, Volume 6, Issue 4, pp 253–257 | Cite as

On the stability of one-dimensional continuous systems with polygenic forces

  • H. H. E. Leipholz
  • K. Huseyin


Using the energy theorem for polygenic systems, it is shown that polygenic systems of the divergence type are pseudoconservative. Hence, their Hamiltonian can be used as a Liapunov functional to investigate the stability of such systems. Furthermore, for polygenic divergence type systems, the eigenvalue curve is strictly monotonic and its first branch is always to the right of the first branch of the corresponding conservative system's eigenvalue curve. Hence, the first critical load of the corresponding conservative system is a lower bound for the first critical load of the polygenic divergence type system.


Mechanical Engineer Civil Engineer Alla Critical Load Type System 
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Attraverso il teorema energetico dei sistemi poligenici, si mostra che i sistemi poligenici di tipo divergenza sono pseudo-conservativi e quindi che il loro Hamiltoniano può essere usato come un funzionale alla Liapunov per studiare la stabilità di tali sistemi. Si mostra inoltre, sempre per i sistemi poligenici di tipo divergenza, che la curva degli autovalori è strettamente monotona e che il suo primo ramo è sempre alla destra del primo ramo della curva degli autovalori del corrispondente sistema conservativo. Dunque il primo carico critico del corrispondente sistema conservativo è un limite inferiore per il carico critico del sistema poligenico di tipo divergenza.


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Copyright information

© Tamburini Editore 1971

Authors and Affiliations

  • H. H. E. Leipholz
    • 1
  • K. Huseyin
    • 1
  1. 1.Civil Engineering, Solid Mechanics DivisionUniversity of WaterlooWaterlooCanada

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