On the (in)stability of quasi-static paths of smooth systems: definitions and sufficient conditions

被引：8
|
作者：
Martins, JAC
Rebrova, NV
Sobolev, VA
机构：
[1] Inst Super Tecn, Dept Engn Civil & Arquitectura, P-1049001 Lisbon, Portugal
[2] Inst Super Tecn, ICIST, P-1049001 Lisbon, Portugal
[3] Univ Samara, Samara, Russia
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2006年 / 29卷 / 06期
关键词：
differential equations; singular perturbations; dynamics; quasi-statics; stability;
D O I：
10.1002/mma.707
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A concept of stability of quasi-static paths is discussed in this paper that takes into account the existence of fast (dynamic) and slow (quasi-static) time scales in the evolution of many mechanical systems. The proposed concept is essentially a continuity property with respect to the smallness of the initial perturbations (as in Lyapunov stability) and the smallness of the quasi-static loading rate (that plays the role of the small parameter in singular perturbation problems). A related concept of attractiveness is also proposed. Several examples illustrate the relevance of the definitions. Sufficient conditions for attractiveness or for instability of quasi-static paths of smooth systems are proved. Copyright (c) 2005 John Wiley & Sons, Ltd.
引用
收藏
页码：741 / 750
页数：10
相关论文
共 50 条
  • [1] Mathematical results on the stability of quasi-static paths of smooth systems
    Rebrova, N. V.
    Martins, J. A. C.
    Sobolev, V. A.
    TOPICS ON MATHEMATICS FOR SMART SYSTEMS, 2007, : 183 - +
  • [2] Assessing the "(in)stability of quasi-static paths"
    Martins, J. A. C.
    Simoes, F. M. F.
    Pinto da Costa, A.
    INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 2012, 55 : 18 - 34
  • [3] (In)stability of quasi-static paths of some finite dimensional smooth or elastic-plastic systems
    Martins, JAC
    Marques, MDPM
    Petrov, A
    Rebrova, NV
    Sobolev, VA
    Coelho, I
    INTERNATIONAL WORKSHOP ON HYSTERESIS & MULTI-SCALE ASYMPTOTICS, 2005, 22 : 124 - 138
  • [4] Some results on the stability of quasi-static paths of elastic-plastic systems with hardening
    Martins, J. A. C.
    Monteiro Marques, M. D. P.
    Petrov, A.
    INTERNATIONAL WORKSHOP ON MULTI-RATE PROCESSES AND HYSTERESIS, 2006, 55 : 155 - +
  • [5] Mathematical results on the stability of quasi-static paths of elastic-plastic systems with hardening
    Petrov, A.
    Martins, J. A. C.
    Marques, M. D. P. Monteiro
    TOPICS ON MATHEMATICS FOR SMART SYSTEMS, 2007, : 167 - +
  • [6] On the stability of quasi-static paths for finite dimensional elastic-plastic systems with hardening
    Martins, J. A. C.
    Monteiro Marques, M. D. P.
    Petrov, A.
    ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2007, 87 (04): : 303 - 313
  • [7] On the stability of quasi-static paths of a linearly elastic system with friction
    Martins, J.A.C.
    Marques, M.D.P. Monteiro
    Rebrova, N.V.
    Lecture Notes in Applied and Computational Mechanics, 2006, 27 : 351 - 358
  • [8] Electron-optical focusing by quasi-static paths
    Wallauschek, Richard
    ZEITSCHRIFT FUR PHYSIK, 1941, 117 (9-10): : 565 - 574
  • [9] A Proposal of Quasi-Static Approach for Analyzing the Stability of IP Telephony Systems
    Aida, Masaki
    Takano, Chisa
    Murata, Masayuki
    Imase, Makoto
    ICN 2008: SEVENTH INTERNATIONAL CONFERENCE ON NETWORKING, PROCEEDINGS, 2008, : 363 - +
  • [10] ELECTRIC FORCES IN QUASI-STATIC SYSTEMS
    SMITH, WE
    AUSTRALIAN JOURNAL OF PHYSICS, 1966, 19 (05): : 591 - &
12345