Non-linear interactions in imperfect beams at veering |
| |
Authors: | Walter Lacarbonara Haider N. Arafat |
| |
Affiliation: | a Dipartimento di Ingegneria Strutturale e Geotecnica, University of Rome La Sapienza, via Eudossiana 18, Rome 00184, Italy b Department of Engineering Science and Mechanics, MC0219, Virginia Polytechnic Institute and State University, Blacksburg, VA 24060, USA |
| |
Abstract: | Non-linear interactions in a hinged-hinged uniform moderately curved beam with a torsional spring at one end are investigated. The two-mode interaction is a one-to-one autoparametric resonance activated in the vicinity of veering of the frequencies of the lowest two modes and results from the non-linear stretching of the beam centerline. The excitation is a base acceleration that is involved in a primary resonance with either the first mode only or with both modes. The ensuing non-linear responses and their stability are studied by computing force- and frequency-response curves via bifurcation analysis tools. Both the sensitivity of the internal resonance detuning—the gap between the veering frequencies—and the linear modal structure are investigated by varying the rise of the beam half-sinusoidal rest configuration and the torsional spring constant. The internal and external resonance detunings are varied accordingly to construct the non-linear system response curves. The beam mixed-mode response is shown to undergo several bifurcations, including Hopf and homoclinic bifurcations, along with the phenomenon of frequency island generation and mode localization. |
| |
Keywords: | Imperfect beam Shallow arch Veering One-to-one internal resonance Mode localization |
本文献已被 ScienceDirect 等数据库收录! |
|