Viscoelastically coupled dynamics of FG Timoshenko microbeams

Viscosity effects on the mechanical behaviour of functionally graded (FG) Timoshenko microbeams are investigated; the model possesses both linear nonlinear viscous terms. The Mori–Tanaka homogenisation method is used for the continuous variations of the material properties of the microsystem along the thickness; the Kelvin–Voigt scheme is employed for the internal damping; the shear deformation and rotary inertia are modelled for the viscoelastic microbeam via the Timoshenko theory; the modified couple stress theory is used for size influences. An energy loss/balance via Hamilton’s principle is used for obtaining the equations of motion. Galerkin’s approach together with a continuation method is employed for the mechanical responses. The simultaneous effects of viscosity, being small, and FG materials on the mechanical behaviour are investigated.