期刊
JOURNAL OF SOUND AND VIBRATION
卷 236, 期 4, 页码 683-703出版社
ACADEMIC PRESS LTD
DOI: 10.1006/jsvi.2000.3039
关键词
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Internal resonance mechanisms between near-commensurate longitudinal and transverse modes of a taut spatial string are identified and studied using an asymptotic method, and the influence of material non-linearities on the resulting solutions is considered. Geometrical non-linearities couple longitudinal motions to in-plane and out-of-plane transverse motions, resulting in resonant and non-resonant interactions between linearly orthogonal string modes. Past studies have included only transverse modes in the description of string motions and have predicted periodic, quasi-periodic, and chaotic whirling motions arising from the geometrical non-linearities. This study considers further the inclusion of longitudinal motions and a non-linear material law, which are both appropriate for the study of rubber-like strings. An asymptotic analysis captures the aforementioned whirling motions, as well as a new class of whirling motions with significant longitudinal content. Periodic, quasi-periodic, and aperiodic (likely chaotic) responses are included among these motions. Their existence, hardening-softening characterization, and stability are found to be highly dependent on the magnitude of the material non-linearities. (C) 2000 Academic Press.
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