Reduced-order models for nonlinear vibrations, based on natural modes: the case of the circular cylindrical shell by Marco Amabili Philosophical Transactions.

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Reduced-order models for nonlinear vibrations, based on natural modes: the case of the circular cylindrical shell by Marco Amabili Philosophical Transactions A Volume 371(1993): June 28, 2013 ©2013 by The Royal Society

Circular cylindrical shell and cylindrical coordinate system. Marco Amabili Phil. Trans. R. Soc. A 2013;371: ©2013 by The Royal Society

First natural frequency of modes with a different number n of circumferential waves of the 0/30° laminated circular cylindrical shell; calculations with model M=4; mode n=1 is torsional. Marco Amabili Phil. Trans. R. Soc. A 2013;371: ©2013 by The Royal Society

Mode shapes for the radial displacement w of the 0/30° laminated circular cylindrical shell; calculations with model M=4. Marco Amabili Phil. Trans. R. Soc. A 2013;371: ©2013 by The Royal Society

Frequency–response curve of the 0/30° laminated circular cylindrical shell (n=3) obtained with the natural mode reduced-order model (thick lines) versus the results presented in Amabili [25] with model M=2 (37 degrees of freedom) shown in thin lines. Marco Amabili Phil. Trans. R. Soc. A 2013;371: ©2013 by The Royal Society

Frequency–response curve of the 0/30° laminated circular cylindrical shell obtained by using the present model (natural mode reduced-order model, thick lines) versus the results presented in Amabili [25] with models M=2 and M=4 shown in thin lines; n=3. Marco Amabili Phil. Trans. R. Soc. A 2013;371: ©2013 by The Royal Society

Frequency–response curve of the 0/30° laminated circular cylindrical shell (n=3) obtained with the natural mode reduced-order model. Marco Amabili Phil. Trans. R. Soc. A 2013;371: ©2013 by The Royal Society