Purpose

The problem of parametric resonance of a base-excited cantilever beam has been studied both analytically and numerically. The support motion of the cantilever beam is generated by a feedback mechanism whereby the feedback signal is generated after modulating the cantilever tip motion with a harmonic time signal. This paper contributes a novel analytical technique for feedback-based parametric excitation. In the studied method, solely transverse displacement is given to the clamped end. It is different from the other methods, where axial displacement is also provided as parametric pumping.

Method

A new analytical method, not requiring any small parameter in the equation of motion, has been proposed to obtain stability boundary in the parametric space. Harmonic balance is carried out in the temporal domain for stability analysis. For numerical study, discrete element method is used.

Results

Numerical analysis is carried out to study unstable and stable behaviour for the applied parametric excitation. The numerical simulation results have been found out to be in excellent agreement with the outputs of analytical study.

中文翻译：

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反馈感应基激励的悬臂梁参数共振

目的

悬臂梁的参数共振问题已经在分析和数值上进行了研究。悬臂梁的支撑运动由反馈机构产生，由此在用谐波时间信号调制悬臂尖端运动之后产生反馈信号。本文为基于反馈的参数激励贡献了一种新颖的分析技术。在所研究的方法中，仅对夹紧端进行横向位移。它与其他方法不同，在其他方法中，轴向位移也作为参数泵提供。

方法

为了获得参数空间中的稳定性边界，已经提出了一种新的分析方法，该方法不需要运动方程中的任何小参数。在时域中进行谐波平衡以进行稳定性分析。对于数值研究，使用离散元法。

结果

进行了数值分析以研究所施加参数激励的不稳定和稳定行为。已经发现数值模拟结果与分析研究的结果非常吻合。