Modeling, nonlinear dynamics, and identification of a piezoelectrically actuated microcantilever sensor
Modeling, nonlinear dynamics, and identification of a piezoelectrically actuated microcantilever sensor
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DOI：
10.1109/tmech.2008.915823
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发表时间：
2008-02-01
影响因子：
6.4
通讯作者：
Daqaq, Mohammed F.
中科院分区：
文献类型：
--
作者：
Mahmoodi, Seyed Nima;Jalili, Nader;Daqaq, Mohammed F.
纳米机械悬臂梁传感器（NMCSs）最近出现作为一种有效的手段，无标记的化学和。生物物种检测它们通过在机械杠杆的功能化表面上吸附物种来操作。通过这种功能化，分子识别被直接转换成微机械响应。为了有效地利用这些传感器在实践中，并正确地与相关的吸附物种的微观力学响应，建模相关的主要技术问题必须得到解决。沿着这些路线，本文提出了一个通用的非线性综合建模框架的压电驱动微悬臂梁和实验验证。所提出的模型考虑了纵向和弯曲振动及其耦合，除了一直存在的几何和材料的非线性。利用Euler-Bernoulli梁理论和不可扩展性条件，将耦合振动-弯曲运动方程化为一个描述传感器弯曲振动的非线性偏微分方程。使用Galerkian展开，得到的方程离散成一组非线性常微分方程。多尺度的方法，然后实施解析构造的传感器的非线性响应的第一模态频率附近（第一振动模式的主共振）。这些解决方案相比，实验结果表明，传感器表现出软化型非线性响应。这种行为可以归因于压电层中二次材料非线性的存在。这一观察结果是至关重要的，因为它表明，不像宏观杠杆的几何硬化非线性占主导地位的响应行为，材料的非线性占主导地位的响应产生软化型响应的微观杠杆。在设计和采用这种传感器用于实际应用时，应考虑这种行为。
Nanomechanical cantilever sensors (NMCSs) have recently emerged as an effective means for label-free chemical and. biological species detection. They operate through the adsorption of species on the functionalized surface of mechanical cantilevers. Through this functionalization, molecular recognition is directly transduced into a micromechanical response. In order to effectively utilize these sensors in practice and correctly relate the micromechanical response to the associated adsorbed species, the chief technical issues related to modeling must be resolved. Along these lines, this paper presents a general nonlinear-comprehensive modeling framework for piezoelectrically actuated microcantilevers and validates it experimentally. The proposed model considers both longitudinal and flexural vibrations and their coupling in addition to the ever-present geometric and material nonlinearities. Utilizing Euler-Bernoulli beam theory and employing the inextensibility conditions, the coupled longitudinal-flexural equations of motion are reduced to one nonlinear partial differential equation describing the flexural vibrations of the sensor. Using a Galerkian expansion, the resulting equation is discretized into a set of nonlinear ordinary differential equations. The method of multiple scales is then implemented to analytically construct the nonlinear response of the sensor near the first modal frequency (primary resonance of the first vibration mode). These solutions are compared to experimental results demonstrating that the sensor exhibits a softening-type nonlinear response. Such behavior can be attributed to the presence of quadratic material nonlinearities in the piezoelectric layer. This observation is critical, as it suggests that unlike macrocantilevers where the geometric hardening nonlinearities dominate the response behavior, material nonlinearities dominate the response of microcantilevers yielding a softening-type response. This behavior should be accounted for when designing and employing such sensors for practical applications.