Abstract

The paper is devoted to study of the parametric resonance of torsional vibrations caused by large-amplitude flexural vibrations of cantilevered plates. In this study we considered the first two resonant modes of flexural vibrations. The analytical study of the original problem which is reduced to Hill equation, is based on the WKB approximation. According to the obtained results, we built a map of instability gaps in the plane of the two process control parameters. The conclusions are made about the possibility of experimentally detection the studied effect in real systems.

中文翻译：

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板的弯曲扭转振动中的不稳定性区域

摘要

本文专门研究悬臂板大振幅弯曲振动引起的扭转振动的参数共振。在这项研究中，我们考虑了弯曲振动的前两个共振模式。简化为希尔方程的原始问题的分析研究基于WKB近似。根据获得的结果，我们在两个过程控制参数的平面中建立了不稳定性间隙的映射。得出有关在实际系统中实验检测所研究效果的可能性的结论。