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.

翻译：在线实时传感与监测复杂结构（如飞机和电站关键部件）的健康状态是动力学研究的重要方向。多种传感器被用于捕获动态响应并监测复杂系统关键部件运行期间的变化。压电材料属于一类电活性材料，可将机械变形转换为电响应。例如，压电陶瓷或PVDF薄膜被用于机械变形时程的在线传感。本文重点研究粘贴压电传感器的悬臂梁结构的动态响应，并结合实验与建模方法以获得准确可靠的结果。通过梁自由端质量载荷的突然移除触发梁的瞬态振动，采用激光测振仪记录了梁表面某点法向速度的时程。同时，使用电子设备测量了压电传感器的输出电压。本文建立了耦合压电传感器的悬臂梁弹性动力学模型，并采用有限元方法进行离散化。该数学模型包含附加项以强制执行浮动电位边界条件，从而保持传感器某一电极上的电荷恒定，并以适用于灵敏度分析或参数识别的扩展形式呈现。通过对应实验设置的数值算例验证了模型实现的有效性。计算结果表明数值结果与实验数据吻合良好。此外，基于实验测量结果识别了瑞利阻尼参数的值。