Numerical stability analysis in structural dynamics. (English) Zbl 0979.74032

From the summary: We introduce a unified stability concept based on Lyapunov exponents. From this, suitable numerical procedures for different stability problems can be derived directly. The efficiency of the proposed algorithms is documented by means of an example.


74H55 Stability of dynamical problems in solid mechanics
74H60 Dynamical bifurcation of solutions to dynamical problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
37N15 Dynamical systems in solid mechanics
74H65 Chaotic behavior of solutions to dynamical problems in solid mechanics
Full Text: DOI


[1] Lyapunow, A. M., Stability of Motion (1966), Academic Press: Academic Press New York
[2] Krätzig, W. B., Eine einheitliche statische und dynamische Stabilitätstheorie für Pfadverfolgungsalgorithmen in der numerischen Festkörpermechanik, ZAMM, 7, 203-213 (1989) · Zbl 0722.73035
[3] Argyris, J.; Mlejnek, H.-P., Dynamics of Structures (1991), North-Holland: North-Holland Amsterdam
[5] Dinkler, D., Stabilität elastischer Tragwerke mit nichtlinearem Verformungsverhalten bei nichtstationären Einwirkungen, Ingenieur Archiv, 60, 51-61 (1989) · Zbl 0693.73037
[7] Eller, C., Finite element procedures for the stability analysis of nonlinear parametric excited shell structures, Computers and Structures, 3, 259-265 (1990) · Zbl 0727.73076
[8] Kreuzer, E., Numerische Untersuchung nichtlinearer dynamischer Systeme (1987), Springer: Springer Berlin · Zbl 0608.65040
[10] Ziegler, H., Principles of Structural Stability (1977), Birkhäuser: Birkhäuser Basel · Zbl 0383.70001
[11] Eller, C.; Krätzig, W. B., Numerische Stabilitätsanalyse linear und nichtlinear deformierbarer parametererregter Schalentragwerke, Ingenieur-Archiv, 59, 345-356 (1989) · Zbl 0694.73029
[12] Wiggins, S., Introduction to Applied Nonlinear Dynamical Systems and Chaos (1990), Springer: Springer Berlin · Zbl 0701.58001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.