On Interactions of Oscillation Modes for a Weakly Non-Linear Undamped Elastic Beam With an External Force

Asymptotic Approach for Non-Linear Periodical Vibrations of Continuous Structures

“…In the subsequent approximations by , representations (18), (19) allow modes resonance interactions to be taken into account and the eigenvalue to be de"ned. Calculating coe$cients in expansions (18), (19) it is supposed "nally that "1.…”

“…The solution is sought as asymptotic series (18), (19). Being restricted by two leading terms in expansion (18), one obtains…”

On the transversal vibrations of a conveyor belt with a low and time-varying velocity. Part I: the string-like case

“…To make the right hand side of (7) odd, terms which are not already in Fourier-sin-series form in x are multiplied with (see also [14,17]):…”

“…In this paper it will be shown that also instabilities can occur when Ω is equal to or close to the difference of two natural frequencies of the constant velocity system. In [4] and in [14][15][16][17][18] several remarks can be found on how and when truncation is allowed. In those papers weakly nonlinear problems for wave and for beam equations have been studied.…”

Asymptotic analysis on weakly forced vibration of axially moving viscoelastic beam constituted by standard linear solid model

“…Maccari [11] determined the external force-response and frequency-response curves in the cases of primary resonance and subharmonic resonance for a weakly periodically forced beam with the quadratic and cubic nonlinearities. Boertjens and van Horssen [12] studied the interactions of modes for a weakly forced beam with the geometric nonlinearity. Chen et al [13] analyzed the nonlinear vibration of a cantilever in a contact atomic force microscope with a nonlinear boundary via an asymptotic approach.…”