load Pressure ◽  
Combined Loads ◽  
Analytical Result ◽  
The Stability ◽  
Good Agreement

The paper deals with stability analysis of shell on the basis FEM via Castem 2000. The numerical results of stability problems of cylinders subjected to different loads as compress load, pressure, concentrated and combined loads are compared with analytical result and give a good agreement. The influence of changing radius of the cylindrical shell on the unstable forms and the influence of angles of fibers on unstable behaviour of laminated composite shell are considered. Numerical results and corresponding programs by languages Gibian given in the paper to realize software Castem 2000 can be applied in the design and in the stability analysis of the shell with more complex conditions

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