Vibration of beams with embedded piezoelectric sensors and actuators

This paper presents a micromechanics approach to the study of the vibration of beams with embedded piezoelectric sensors and actuators. The natural frequency of the beam is determined from the variational principle in Rayleigh quotient form. The piezoelectric sensors and actuators embedded in the beam are analysed using Eshelby's equivalent inclusion method. In addition, the Euler-Bernoulli beam theory and Rayleigh-Ritz approximation technique are used in the analysis. Results show that the size, volume fraction and location of the piezoelectric inclusions significantly influence the natural frequency of the beam. The results of the present model agree well with the theoretical results presented in the literature.