Vibrations of shear deformable FG viscoelastic microbeams

This is the first paper which investigates the nonlinear forced dynamic response of shear deformable functionally graded (SDFG) microscale beams with viscoelastic properties. A third-order model of shear deformations, which satisfies both the lower and upper boundary conditions, is utilised. The influences of viscoelastic properties are incorporated via the Kelvin-Voigt scheme. Furthermore, the influences of being at a miniature scale are captured via a modified couple stress theory (MCST). The material distribution of the microsystem is modelled via application of the Mori-Tanaka approach. Nonlinear three-dimensional coupled equations, which govern the size-dependent motions of the SDFG microbeam, are derived and then numerically solved. The present results show that for large coupled motions, the nonlinearity caused by viscosity plays a crucial role in the dynamics of SDFG microbeams.