Vibration of Cracked FGM Beam with Piezoelectric Layer Under Moving Load

Introduction The frequency response function of a structure is an important attribute that should be gathered for vibration-based damage detection in structural health monitoring. However, the function is strongly dependent upon the location of applied load and position of response measurement. So, it needs to use a lot of sensors and exciters for collecting the number of frequency response functions sufficient for the damage detection problem. Therefore, the use of moving load and distributed sensor for gathering the frequency response of a structure is a good idea to improve the solution to the problem of structural health monitoring. The present paper addresses frequency response analysis of a cracked FGM beam bonded with a piezoelectric layer as distributed sensor under moving load with the aim to directly use the frequency response for crack detection. Method The governing equations of the integrated beam structure are derived with Hamilton's principle and solved by the analytical method in the frequency domain. Solutions have been obtained explicitly in the form of mechanical response (midspan defection) and electrical (sensor output charge) responses that are numerically examined in dependence on material gradient index, load frequency and speed, and crack depth and position. Results It was shown that vibration behaviour of FGM beam with a piezoelectric layer under moving harmonic load is dominated mainly by two components acknowledged as forced and eigenmode vibrations, amplitudes of which are strongly dependent on load speed and frequency. It has also been demonstrated that amplitudes of the mechanical and electrical responses at the generic resonance, when load frequency equals to natural frequency of undamaged beam, are strongly sensitive to crack. Sensitivity of the eigenmode resonant amplitude to crack increases with increasing thickness of piezoelectric layer and decreasing material gradient index. The obtained numerical results have proved that mechanical and electrical responses are spectrally identical and similarly sensitive to crack. Conclusion Moving load speed and frequency are the control parameters useful for obtaining the frequency response preferred for crack detection purpose; eigenmode vibration amplitude at generic resonance provides an efficient scalar indicator for crack detection like natural frequency; as a more easily gathered signal in the practice, the electrical response would be a useful alternative signature for crack detection in FGM beams using a distributed piezoelectric sensor.