The nonlinear dynamics of a simply supported beam resting on a nonlinear spring bed with cubic stiffness is analyzed. The continuous differential operator describing the mathematical model of the system is discretized through the classical Galerkin procedure and its nonlinear dynamic behavior is investigated using the method of Normal Forms. This model can be regarded as a simple system describing the oscillations of flexural structures vibrating on nonlinear supports and then it can be considered as a simple investigation for the analysis of more complex systems of the same type. Indeed, the possibility of the model to exhibit actually interesting nonlinear phenomena (primary, superharmonic, subharmonic and internal resonances) has been shown in a range of feasibility of the physical parameters. The singular perturbation approach is used to study both the free and the forced oscillations; specifically two parameter families of stationary solutions are obtained for the forced oscillations.

Nonlinear dynamics of a beam on elastic foundation / F., Pellicano; Mastroddi, Franco. - In: NONLINEAR DYNAMICS. - ISSN 0924-090X. - STAMPA. - 14:4(1997), pp. 335-355. [10.1023/a:1008297721253]

Nonlinear dynamics of a beam on elastic foundation

MASTRODDI, Franco
1997

Abstract

The nonlinear dynamics of a simply supported beam resting on a nonlinear spring bed with cubic stiffness is analyzed. The continuous differential operator describing the mathematical model of the system is discretized through the classical Galerkin procedure and its nonlinear dynamic behavior is investigated using the method of Normal Forms. This model can be regarded as a simple system describing the oscillations of flexural structures vibrating on nonlinear supports and then it can be considered as a simple investigation for the analysis of more complex systems of the same type. Indeed, the possibility of the model to exhibit actually interesting nonlinear phenomena (primary, superharmonic, subharmonic and internal resonances) has been shown in a range of feasibility of the physical parameters. The singular perturbation approach is used to study both the free and the forced oscillations; specifically two parameter families of stationary solutions are obtained for the forced oscillations.
1997
beam on nonlinear supports; external and internal resonances; nonlinear vibrations; normal forms
01 Pubblicazione su rivista::01a Articolo in rivista
Nonlinear dynamics of a beam on elastic foundation / F., Pellicano; Mastroddi, Franco. - In: NONLINEAR DYNAMICS. - ISSN 0924-090X. - STAMPA. - 14:4(1997), pp. 335-355. [10.1023/a:1008297721253]
File allegati a questo prodotto
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/71541
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 29
  • ???jsp.display-item.citation.isi??? 25
social impact