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.

A PREY-PREDATOR MODEL WITH DIFFUSION AND A SUPPLEMENTARY RESOURCE FOR THE PREY IN A TWO‐PATCH ENVIRONMENT

2005 ◽  
Vol 9 (1) ◽  
pp. 9-24 ◽  
Author(s):  
J. Dhar
Keyword(s):  
Steady State ◽  
Asymptotic Stability ◽  
Prey Species ◽  
Steady State Solution ◽  
State Solution ◽  
Prey Population ◽  
Predator Species ◽  
Additional Resource ◽  
Linear And Nonlinear ◽  
Predator Model

In this paper, a prey‐predator dynamics, where the predator species partially depends upon the prey species, in a two patch habitat with diffusion and there is a non‐diffusing additional resource for the prey population, is modeled and analyzed. It is shown, that there exists a positive, monotonic, continuous steady state solution with continuous matching at the interface for both the species separately. Further, we obtain conditions for asymptotic stability for both linear and nonlinear cases. Šiame straipsnyje modeliuojama ir analizuojama plešr‐unu ir auku dinamika, laikant, kad plešr-unu populiacija dalinai priklauso nuo auku skačiaus. Areala sudaro dvi sritys, kuriose vyksta populiaciju individu difuzija, be to, aukoms yra išskirtas nedifunduojantis resursas. Irodyta, kad egzistuoja teigiamas, monotoniškas, tolydus stacionarusis sprendinys, tenkinantis tolydumo salyga abiems populiacijoms atskirai. Gautos asimptotinio stabilumo salygos tiesiniu ir netiesiniu atvejais.

scholarly journals Dynamic properties of piecewise linear systems with fractional time-delay feedback

2021 ◽  
pp. 146134842110076
Author(s):  
Jianchao Zhang ◽  
Jun Wang ◽  
Jiangchuan Niu ◽  
Yufei Hu
Keyword(s):  
Steady State ◽  
Time Delay ◽  
Analytical Solution ◽  
Goodness Of Fit ◽  
Numerical Solutions ◽  
Dynamic Properties ◽  
Piecewise Linear ◽  
Steady State Solution ◽  
State Solution ◽  
Comparison Results

The forced vibration of a single-degree-of-freedom piecewise linear system containing fractional time-delay feedback was investigated. The approximate analytical solution of the system was obtained by employing an averaging method. A frequency response equation containing time delay was obtained by studying a steady-state solution. The stability conditions of the steady-state solution, the amplitude–frequency results, and the numerical solutions of the system under different time-delay parameters were compared. Comparison results indicated a favorable goodness of fit between the two parameters and revealed the correctness of the analytical solution. The effects of the time-delay and fractional parameters, piecewise stiffness, and piecewise gap on the principal resonance and bifurcation of the system were emphasized. Results showed that fractional time delay occurring in the form of equivalent linear dampness and stiffness under periodic variations in the system and influenced the vibration characteristic of the system. Moreover, piecewise stiffness and gap induced the nonlinear characteristic of the system under certain parameters.

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.

scholarly journals A Semigroup Approach to the System with Primary and Secondary Failures

2010 ◽  
Vol 2010 ◽  
pp. 1-33 ◽  
Author(s):  
Abdukerim Haji
Keyword(s):  
Functional Analysis ◽  
Steady State ◽  
Asymptotic Stability ◽  
Positive Solution ◽  
Steady State Solution ◽  
Linear Operators ◽  
Time Dependent ◽  
Well Posedness ◽  
Semigroup Approach ◽  
Time Dependent Solution

We investigate the solution of a repairable parallel system with primary as well as secondary failures. By using the method of functional analysis, especially, the spectral theory of linear operators and the theory ofC0-semigroups, we prove well-posedness of the system and the existence of positive solution of the system. And then we show that the time-dependent solution strongly converges to steady-state solution, thus we obtain the asymptotic stability of the time-dependent solution.

scholarly journals Global Asymptotic Stability of 3-Species Mutualism Models with Diffusion and Delay Effects

2009 ◽  
Vol 2009 ◽  
pp. 1-20 ◽  
Author(s):  
Chang-you Wang ◽  
Shu Wang ◽  
Xiang-ping Yan
Keyword(s):  
Steady State ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Upper And Lower Solutions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Steady State Solution ◽  
State Problem ◽  
Delay Effects ◽  
Steady State Problem

In this paper, the Lotka-Volterra 3-species mutualism models with diffusion and delay effects is investigated. A simple and easily verifiable condition is given to ensure the global asymptotic stability of the unique positive steady-state solution of the corresponding steady-state problem in a bounded domain with Neumann boundary condition. Our approach to the problem is based on inequality skill and the method of the upper and lower solutions for a more general reaction—diffusion system. Finally, some numerical simulations are given to illustrate our results.

An airfoil theory of bifurcating laminar separation from thin obstacles

1990 ◽  
Vol 216 ◽  
pp. 255-284 ◽  
Author(s):  
C. J. Lee ◽  
H. K. Cheng
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Steady State ◽  
Steady State Solution ◽  
Equation System ◽  
Branch Points ◽  
Laminar Separation ◽  
Kutta Condition ◽  
Numerical Studies ◽  
Steady State Solutions

Global interaction of the boundary layer separating from an obstacle with resulting open/closed wakes is studied for a thin airfoil in a steady flow. Replacing the Kutta condition of the classical theory is the breakaway criterion of the laminar triple-deck interaction (Sychev 1972; Smith 1977), which, together with the assumption of a uniform wake/eddy pressure, leads to a nonlinear equation system for the breakaway location and wake shape. The solutions depend on a Reynolds numberReand an airfoil thickness ratio or incidence τ and, in the domain$Re^{\frac{1}{16}}\tau = O(1)$considered, the separation locations are found to be far removed from the classical Brillouin–Villat point for the breakaway from a smooth shape. Bifurcations of the steady-state solution are found among examples of symmetrical and asymmetrical flows, allowing open and closed wakes, as well as symmetry breaking in an otherwise symmetrical flow. Accordingly, the influence of thickness and incidence, as well as Reynolds number is critical in the vicinity of branch points and cut-off points where steady-state solutions can/must change branches/types. The study suggests a correspondence of this bifurcation feature with the lift hysteresis and other aerodynamic anomalies observed from wind-tunnel and numerical studies in subcritical and high-subcriticalReflows.

Dependency of Unsteady Time-Linearized Flutter Investigations on the Steady State Flow Field

2011 ◽  
Author(s):  
Michael Blocher ◽  
Markus May ◽  
Harald Schoenenborn
Keyword(s):  
Steady State ◽  
Steady State Solution ◽  
Elastic Stability ◽  
Compressor Cascade ◽  
Steady State Flow ◽  
State Flow ◽  
Flow Parameters ◽  
Pressure Distributions ◽  
German Aerospace ◽  
École Polytechnique

The influence of the steady state flow solution on the aero-elastic stability behaviour of an annular compressor cascade shall be studied in order to determine sensitivities of the aero-dynamic damping with respect to characteristic flow parameters. In this context two different flow regimes — a subsonic and a transonic case — are subject to the analysis. The pressure distributions, steady as well as unsteady, on the blade surface of the NACA3506 profile are compared to experimental data that has been gained by the Institute of Aeroelasticity of the German Aerospace Center (DLR) during several wind tunnel tests at the annular compressor cascade facility RGP-400 of the Ecole Polytechnique Fe´de´rale de Lausanne (EPFL). Whereas a certain robustness of the unsteady CFD results can be stated for the subsonic flow regime, the transonic regime proves to be very sensitive with respect to the steady state solution.

On the steady-state solution of the M/G/2 queue

1979 ◽  
Vol 11 (01) ◽  
pp. 240-255 ◽  
Author(s):  
Per Hokstad
Keyword(s):  
Steady State ◽  
General Solution ◽  
Laplace Transform ◽  
Queue Length ◽  
Joint Distribution ◽  
Length Distribution ◽  
Steady State Solution ◽  
Queue Length Distribution ◽  
The Difference ◽  
Number Of Customers

The asymptotic behaviour of the M/G/2 queue is studied. The difference-differential equations for the joint distribution of the number of customers present and of the remaining holding times for services in progress were obtained in Hokstad (1978a) (for M/G/m). In the present paper it is found that the general solution of these equations involves an arbitrary function. In order to decide which of the possible solutions is the answer to the queueing problem one has to consider the singularities of the Laplace transforms involved. When the service time has a rational Laplace transform, a method of obtaining the queue length distribution is outlined. For a couple of examples the explicit form of the generating function of the queue length is obtained.

Observations on the Steady-State Solution of an Extremely Flexible Spinning Disk With a Transverse Load

1983 ◽  
Vol 50 (3) ◽  
pp. 525-530 ◽  
Author(s):  
R. C. Benson
Keyword(s):  
Steady State ◽  
Hybrid System ◽  
Fourth Order ◽  
Steady State Solution ◽  
Transverse Load ◽  
System Of Differential Equations ◽  
Membrane Theory ◽  
Small Disk ◽  
Spinning Disk ◽  
Flexible Disk

The steady deflection of a transversely loaded, extremely flexible, spinning disk is studied. Membrane theory is used to predict the shapes and locations of waves that dominate the response. It is found that waves in disconnected regions are possible. Some results are presented to show how disk stiffness moderates the membrane waves, the most important result being an upper bound on the highest ordered wave of significant amplitude. A hybrid system of differential equations and boundary conditions is developed to replace the pure membrane formulation that is singular, and the full fourth-order plate formulation that is numerically sensitive. The hybrid formulation retains the salient features of the flexible disk response and facilitates calculations for very small disk stiffnesses.

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