Electro-Mechanical Receptance Concept for Cracked Piezoelectric Timoshenko Beams and Application

IntroductionThe frequency response function of a structure is an important attribute that should be gathered for vibration-based damage detection in structural health monitoring (SHM). However, to collect a sufficient number of frequency response functions for the damage detection problem, a large number of sensors and exciters is required. Using smart materials such as piezoelectric material leads to the electro-mechanical impedance (EMI) technique, a powerful tool for remote and real-time performing the SHM. However, the EMI technique is still limited to a small area of damage monitoring and is efficient only in the very high-frequency range. The present paper is devoted to modifying the EMI technique by using the full-length distributed sensor in combination with point mechanical excitation instead of the impedance transducer employed in the EMI technique. This leads to a novel concept of electro-mechanical receptance (EMR) proposed for crack monitoring overlength of beam structure and conducting SHM in the lowest frequency range.MethodThe electro-mechanical receptance defined as elelectric charge generated in the piezoelectric layer under concentrated unit mechanical excitation is conducted by analytical method. So, an explicit expression of the electro-mechanical receptance is derived and used for extracting so-called spectral damage index and spectral assurance criterion that are then employed for numerical analysis of EMR's sensitivity to crack and establishing diagnostic database. Crack detection problem is solved by the contour method using constructed diagnostic database.ResultsA concept of electro-mechanical receptance is proposed and its analytical expression has been derived for cracked Timoshenko beam integrated with a piezoelectric layer.It was demonstrated that the proposed electro-mechanical receptance is much more sensitive to crack than modal parameters in the lowest frequency range and this high sensitivity is maintained only for piezoelectric layer thickness less than 15% beam thickness.A so-called spectral assurance criterion that is extracted from electro-mechanical receptance provides an efficient indicator for crack detection in beam structures by measurements of the electro-mechanical receptance.Numerical results show that small crack of 5% beam thickness could be consistently identified from measured electro-mechanical receptance.ResultsA concept of electro-mechanical receptance is proposed and its analytical expression has been derived for cracked Timoshenko beam integrated with a piezoelectric layer.It was demonstrated that the proposed electro-mechanical receptance is much more sensitive to crack than modal parameters in the lowest frequency range and this high sensitivity is maintained only for piezoelectric layer thickness less than 15% beam thickness.A so-called spectral assurance criterion that is extracted from electro-mechanical receptance provides an efficient indicator for crack detection in beam structures by measurements of the electro-mechanical receptance.Numerical results show that small crack of 5% beam thickness could be consistently identified from measured electro-mechanical receptance.ResultsA concept of electro-mechanical receptance is proposed and its analytical expression has been derived for cracked Timoshenko beam integrated with a piezoelectric layer. It was demonstrated that the proposed electro-mechanical receptance is much more sensitive to crack than modal parameters in the lowest frequency range and this high sensitivity is maintained only for piezoelectric layer thickness less than 15% beam thickness.A so-called spectral assurance criterion that is extracted from electro-mechanical receptance provides an efficient indicator for crack detection in beam structures by measurements of the electro-mechanical receptance.Numerical results show that small crack of 5% beam thickness could be consistently identified from measured electro-mechanical receptance.ResultsA concept of electro-mechanical receptance is proposed and its analytical expression has been derived for cracked Timoshenko beam integrated with a piezoelectric layer.It was demonstrated that the proposed electro-mechanical receptance is much more sensitive to crack than modal parameters in the lowest frequency range and this high sensitivity is maintained only for piezoelectric layer thickness less than 15% beam thickness.A so-called spectral assurance criterion that is extracted from electro-mechanical receptance provides an efficient indicator for crack detection in beam structures by measurements of the electro-mechanical receptance.Numerical results show that small crack of 5% beam thickness could be consistently identified from measured electro-mechanical receptance.ConclusionThe coupled electro-mechanical dynamic behavior of a cracked Timoshenko beam bonded with a piezoelectric layer has been analytically studied. An analytical expression of electric charge produced in the piezoelectric layer under concentrated unit mechanical excitation was derived and called herein electro-mechanical receptance for the integrated beam structure. The proposed electro-mechanical receptance is much more sensitive to crack than modal parameters and more easily measured in the lowest frequency range compared to the electro-mechanical impedance. The so-called spectral assurance criterion extracted from measured electro-mechanical receptance enables consistently detecting small cracks of 5% beam thickness.