Methods for the study of nonlinear continuous systems are discussed using nonlinear planar vibrations of a buckled beam about its first buckled mode shape. Fixed-fixed boundary conditions are considered. The case of primary resonance of the nth mode is investigated. Approximate solutions are obtained by using a single-mode discretization via the Galerkin method and by directly applying the method of multiple scales to the governing integro-partial-differential equation and boundary conditions. Frequency-response curves are generated using both approaches for several buckling levels and are contrasted with experimentally obtained frequency-response curves for two test beams. For odd modes, there are ranges where the computed frequency-response curves are qualitatively as well as quantitatively different. The experimentally obtained frequency-response curves are in agreement with those obtained with the direct approach and in disagreement with those obtained with the discretization approach.
Nonlinear response of a buckled beam to a harmonic excitation / Lacarbonara, Walter; Nayfeh, Ali H.; Kreider, Wayne. - STAMPA. - 1:(1997), pp. 798-808. (Intervento presentato al convegno Proceedings of the 1997 38th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Part 4 (of 4) tenutosi a Kissimmee, FL, USA, null nel 1997).
Nonlinear response of a buckled beam to a harmonic excitation
Lacarbonara, Walter;
1997
Abstract
Methods for the study of nonlinear continuous systems are discussed using nonlinear planar vibrations of a buckled beam about its first buckled mode shape. Fixed-fixed boundary conditions are considered. The case of primary resonance of the nth mode is investigated. Approximate solutions are obtained by using a single-mode discretization via the Galerkin method and by directly applying the method of multiple scales to the governing integro-partial-differential equation and boundary conditions. Frequency-response curves are generated using both approaches for several buckling levels and are contrasted with experimentally obtained frequency-response curves for two test beams. For odd modes, there are ranges where the computed frequency-response curves are qualitatively as well as quantitatively different. The experimentally obtained frequency-response curves are in agreement with those obtained with the direct approach and in disagreement with those obtained with the discretization approach.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
