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- Politecnico di Milano
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- Mechanical Engineering
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- Mechanical Systems Dynamics
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Study material for Mechanical Systems Dynamics, shared by the Studwiz community and reviewed by moderators.
Mechanical Systems DynamicsOther
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Page 1
Dinamica dei Sistemi Meccanici Federico Travaini 19 luglio 2014 Indice 1 Approccio Lagrangiano 1 1.1 Approccio di Lagrange . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Sistemi continui 3 2.1 Vibrazioni trasversali nelle funi . . . . . . . . . . . . . . . . . . . 3 2.1.1 Equazione di equilibrio . . . . . . . . . . . . . . . . . . . . 3 2.1.2 Soluzione (stazionaria) dell’EDP . . . . . . . . . . . . . . 5 2.2 Condizioni al contorno . . . . . . . . . . . . . . . . . . . . . . . . 6 3 Approccio modale 7 3.1 Approccio modale per sistemi ad n gdl . . . . . . . . . . . . . . . 8 3.1.1 Forzamento in coordinate principiali . . . . . . . . . . . . 9 3.2 Approccio discretizzato per i continui . . . . . . . . . . . . . . . 10 3.3 Approccio modale nei continui . . . . . . . . . . . . . . . . . . . 11 3.3.1 Forme di energia . . . . . . . . . . . . . . . . . . . . . . . 11 3.3.2 Sostituzione legami cinematici . . . . . . . . . . . . . . . 13 3.3.3 Pulsazione propria ωi . . . . . . . . . . . . . . . . . . . . 13 3.3.4 Smorzamento . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.3.5 Componente lagrangiana . . . . . . . . . . . . . . . . . . 15 3.3.6 Letto elastico . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.3.7 Carico Mobile . . . . . . . . . . . . . . . . . . . . . . . . . 15 4 Approccio rigoroso analitico caso trave 18 5 Elementi finiti 22 5.1 Introduzione . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5.2 Caso fune . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 5.2.1 Funzioni di forma . . . . . . . . . . . . . . . . . . . . . . . 23 5.2.2 Forme di energia . . . . . . . . . . . . . . . . . . . . . . . 24 5.2.3 Equazioni di moto . . . . . . . . . . . . . . . . . . . . . . 30 5.3 Caso Trave . . . . . . . . . . . . . . . . . . . .…
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