[论文解读] Experimental and Numerical Study of the Transient Response of a Cantilever Beam with a Piezoelectric Disc Sensor

Radek Kolman, Robert Cimrman+7 more|arXiv (Cornell University)|Feb 18, 2026

Aeroelasticity and Vibration Control被引用 0

一句话总结

论文将实验测量与有限元建模结合，研究带粘接压电片传感器的悬臂梁的瞬态响应，并使用参数辨识框架识别阻尼与电参数。

ABSTRACT

Online and real-time sensing and monitoring of the health state of complex structures, such as aircraft and critical components of power stations, are essential aspects of research in dynamics. Several types of sensors are used to capture dynamic responses and monitor changes during the operation of critical parts of complex systems. Piezoelectric (PZ) materials belong to a class of electroactive materials that convert mechanical deformation into an electrical response. For example, PZ ceramics or PVDF foils are employed for online sensing of the time history of mechanical deformation. This paper focuses on the dynamical response of a cantilever beam structure equipped with a glued PZ sensor and combines experimental and modelling approaches to achieve accurate and reliable results. The time history of the normal velocity at a point on the beam surface was recorded with a laser vibrometer during transient vibrations of the beam, triggered by the sudden removal of a mass load at the beam's free end. Simultaneously, the output voltage of the PZ sensor was measured with an electronic device. An elastodynamic model of a cantilever beam coupled with a piezoelectric sensor is introduced, along with its discretization using the finite element method. The mathematical model includes additional terms that enforce a floating-potential boundary condition to maintain a constant charge on one of the sensor's electrodes and is presented in an extended form suitable for sensitivity analysis or parameter identification. The model implementation is validated using a numerical example corresponding to the experimental setup. The computed results show good agreement with the experimental data. Furthermore, values of the Rayleigh damping parameters were identified based on the experimental measurements.

研究动机与目标

• 使用压电传感器实现复杂结构的在线感知与健康监测的动机。
• 为带附着PZ传感器的悬臂梁建立耦合弹性-压电脉模型。
• 通过实验验证模型并通过辨识细化参数。
• 探索粘接层对传感器附着对动力响应的影响。

提出的方法

• 在瞬态振动过程中用激光多普勒测振仪和压电传感器对梁的响应进行实验测量。
• 建立压弹致动耦合的力学-电场耦合模型，并强制自由势边界条件。
• 对模型进行有限元离散，并通过扩展弱形式（包含Nitsche型强制约束）及外电路模型进行求解。
• 在SfePy中实现数值方案，并与COMSOL结果比较以确保一致性。
• 提供最小二乘的参数辨识框架，从测量的速度和电压数据中估计阻尼与电路参数。

实验结果

研究问题

• RQ1 提出的压弹致动耦合模型是否能够重现梁的实验瞬态响应。
• RQ2 从实验数据中是否能够可靠地辨识出阻尼（质量和刚度成分）与外部电路参数。
• RQ3 梁与压电圆片之间粘接层的存在如何影响第一模态频率和电响应。
• RQ4 数值结果与独立仿真（如COMSOL）在模态与瞬态分析方面的吻合程度如何。

主要发现

• 实验的第一模态频率为147.59 Hz，解析估计为143.62 Hz，未粘接时的初始FE预测为145.44–150.74 Hz，取决于模型。
• 在梁与压电圆片之间引入薄粘接层会降低主频并使其更接近实验值。
• 使用SfePy得到的模型结果在模态分析方面与COMSOL对用相应网格时吻合良好。
• 参数辨识程序能够从速度和电压测量中估计阻尼系数与外部电路参数。
• 模型改进（如将示波器建模为电阻并包含粘接层）提高了模拟与测量电响应之间的吻合。