Random Response of Functionally Graded Material Beam with Viscoelastic Damping

Abstract

The random response of the functionally graded material beam with viscoelastic damping under Gaussian white noise is investigated by an approximate transformation procedure and equivalent non-linearization technique. Firstly, the dimensionless equation of the functionally graded material beam is obtained by the Galerkin method, and the viscoelastic force is approximated to the equivalent damping and the equivalent stiffness, which depend on the system averaged frequency. Secondly, the equivalent non-linearization technique is used, and the random response of the original system is obtained. Finally, the influences of the different parameters on the system response are discussed, especially the viscoelastic parameter 1 b and 1 l .