Modal actuation and sensing are implemented on a microfabricated AFM cantilever with a two-layer piezoelectric stack transducer. The top transducer is shaped as the second derivative of the first mode shape. The bottom transducer is uniformly distributed along the cantilever length. The purpose of this work is to demonstrate that modal actuation and sensing can be used to eliminate other resonances from frequency response function of the active cantilever, except the first mode. First-order mathematical formulations are presented to model transverse vibrations of the cantilevers under this study. Microfabrication steps and characterization of these cantilevers are reported. Their respective actuation and sensing gains are determined for comparison with conventional active cantilevers. Electromechanical coupling coefficients are also calculated to exhibit reciprocity of modal actuation and sensing in eliminating higher modes from the frequency response. The advantages of modal actuation and sensing in avoiding instabilities in feedback controlled AFM active cantilevers are also demonstrated.

中文翻译：

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有源AFM悬臂的模态驱动和传感

模态驱动和感测是在带有两层压电叠层换能器的微型AFM悬臂上实现的。顶部换能器成形为第一模式形状的二阶导数。底部换能器沿悬臂长度均匀分布。这项工作的目的是证明除第一模式外，模态致动和传感可用于消除活动悬臂的频率响应功能中的其他共振。提出了一阶数学公式来模拟悬臂的横向振动。报告了微细加工步骤和这些悬臂的表征。确定它们各自的致动和感测增益，以与传统的主动悬臂进行比较。还计算出机电耦合系数，以表现出模态驱动和感应的互易性，从而消除了频率响应中的较高模态。还展示了模态致动和感测在避免反馈控制的AFM主动悬臂中产生不稳定性方面的优势。