caa a22 4500 445361603 CHVBK 20180317142916.0 cr unu---uuuuu 170323e20111101xx s 000 0 eng 10.1007/s11071-011-0016-4 doi (NATIONALLICENCE)springer-10.1007/s11071-011-0016-4 Nonlinear resonances in infinitely long 1D continua on a tensionless substrate [Elektronische Daten] [Lucio Demeio, Giovanni Lancioni, Stefano Lenci] 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. Springer Science+Business Media B.V., 2011 Nonlinear oscillations nationallicence Wave equation nationallicence Klein-Gordon equation nationallicence Moving boundary problems nationallicence Multiple time scales expansions nationallicence Backbones nationallicence Hardening and softening behavior nationallicence Demeio Lucio Dipartimento di Scienze Matematiche, Università Politecnica delle Marche, Ancona, Italy aut Lancioni Giovanni Dipartimento di Architettura, Costruzioni e Strutture, Università Politecnica delle Marche, Ancona, Italy aut Lenci Stefano Dipartimento di Architettura, Costruzioni e Strutture, Università Politecnica delle Marche, Ancona, Italy aut Nonlinear Dynamics Springer Netherlands 66/3(2011-11-01), 271-284 0924-090X 66:3<271 2011 66 11071 https://doi.org/10.1007/s11071-011-0016-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-011-0016-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Demeio Lucio Dipartimento di Scienze Matematiche, Università Politecnica delle Marche, Ancona, Italy aut NATIONALLICENCE 700 1- Lancioni Giovanni Dipartimento di Architettura, Costruzioni e Strutture, Università Politecnica delle Marche, Ancona, Italy aut NATIONALLICENCE 700 1- Lenci Stefano Dipartimento di Architettura, Costruzioni e Strutture, Università Politecnica delle Marche, Ancona, Italy aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 66/3(2011-11-01), 271-284 0924-090X 66:3<271 2011 66 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer