Natural frequency of beams with embedded piezoelectric sensors and actuators

Abstract

A mathematical model is developed to study the natural frequency of beams with embedded piezoelectric sensors and actuators. The piezoelectric sensors/actuators in a non-piezoelectric matrix (host beam) are analyzed as two inhomogeneity problems by using Eshelby’s equivalent inclusion method. The natural frequency of the beam is determined from the variational principle in Rayleigh quotient form, which is expressed as functions of the elastic strain energy and dielectric energy of the piezoelectric sensors/actuators. The Euler-Bernoulli beam theory and Rayleigh-Ritz approximation technique are used in the present analysis. Parametric studies show that the size, volume fraction and location of the piezoelectric inclusions significantly influence the natural frequency of the beam