Abstract
The amplitude — frequency relations of beams, membranes and plates in free vibration with moderately large amplitude are of interest. A two harmonics solution of motion equation and the reciprocal interaction of two modes of vibration are taken into account. The resulting backbone curves with loops, additional branches and bifurcation points are determined and discussed. The physical meaning of the considered curves is also explained.
Sommario
Si studiano le vibrazioni libere di ampiezza moderatamente grande di travi, membrane e piastre. Si sviluppano soluzioni approssimate con due armoniche delle relative equazioni di moto in due diversi casi di risonanza interna, e si analizza l'effetto dell'interazione di due modi di vibrazione. Vengono determinate e discusse le curve frequenza-ampiezza con l'associata ricchezza di rami addizionali e punti di biforcazione. Il significato fisico di tali curve viene altresì evidenziato.
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Lewandowski, R. On beams membranes and plates vibration backbone curves in cases of internal resonance. Meccanica 31, 323–346 (1996). https://doi.org/10.1007/BF00426994
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DOI: https://doi.org/10.1007/BF00426994