scholarly journals Dilatancy and compaction of a rate‐and‐state fault in a poroelastic medium: Linearized stability analysis

2021 ◽  
Author(s):  
Elías Rafn Heimisson ◽  
John Rudnicki ◽  
Nadia Lapusta
Keyword(s):  
Stability Analysis ◽  
Poroelastic Medium ◽  
Linearized Stability

Instability of Viscoelastic Fluids in Blasius Flow

2010 ◽  
Author(s):  
Amin Doostmohammadi ◽  
Seyyedeh Negin Mortazavi
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Orthogonal Polynomials ◽  
Hydrodynamic Stability ◽  
Analytical Approach ◽  
Critical Reynolds Number ◽  
Blasius Flow ◽  
Linearized Stability ◽  
De Moivre’S Formula ◽  
Elasticity Number

In this paper, we study the hydrodynamic stability of a viscoelastic Walters B liquid in the Blasius flow. A linearized stability analysis is used and orthogonal polynomials which are related to de Moivre’s formula are implemented to solve Orr–Sommerfeld eigenvalue equation. An analytical approach is used in order to find the conditions of instability for Blasius flow and Critical Reynolds number is found for various combinations of the elasticity number. Based on the results, the destabilizing effect of elasticity on Blasius flow is determined and interpreted.

Stability Analysis of Complex Multibody Systems

2005 ◽  
Vol 1 (1) ◽  
pp. 71-80 ◽  
Author(s):  
Olivier A. Bauchau ◽  
Jielong Wang
Keyword(s):  
Stability Analysis ◽  
Multibody Systems ◽  
Floquet Theory ◽  
Numerical Models ◽  
Characteristic Exponent ◽  
Prony's Method ◽  
Linearized Stability ◽  
The Stability ◽  
Curve Fitting Method ◽  
Prony’S Method

The linearized stability analysis of dynamical systems modeled using finite element-based multibody formulations is addressed in this paper. The use of classical methods for stability analysis of these systems, such as the characteristic exponent method or Floquet theory, results in computationally prohibitive costs. Since comprehensive multibody models are “virtual prototypes” of actual systems, the applicability to numerical models of the stability analysis tools that are used in experimental settings is investigated in this work. Various experimental tools for stability analysis are reviewed. It is proved that Prony’s method, generally regarded as a curve-fitting method, is equivalent, and sometimes identical, to Floquet theory and to the partial Floquet method. This observation gives Prony’s method a sound theoretical footing, and considerably improves the robustness of its predictions when applied to comprehensive models of complex multibody systems. Numerical and experimental applications are presented to demonstrate the efficiency of the proposed procedure.

3D linearized stability analysis of various forms of Burnett equations

2014 ◽  
Author(s):  
Wenwen Zhao ◽  
Weifang Chen ◽  
Hualin Liu ◽  
Ramesh K. Agarwal
Keyword(s):  
Stability Analysis ◽  
Burnett Equations ◽  
Linearized Stability

A Nonlinear Stability Analysis for Difference Equations Using Semi-Implicit Mobility

1977 ◽  
Vol 17 (01) ◽  
pp. 79-91 ◽  
Author(s):  
D.W. Peaceman
Keyword(s):  
Porous Media ◽  
Stability Analysis ◽  
Finite Difference ◽  
Nonlinear Stability ◽  
Difference Equations ◽  
Nonlinear Stability Analysis ◽  
Time Step ◽  
Two Phase ◽  
Linearized Stability ◽  
The Stability

Abstract The usual linearized stability analysis of the finite-difference solution for two-phase flow in porous media is not delicate enough to distinguish porous media is not delicate enough to distinguish between the stability of equations using semi-implicit mobility and those using completely implicit mobility. A nonlinear stability analysis is developed and applied to finite-difference equations using an upstream mobility that is explicit, completely implicit, or semi-implicit. The nonlinear analysis yields a sufficient (though not necessary) condition for stability. The results for explicit and completely implicit mobilities agree with those obtained by the standard linearized analysis; in particular, use of completely implicit mobility particular, use of completely implicit mobility results in unconditional stability. For semi-implicit mobility, the analysis shows a mild restriction that generally will not be violated in practical reservoir simulations. Some numerical results that support the theoretical conclusions are presented. Introduction Early finite-difference, Multiphase reservoir simulators using explicit mobility were found to require exceedingly small time steps to solve certain types of problems, particularly coning and gas percolation. Both these problems are characterized percolation. Both these problems are characterized by regions of high flow velocity. Coats developed an ad hoc technique for dealing with gas percolation, but a more general and highly successful approach for dealing with high-velocity problems has been the use of implicit mobility. Blair and Weinaug developed a simulator using completely implicit mobility that greatly relaxed the time-step restriction. Their simulator involved iterative solution of nonlinear difference equations, which considerably increased the computational work per time step. Three more recent papers introduced the use of semi-implicit mobility, which proved to be greatly superior to the fully implicit method with respect to computational effort, ease of use, and maximum permissible time-step size. As a result, semi-implicit mobility has achieved wide use throughout the industry. However, this success has been pragmatic, with little or no theoretical work to justify its use. In this paper, we attempt to place the use of semi-implicit mobility on a sounder theoretical foundation by examining the stability of semi-implicit difference equations. The usual linearized stability analysis is not delicate enough to distinguish between the semi-implicit and completely implicit difference equation. A nonlinear stability analysis is developed that permits the detection of some differences between the stability of difference equations using implicit mobility and those using semi-implicit mobility. DIFFERENTIAL EQUATIONS The ideas to be developed may be adequately presented using the following simplified system: presented using the following simplified system: horizontal, one-dimensional, two-phase, incompressible flow in homogeneous porous media, with zero capillary pressure. A variable cross-section is included so that a variable flow velocity may be considered. The basic differential equations are (1) (2) The total volumetric flow rate is given by (3) Addition of Eqs. 1 and 2 yields =O SPEJ P. 79

Steinkamp's Toy Can Hop 100 Times But Can't Stand Up

2017 ◽  
Vol 9 (1) ◽  
Author(s):  
Gregg Stiesberg ◽  
Tim van Oijen ◽  
Andy Ruina
Keyword(s):  
Stability Analysis ◽  
Experimental Observation ◽  
Limit Cycle ◽  
Periodic Motion ◽  
Largest Eigenvalue ◽  
Unstable Limit Cycle ◽  
Stable Attractor ◽  
Linearized Stability ◽  
The Stability ◽  
Basic Motion

We have experimented with and simulated Steinkamp's passive-dynamic hopper. This hopper cannot stand up (it is statically unstable), yet it can hop the length of a 5 m 0.079 rad sloped ramp, with n≈100 hops. Because, for an unstable periodic motion, a perturbation Δx0 grows exponentially with the number of steps (Δxn≈Δx0×λn), where λ is the system eigenvalue with largest magnitude, one expects that if λ>1 that the amplification after 100 steps, λ100, would be large enough to cause robot failure. So, the experiments seem to indicate that the largest eigenvalue magnitude of the linearized return map is less than one, and the hopper is dynamically stable. However, two independent simulations show more subtlety. Both simulations correctly predict the period of the basic motion, the kinematic details, and the existence of the experimentally observed period ∼11 solutions. However, both simulations also predict that the hopper is slightly unstable (|λ|max>1). This theoretically predicted instability superficially contradicts the experimental observation of 100 hops. Nor do the simulations suggest a stable attractor near the periodic motion. Instead, the conflict between the linearized stability analysis and the experiments seems to be resolved by the details of the launch: a simulation of the hand-holding during launch suggests that experienced launchers use the stability of the loosely held hopper to find a motion that is almost on the barely unstable limit cycle of the free device.

Stability Analysis of On-Board Friction Modifier Systems at the Wheel–Rail Interface

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
C. P. Sharma ◽  
A. Srikantha Phani
Keyword(s):  
Stability Analysis ◽  
Frictional Contact ◽  
Strong Dependence ◽  
Friction Modifier ◽  
Design Engineers ◽  
Design Changes ◽  
Linearized Stability ◽  
Stability Maps ◽  
And Performance ◽  
The Stability

Friction control at the wheel–rail interface, using on-board solid stick friction modifier systems can lead to enhanced track life, reduced wear, and increased fuel economy in railroads. Frictional contact between the solid stick and the railway wheel itself can potentially cause vibrations within the modifier systems, influencing their stability and performance. A frequency domain linearized stability analysis of the state of steady sliding at the frictional contact between the solid stick and the wheel is performed. The proposed approach relies on individual frequency response functions (FRFs) of the wheel and the applicator–bracket subsystems of the on-board friction modifier. Stability characteristics of three representative bracket designs are qualitatively compared, using the FRFs generated by their respective finite element (FE) models. The FE models are validated by comparing the predicted natural frequencies with corresponding experimentally measured values on a full wheel test rig (FWTR) facility. The validated FE models are then used to compute stability maps which delineate stable and unstable regions of operation in the design parameter space, defined by train speed, angle of applicator, friction coefficient, and bracket design. Strong dependence of stability upon the bracket designs is observed. The methodology developed here can be used by design engineers to assess the effectiveness of design changes on the stability of the applicator–bracket assembly in a virtual environment—thus avoiding costly retrofitting and prototyping. Directions for further model refinement and testing are provided.

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