Sommario
Nelle oscillazioni di grande ampiezza di un cavo sospeso, il moto nel piano e fuori del piano risulta accoppiato, a differenza di quanto predetto dalla teoria delle piccole oscillazioni. Questo problema viene studiato facendo riferimento ad un modello del cavo, semplice ma significativo, a due soli gradi di libertà, dei quali uno tiene conto del moto pendolare e l'altro del moto nel piano. La soluzione delle equazioni di moto è ottenuta con una tecnica perturbativa fino al terzo ordine, adatta al problema con nonlinearità quadratiche e cubiche. Si studia la modificazione della legge del moto dovuta al trasferimento di energia tra i due modi per differenti condizioni iniziali in assenza di risonanza interna e si valutano gli effetti dell'ac-coppiamento modale nel problema nonlineare.
Summary
In the finite motions of a suspended elastic cable the in-plane and out-of-plane oscillations are coupled, which is in contrast with what is predicted by the theory of small oscillations. To study the phenomenon of nonlinear coupling, a simple but meaningful two degree-of-freedom model is referred here, one parameter being used to describe the in-plane motion and the other the out-of-plane motion. The solution of the dynamic equilibrium equations is accomplished by an order-three perturbational expansion, which furnishes the time solution of the two displacement parameters. The modification of the free oscillations due to the exchange of energy between the two modes in absence of internal resonance is studied for different initial conditions and the effect of modal coupling is evidenced.
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Benedettini, F., Rega, G. & Vestroni, F. Modal coupling in the free nonplanar finite motion of an elastic cable. Meccanica 21, 38–46 (1986). https://doi.org/10.1007/BF01556315
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DOI: https://doi.org/10.1007/BF01556315