Modal analysis of cracked FGM beam with piezoelectric layer

Abstract

The present paper addresses modal analysis of cracked Timoshenko beam bonded with piezoelectric layer. The host beam is made of functionally graded material with the power law and crack appeared in the host beam is modeled by a pair of axial and rotational springs with stiffness calculated from its depth. The piezoelectric layer is represented as a homogeneous Timoshenko beam. Governing equations and general solution for free vibration of the cracked double beam are conducted in the frequency domain. The obtained solution has been used for examining modal parameters of the coupled beam that include natural frequencies, mode shapes and so-called modal sensor charge in dependence on crack parameter, material gradient index and thickness of piezoelectric layer. Analysis of the modal sensor charge in dependence upon crack parameters provides a novel indicator that is expected to be more efficient than the traditional ones for crack detection in functionally graded beam using distributed smart sensors. The theoretical development is validated and illustrated by numerical analysis accomplished for simply supported beam.