Computation method for complete D-stability intervals of a class of matrices based on generalization of the stability feeler

2010 ◽  
Author(s):  
Tadasuke Matsuda ◽  
Michihiro Kawanishi ◽  
Tatsuo Narikiyo
Keyword(s):  
Computation Method ◽  
Stability Intervals ◽  
Class Of Matrices ◽  
The Stability

Optimization of the Robust Stability Limit for Multi-Cutter Turning Processes

2015 ◽  
Author(s):  
Marta J. Reith ◽  
Daniel Bachrathy ◽  
Gabor Stepan
Keyword(s):  
Robust Stability ◽  
Optimal Parameter ◽  
Stability Limit ◽  
Boundary Function ◽  
Lower Envelope ◽  
Computation Method ◽  
Parameter Region ◽  
Dynamical Parameters ◽  
The Stability ◽  
Machining Parameter

Multi-cutter turning systems bear huge potential in increasing cutting performance. In this study we show that the stable parameter region can be extended by the optimal tuning of system parameters. The optimal parameter regions can be identified by means of stability charts. Since the stability boundaries are highly sensitive to the dynamical parameters of the machine tool, the reliable exploitation of the so-called stability pockets is limited. Still, the lower envelope of the stability lobes is an appropriate upper boundary function for optimization purposes with an objective function taken for maximal material removal rates. This lower envelope is computed by the Robust Stability Computation method presented in the paper. It is shown in this study, that according to theoretical results obtained for optimally tuned cutters, the safe stable machining parameter region can significantly be extended, which has also been validated by machining tests.

scholarly journals Estimation of Longest Stability Interval for a Kind of Explicit Linear Multistep Methods

2010 ◽  
Vol 2010 ◽  
pp. 1-18 ◽  
Author(s):  
Y. Xu ◽  
J. J. Zhao
Keyword(s):  
Absolute Stability ◽  
Numerical Experiments ◽  
Multistep Methods ◽  
Linear Multistep Methods ◽  
Stability Intervals ◽  
The Stability ◽  
Order Four

The new explicit linear three-order four-step methods with longest interval of absolute stability are proposed. Some numerical experiments are made for comparing different kinds of linear multistep methods. It is shown that the stability intervals of proposed methods can be longer than that of known explicit linear multistep methods.

An Accurate SPH Scheme for Hypervelocity Impact Modeling

2019 ◽  
Author(s):  
Anthony Collé ◽  
Jérôme Limido ◽  
Thomas Unfer ◽  
Jean-Paul Vila
Keyword(s):  
Shear Bands ◽  
Hypervelocity Impact ◽  
Stability Field ◽  
Nonlinear Stability Analysis ◽  
Alternative Scheme ◽  
Particle Hydrodynamics ◽  
Stability Intervals ◽  
The Stability ◽  
Stability And Accuracy ◽  
Repulsive Forces

Abstract We focus in this paper on the use of a meshless numerical method called Smooth Particle Hydrodynamics (SPH), to solve fragmentation issues as Hyper Velocity Impact (HVI). Contrary to classical grid-based methods, SPH does not need any opening criteria which makes it naturally well suited to handle material failure. Nevertheless, SPH schemes suffer from well-known instabilities questioning their accuracy and activating nonphysical processes as numerical fragmentation. Many stabilizing tools are available in the literature based for instance on dissipative terms, artificial repulsive forces, stress points or Particle Shifting Techniques (PST). However, they either raise conservation and consistency issues, or drastically increase the computation times. It limits then their effectiveness as well as their industrial application. To achieve robust and consistent stabilization, we propose an alternative scheme called γ -SPH-ALE. Firstly implemented to solve Monophasic Barotropic flows, it is secondly extended to the solid dynamics. Particularly, based on the ALE framework, its governing equations include advective terms allowing an arbitrary description of motion. Thus, in addition of accounting for a stabilizing low-Mach scheme, a PST is implemented through the arbitrary transport velocity field, the asset of ALE formulations. Through a nonlinear stability analysis, CFL-like conditions are formulated ensuring the scheme conservativity, robustness, stability and consistency. Besides, stability intervals are defined for the scheme parameters determining entirely the stability field. Its implementation on several test cases reveals particularly that the proposed scheme faithfully reproduces the strain localization in adiabatic shear bands, a precursor to failure. By preventing spurious oscillations in elastic waves and correcting the so-called tensile instability, it increases both stability and accuracy with respect to classical approaches.

INVESTIGATION OF THE GEOMETRY OF THE D-PARTITION OF ONE-DIMENSIONAL PLANE OF PARAMETER OF THE CHARACTERISTIC EQUATION OF A CONTINUOUS SYSTEM

2021 ◽  
Vol 4 ◽  
pp. 125-136
Author(s):  
Leonid Movchan ◽  
◽  
Sergey Movchan ◽  
Keyword(s):  
Imaginary Part ◽  
Characteristic Equation ◽  
Stability Region ◽  
Practical Interest ◽  
Stability Regions ◽  
Odd Order ◽  
Stability Intervals ◽  
Even Order ◽  
The Stability ◽  
Two Parameters

The paper considers two types of boundaries of the D-partition in the plane of one parameter of linear continuous systems given by the characteristic equation with real coefficients. The number of segments and intervals of stability of the X-partition curve is estimated. The maximum number of stability intervals is determined for different orders of polynomials of the equation of the boundary of the D-partition of the first kind (even order, odd order, one of even order, and the other of odd order). It is proved that the maximum number of stability intervals of a one-parameter family is different for all cases and depends on the ratio of the degrees of the polynomials of the equation of the D-partition curve. The derivative of the imaginary part of the expression of the investigated parameter at the initial point of the D-partition curve is obtained in an analytical form, the sign of which depends on the ratio of the coefficients of the characteristic equation and establishes the stability of the first interval of the real axis of the parameter plane. It is shown that for another type of the boundary of the D-partition in the plane of one parameter, there is only one interval of stability, the location of which, as for the previous type of the boundary of the stability region (BSR), is determined by the sign of the first derivative of the imaginary part of the expression of the parameter under study. Consider an example that illustrates the effectiveness of the proposed approach for constructing a BSR in a space of two parameters without using «Neimark hatching» and constructing special lines. In this case, a machine implementation of the construction of the stability region is provided. Considering that the problem of constructing the boundary of the stability region in the plane of two parameters is reduced to the problem of determining the BSR in the plane of one parameter, then the given estimates of the maximum number of stability regions in the plane of one parameter allow us to conclude about the number of maximum stability regions in the plane of two parameters, which are of practical interest. In this case, one of the parameters can enter nonlinearly into the coefficients of the characteristic equation.

scholarly journals Normal Form for High-Dimensional Nonlinear System and Its Application to a Viscoelastic Moving Belt

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
S. P. Chen ◽  
Y. H. Qian
Keyword(s):  
Normal Form ◽  
Nonlinear Dynamical Systems ◽  
High Dimensional ◽  
Computation Method ◽  
Double Zero ◽  
Nonlinear Dynamical ◽  
Novel Method ◽  
Explicit Formulae ◽  
The Stability ◽  
Pure Imaginary Eigenvalues

This paper is concerned with the computation of the normal form and its application to a viscoelastic moving belt. First, a new computation method is proposed for significantly refining the normal forms for high-dimensional nonlinear systems. The improved method is described in detail by analyzing the four-dimensional nonlinear dynamical systems whose Jacobian matrices evaluated at an equilibrium point contain three different cases, that are, (i) two pairs of pure imaginary eigenvalues, (ii) one nonsemisimple double zero and a pair of pure imaginary eigenvalues, and (iii) two nonsemisimple double zero eigenvalues. Then, three explicit formulae are derived, herein, which can be used to compute the coefficients of the normal form and the associated nonlinear transformation. Finally, employing the present method, we study the nonlinear oscillation of the viscoelastic moving belt under parametric excitations. The stability and bifurcation of the nonlinear vibration system are studied. Through the illustrative example, the feasibility and merit of this novel method are also demonstrated and discussed.

Delayed Feedback Control in Bilateral Teleoperation

2006 ◽  
Author(s):  
Naci Zafer
Keyword(s):  
Time Delays ◽  
Communication Channel ◽  
Oscillatory System ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Delay Systems ◽  
Bilateral Teleoperation ◽  
Delayed Feedback Controller ◽  
Stability Intervals ◽  
The Stability

Stabilization of time delay systems is currently a mainstream of research. In this paper, a delayed feedback controller is considered for internet-based teleoperation, where the master and the slave manipulators are bilaterally connected through a communication channel. A frequency based approach is employed for the stability analysis of teleoperation in spite of varying time delays. The derived approach is exact in telling weather the system is stable, whenever the system parameters including the delay are prescribed. The analysis formulates the stability intervals as delay varies. It is also shown how delayed negative feedback is able to stabilize oscillatory system dynamics. The results are illustrated with numerical examples.

The Cluster Treatment of Characteristic Roots and the Neutral Type Time-Delayed Systems

2004 ◽  
Author(s):  
Nejat Olgac ◽  
Rifat Sipahi
Keyword(s):  
Time Delay ◽  
Linear Time ◽  
Neutral Type ◽  
Direct Consequence ◽  
Necessary Condition ◽  
Delayed Systems ◽  
Linear Time Invariant ◽  
Characteristic Roots ◽  
Stability Intervals ◽  
The Stability

A new methodology is presented for assessing the stability posture of a general class of linear time-invariant – neutral time-delayed systems (LTI-NTDS). It is based on a “Cluster Treatment of Characteristic Roots CTCR” paradigm. The technique offers a number of unique features: It returns exact bounds of time delay for stability, furthermore it yields the number of unstable characteristic roots of the system in an explicit and non-sequentially evaluated function of time delay. As a direct consequence of the latter feature, the new methodology creates entirely, all existing stability intervals of delay, τ. It is shown that the CTCR inherently enforces an intriguing necessary condition for τ-stabilizability, which is the main contribution of this paper. This, so called “small delay” effect, was recognized earlier for NTDS, only through some cumbersome mathematics. In addition to the above listed characteristics, the CTCR is also unique in handling systems with unstable starting posture for τ = 0, which may be τ-stabilized for higher values of delay. Example cases are provided.

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