[en] The present paper addresses the problem of free vibration in multiple cracked beams made of functionally graded material (FGM). Governing equations of the beam vibration are established using the Timoshenko beam theory, power law of material grading along the beam thickness and rotational spring model of crack. The actual position of neutral plane differed from the mid-plane due to the material properties variation is also taken into account. The frequency equation obtained in a simple form provides an efficient tool for natural frequency analysis and may also be used for solving the inverse problems such as identification of material properties or cracks in the beams from natural frequencies. Numerical examples have been carried out to validate the proposed theory and to investigate the effect of cracks, material and geometry parameters on natural frequencies of the beams.

[en] The present paper addresses developing the Dynamic Stiffness Method (DSM) for natural frequency analysis of functionally graded beam with piezoelectric patch based on the Timoshenko beam theory and power law of material grading. Governing equations and general solution of free vibration are conducted for the beam element with piezoelectric layer that is modelled as a homogeneous Timoshenko beam. The obtained solution allows establishing dynamic stiffness matrix for modal analysis of FGM beam with bonded piezoelectric distributed sensors/actuators. Effect of thickness and position of the smart sensors/actuators and material parameters on natural frequencies is studied with the aim for dynamic testing and health monitoring of FGM structures. The theoretical developments are validated and illustrated by numerical examples. (paper)