The linear stability of a cantilever beam subject to a follower force is investigated. A system of distributed piezoelectric devices is attached to the beam with the purpose of improving the dynamic stability of the structure. They are connected to a second-order network and second-order analog electrical circuit. The assembly of the mechanical and piezoelectric subsystems constitutes a coupled Piezo-Electro-Mechanical (PEM) system, whose equations of motion, derived within a variational approach, are discretized via the Galerkin weighted residual method and the stability of the trivial equilibrium is addressed by numerically solving the associated eigenvalue problem. A sensitivity analysis, carried out on a numerical ground, is thus conducted on a wide range of the electrical parameters to investigate the effectiveness of the proposed controller.

中文翻译：

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一种提高粘弹性贝克梁线性稳定性的棒状压电控制器

研究了受随动力作用下悬臂梁的线性稳定性。为了提高结构的动态稳定性，将分布式压电装置系统附加到梁上。它们连接到二阶网络和二阶模拟电路。机械和压电子系统的组装构成了一个耦合的压电-机电 (PEM) 系统，其运动方程是通过变分方法导出的，通过 Galerkin 加权残差法离散化，并且平凡平衡的稳定性通过以下方式解决数值求解相关的特征值问题。因此，对广泛的电气参数进行了在数值基础上进行的灵敏度分析，以研究所提出的控制器的有效性。