NDLI: Nonlinear resonances in infinitely long 1D continua on a tensionless substrate

Content Provider	Springer Nature Link
Author	Demeio, Lucio Lancioni, Giovanni Lenci, Stefa
Copyright Year	2011
Abstract	In this work, we investigate the primary nonlinear resonance response of a one-dimensional continuous system, which can be regarded as a model for semi-infinite cables resting on an elastic substrate reacting in compression only, and subjected to a constant distributed load and to a small harmonic displacement applied to the finite boundary. By introducing a straightforward small amplitude expansion characterized by a smallness parameter ε and by performing a Fourier analysis, we first determine the frequencies of the oscillations of the system about the static solution at all orders. We find that, at each order, there exists a critical (cutoff) frequency, above which the solution behaves as a traveling wave toward infinity, while it decays exponentially below it. We then examine the resonance response of the system when an external harmonic excitation is applied at the finite boundary. To this aim, we scale the external excitation with the third power of ε and perform a Multiple-Time-Scale analysis, whose third-order consistency conditions give the differential equations which govern the behavior of the amplitude on the long time scale. In this way, we determine the third-order bending of the resonance curves, whose hardening or softening behavior depends upon the frequency of the chosen primary resonance.
Starting Page	271
Ending Page	284
Page Count	14
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	66
Issue Number	3
e-ISSN	1573269X
Language	English
Publisher	Springer Netherlands
Publisher Date	2011-04-08
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Nonlinear oscillations Wave equation Klein–Gordon equation Moving boundary problems Multiple time scales expansions Backbones Hardening and softening behavior Mechanics Mechanical Engineering Vibration, Dynamical Systems, Control Automotive Engineering
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

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