Experimental and Numerical Study of the Transient Response of a Cantilever Beam with a Piezoelectric Disc Sensor

📅 2026-02-18
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This study addresses the need for accurate real-time monitoring of structural health by precisely capturing dynamic responses of complex systems. Focusing on a cantilever beam bonded with piezoelectric sensors under transient excitation, the authors develop a coupled electromechanical finite element model that integrates laser vibrometry and synchronized voltage measurements. An innovative floating electrical potential boundary condition is introduced to maintain constant electrode charge, enabling an extended multiphysics framework suitable for sensitivity analysis and parameter identification. Through finite element discretization and direct comparison with experimental data, the numerical simulations demonstrate excellent agreement with measured responses. The proposed approach successfully identifies Rayleigh damping parameters via inverse modeling, thereby validating both the accuracy and effectiveness of the methodology.

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📝 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.
Problem

Research questions and friction points this paper is trying to address.

piezoelectric sensor
cantilever beam
transient response
structural health monitoring
dynamic response
Innovation

Methods, ideas, or system contributions that make the work stand out.

piezoelectric sensor
floating-potential boundary condition
transient response
finite element modeling
Rayleigh damping identification
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Radek Kolman
Institute of Thermomechanics, v.v.i., The Czech Academy of Sciences, Dolejškova 1402/5, 182 00 Prague 8, Czech Republic; The College of Polytechnics Jihlava, Tolstého 16, 586 01 Jihlava, Czech Republic
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Robert Cimrman
Institute of Thermomechanics, v.v.i., The Czech Academy of Sciences, Dolejškova 1402/5, 182 00 Prague 8, Czech Republic; New Technologies - Research Centre and Faculty of Applied Sciences, University of West Bohemia, Pilsen, Czech Republic
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Ladislav Musil
Institute of Thermomechanics, v.v.i., The Czech Academy of Sciences, Dolejškova 1402/5, 182 00 Prague 8, Czech Republic
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Moritz Frey
Institute for Mathematics and Computer-Based Simulation, University of the Bundeswehr Munich, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany
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Jaromír Kylar
Institute of Thermomechanics, v.v.i., The Czech Academy of Sciences, Dolejškova 1402/5, 182 00 Prague 8, Czech Republic
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Sebastian Brandstaeter
Institute for Mathematics and Computer-Based Simulation, University of the Bundeswehr Munich, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany
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Vojtěch Kotek
Institute of Thermomechanics, v.v.i., The Czech Academy of Sciences, Dolejškova 1402/5, 182 00 Prague 8, Czech Republic
Alexander Popp
Alexander Popp
Professor of Computer-Based Simulation, Universität der Bundeswehr München
Computational MechanicsFinite Element AnalysisContact Mechanics
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Jan Kober
Institute of Thermomechanics, v.v.i., The Czech Academy of Sciences, Dolejškova 1402/5, 182 00 Prague 8, Czech Republic