悬索桥梁模型中扭转孤子的存在性
Existence of torsional solitons in a beam model of suspension bridge
摘要：
本文研究了悬索桥中孤子即稳定孤波的存在性。桥梁被建模为退化板，即，一个中心梁与截面，并显示两个自由度：梁的垂直位移和扭转角的截面。在一般假设下，证明了孤子的存在性。在大张力的附加假设下，我们证明了这些孤子具有非平凡的扭转分量。这似乎与安全有关，因为几座悬索桥由于扭转振动而倒塌。
英文摘要：
This paper studies the existence of solitons, namely stable solitary waves, in a suspension bridge. The bridge is modeled as a degenerate plate, that is, a central beam with cross sections, and displays two degrees of freedom: the vertical displacement of the beam and the torsional angles of the cross sections. Under fairy general assumptions, we prove the existence of solitons. Under the additional assumption of large tension in the sustaining cables, we prove that these solitons have a nontrivial torsional component. This appears relevant for the security since several suspension bridges collapsed due to torsional oscillations.
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