Dynamic Stability of a Vibrating Hammer

1969 ◽  
Vol 91 (4) ◽  
pp. 1175-1179 ◽  
Author(s):  
C. C. Fu ◽  
B. Paul
Keyword(s):  
Computer Simulation ◽  
Steady State ◽  
Asymptotic Stability ◽  
Drill Bit ◽  
Asymptotically Stable ◽  
Stability Of Motion ◽  
Rock Drill ◽  
The Stability ◽  
Energy Absorbing ◽  
Steady State Solutions

This paper deals with the stability of motion of an elastically suspended vibrating hammer that impacts upon an energy absorbing surface. The energy absorber could represent, for example, a rock drill bit or drill steel, or a spike being driven by the hammer. The problem is intrinsically nonlinear because the instant of impact depends upon the motion of the hammer. “Simple steady-state solutions” are derived, and their asymptotic stability is examined. Regions in which the analytically constructed simple solutions are asymptotically stable are determined in parameter space. Results have been checked by a digital computer simulation.

Stability and instability of steady-state solutions for a hydrodynamic model of semiconductors

1997 ◽  
Vol 127 (4) ◽  
pp. 781-796 ◽  
Author(s):  
Harumi Hattori
Keyword(s):  
Steady State ◽  
Initial Data ◽  
Positive Constant ◽  
Hydrodynamic Model ◽  
Steady State Solution ◽  
Doping Profile ◽  
Asymptotically Stable ◽  
Stability And Instability ◽  
The Stability ◽  
Steady State Solutions

We discuss the stability and instability of steady-state solutions for a hydrodynamic model of semiconductors. We study the case where the doping profile is close to a positive constant and depends on the special variable x. We shall show that a given steady-state solution is asymptotically stable or unstable, depending on whether or not the density of the initial data satisfies P = 0, where P is defined in (3.12).

Dynamic Stability of an Impact System Connected With Rock Drilling

1969 ◽  
Vol 36 (4) ◽  
pp. 743-749 ◽  
Author(s):  
C. C. Fu
Keyword(s):  
Computer Simulation ◽  
Exact Solution ◽  
Steady State ◽  
Asymptotic Stability ◽  
Piecewise Linear ◽  
Steady State Solution ◽  
External Excitation ◽  
Rock Drilling ◽  
Impact System ◽  
Number Of Cycles

This paper deals with asymptotic stability of an analytically derived, synchronous as well as nonsynchronous, steady-state solution of an impact system which exhibits piecewise linear characteristics connected with rock drilling. The exact solution, which assumes one impact for a given number of cycles of the external excitation, is derived, its asymptotic stability is examined, and ranges of parameters are determined for which asymptotic stability is assured. The theoretically predicted stability or instability is verified by a digital computer simulation.

Stability Considerations in Thermoelastic Contact

1980 ◽  
Vol 47 (4) ◽  
pp. 871-874 ◽  
Author(s):  
J. R. Barber ◽  
J. Dundurs ◽  
M. Comninou
Keyword(s):  
Steady State ◽  
Perturbation Method ◽  
Energy Function ◽  
First Principles ◽  
Dimensional Model ◽  
Contact Conditions ◽  
One Dimensional ◽  
Thermoelastic Contact ◽  
The Stability ◽  
Steady State Solutions

A simple one-dimensional model is described in which thermoelastic contact conditions give rise to nonuniqueness of solution. The stability of the various steady-state solutions discovered is investigated using a perturbation method. The results can be expressed in terms of the minimization of a certain energy function, but the authors have so far been unable to justify the use of such a function from first principles in view of the nonconservative nature of the system.

scholarly journals Controlling the dynamics of Burgers equation with a high-order nonlinearity

2004 ◽  
Vol 2004 (62) ◽  
pp. 3321-3332 ◽  
Author(s):  
Nejib Smaoui
Keyword(s):  
Steady State ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Nonlinear Boundary ◽  
Burgers Equation ◽  
High Order ◽  
Time Stepping ◽  
Backward Euler ◽  
High Order Nonlinearity ◽  
Steady State Solutions

We investigate analytically as well as numerically Burgers equation with a high-order nonlinearity (i.e.,ut=νuxx−unux+mu+h(x)). We show existence of an absorbing ball inL2[0,1]and uniqueness of steady state solutions for all integern≥1. Then, we use an adaptive nonlinear boundary controller to show that it guarantees global asymptotic stability in time and convergence of the solution to the trivial solution. Numerical results using Chebychev collocation method with backward Euler time stepping scheme are presented for both the controlled and the uncontrolled equations illustrating the performance of the controller and supporting the analytical results.

Dynamics and pattern formation in a modified Leslie–Gower model with Allee effect and Bazykin functional response

2017 ◽  
Vol 10 (05) ◽  
pp. 1750073 ◽  
Author(s):  
Peng Feng
Keyword(s):  
Steady State ◽  
Pattern Formation ◽  
Spatial Pattern ◽  
Numerical Simulations ◽  
Functional Response ◽  
Allee Effect ◽  
Turing Instability ◽  
Spatial Pattern Formation ◽  
The Stability ◽  
Steady State Solutions

In this paper, we study the dynamics of a diffusive modified Leslie–Gower model with the multiplicative Allee effect and Bazykin functional response. We give detailed study on the stability of equilibria. Non-existence of non-constant positive steady state solutions are shown to identify the rage of parameters of spatial pattern formation. We also give the conditions of Turing instability and perform a series of numerical simulations and find that the model exhibits complex patterns.

Dynamic Analysis of the Optical Disk Drive System Equipped With an Automatic Ball Balancer With Consideration of Torsional Motion

2003 ◽  
Author(s):  
Chun-Chieh Wang ◽  
Cheng-Kuo Sung ◽  
Paul C. P. Chao
Keyword(s):  
Steady State ◽  
Multiple Scales ◽  
Substantial Reduction ◽  
Disk Drive ◽  
Optical Disk ◽  
Balance System ◽  
Optical Disk Drive ◽  
The Stability ◽  
Steady State Solutions ◽  
Theoretical Results

This study is dedicated to evaluate the stability of an automatic ball-type balance system (ABS) installed in Optical Disk Drives (ODD). There have been researchers devoted to study the performance of ABS by investigating the dynamics of the system, but few consider the motions in torsional direction of ODD foundation. To solve this problem, a mathematical model including the foundation is established. The method of multiple scales is then utilized to find all possible steady-state solutions and perform related stability analysis. The obtained results are used to predict the level of residual vibrations and then the performance of the ABS can be evaluated. Numerical simulations are conducted to verify the theoretical results. It is obtained from both analytical and numerical results that the spindle speed of the motor ought to be operated above primary translational and secondary torsional resonances to stabilize the desired steady-state solutions for a substantial reduction in radial vibration.

scholarly journals On Oscillatory Pattern of Malaria Dynamics in a Population with Temporary Immunity

2007 ◽  
Vol 8 (3) ◽  
pp. 191-203 ◽  
Author(s):  
J. Tumwiine ◽  
J. Y. T. Mugisha ◽  
L. S. Luboobi
Keyword(s):  
Steady State ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Oscillatory Pattern ◽  
The Stability ◽  
Disease Free ◽  
The Basic Reproduction Number ◽  
Temporary Immunity

We use a model to study the dynamics of malaria in the human and mosquito population to explain the stability patterns of malaria. The model results show that the disease-free equilibrium is globally asymptotically stable and occurs whenever the basic reproduction number,R0is less than unity. We also note that whenR0>1, the disease-free equilibrium is unstable and the endemic equilibrium is stable. Numerical simulations show that recoveries and temporary immunity keep the populations at oscillation patterns and eventually converge to a steady state.

scholarly journals The Stability of Two-Step Runge-Kutta Methods for Neutral Delay Integro Differential-Algebraic Equations with Many Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Haiyan Yuan ◽  
Jihong Shen
Keyword(s):  
Asymptotic Stability ◽  
Differential Algebraic Equations ◽  
Asymptotically Stable ◽  
Algebraic Equations ◽  
Neutral Delay ◽  
Runge Kutta ◽  
The Stability

This paper studies the asymptotic stability of the two-step Runge-Kutta methods for neutral delay integro differential-algebraic equations with many delays. It proves that A-stable two-step Runge-Kutta methods are asymptotically stable for neutral delay integro differential-algebraic equations with many delays.

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