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  • 1
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    International Journal of Non-Linear Mechanics 27 (1992), S. 219-232 
    ISSN: 0020-7462
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    International Journal of Non-Linear Mechanics 15 (1980), S. 159-172 
    ISSN: 0020-7462
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    International Journal of Non-Linear Mechanics 8 (1973), S. 431-443 
    ISSN: 0020-7462
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 4
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    International Journal of Non-Linear Mechanics 7 (1972), S. 31-50 
    ISSN: 0020-7462
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    International Journal of Non-Linear Mechanics 26 (1991), S. 727-740 
    ISSN: 0020-7462
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Journal of Sound and Vibration 33 (1974), S. 201-210 
    ISSN: 0022-460X
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 34 (1983), S. 807-815 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Ein einfaches Stabilitätskriterium für lineare konservative Systeme mit gyroskopischen Kräften wird hergeleitet. Hierbei wird zuerst eine hinreichende Stabilitätsbedingung angegeben, zu deren Beweis das ursprünglich autonome System in ein nichtautonomes System transformiert wird. Auf letzteres wird dann Liapunov's direkte Methode angewandt. Für eine eingeschränkte Klasse von Systemen wird im weiteren ein Satz bewiesen, der eine notwendige und hinreichende Bedingung für Stabilität darstellt. Anschauliche Beispiele zur Anwendung des Stabilitätssatzes werden gegeben.
    Notes: Abstract A simple criterion concerning the stability of linear gyroscopic conservative systems is developed. First, a sufficient condition for stability is established. The proof is based on a transformation converting the original autonomous system into a nonautonomous system, and applying Liapunov's direct method to the latter. Then a theorem is given which provides a necessary and sufficient condition for a restricted class of systems. Illustrative examples are provided.
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Archive of applied mechanics 47 (1978), S. 35-45 
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Übersicht Es wird die Parameter-Empfindlichkeit eines Systems von N Freiheitsgraden untersucht, das zwei zusammenfallende kritische Punkte besitzt. Dabei wird sowohl in einer als auch in beiden kritischen Koordinaten Symmetrie vorausgesetzt. Die Begriffe der allgemeinen und der speziellen kritischen Punkte, abgeleitet von den Eigenschaften der Gleichgewichtsoberflächen, werden dazu verwendet, alle wichtigen Stabilitätseigenschaften zu untersuchen, ohne daß die üblichen Stabilitätsbetrachtungen angestellt werden müssen. Als Beispiel wird eine Säule auf nachgiebiger Unterlage untersucht.
    Notes: Summary The imperfection sensitivity of an N-degree-of-freedom symmetric system exhibiting a two-fold coincident critical point is studied. Symmetry in one as well as in both the critical coordinates is considered. The concepts of general and special critical points, associated with smooth and improper equilibrium surfaces respectively, are used to explore all the relevant stability properties of the system without resorting to formal stability considerations. An illustrative example concerning a column on elastic foundation is analyzed.
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Archive of applied mechanics 46 (1977), S. 213-222 
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Übersicht Es wird der Einfluß kleiner Abweichungen auf die Stabilität von Systemen mit N Freiheitsgraden mit einem zweifachen kritischen Punkt untersucht. Die Analyse beruht auf der Betrachtung von Gleichgewichtsflächen und auf der Störungsrechnung für mehrere Parameter. Die Beziehungen zwischen den auftretenden Gleichgewichtsflächen und der Katastrophentheorie werden erörtert. An einem Strukturmodell wird die Vorgehensweise erläutert.
    Notes: Summary The effect of small imperfections on the stability behaviour of an N-degree-of-freedom system exhibiting 2-fold coincident critical points is investigated. The analysis is based on equilibrium surfaces and the multiple-parameter perturbation technique. The relationship between certain forms of the equilibrium surface and the Catastrophe theory is discussed. An illustrative structural model is analyzed.
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Acta mechanica 53 (1984), S. 213-232 
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary Two distinct bifurcation phenomena associated with non-linear autonomous lumpedparameter systems are analyzed fully in ann-dimensional state space. The analysis is asymptotic and is performed via an intrinsic harmonic balancing technique. In one case a pair of complex conjugate eigenvalues touches the imaginary axis tangentially without crossing it in violation of the main Hopf condition associated with the so-called Hopf bifurcation. It is shown that under the new condition a bifurcating family of limit cycles may or may not axist. If it exists, the family is represented by two paths in the parameteramplitude space which have finite slopes and are symmetrically located with respect to the amplitude axis. The second case is concerned with aflat Hopf bifurcation, and the limit cycles always exist. This phenomenon occurs when the Hopf condition, that a pair of complex conjugate eigenvalues crosses the imaginary axis with non-zero velocity, is satisfied but another significant coefficient vanishes. In both cases, the asymptotic equations of the limit cycles, bifurcating paths and the frequency-parameter relationships are derived in general termsexplicitly. An illustrative example is provided.
    Type of Medium: Electronic Resource
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