Mechanics of viscoelastic functionally graded microcantilevers

An elastically supported viscoelastic functionally graded (FG) microcantilever is considered and its nonlinear mechanics is analysed for the first time. Moreover, for the first time, energy transfer via internal resonances and motion complexity are analysed. A nonlinear spring model is incorporated as an elastic support which is representative of elasticity induced from neighbouring devices. Size effects are incorporated using the modified couple stress theory (MCST). Mori-Tanaka formula is utilised for FG-material-property variations. Kinematics/kinetics for an infinitesimal beam elements in conjunction with Hamilton's method are used for large curvatures. Galerkin's technique is used for reductions and truncations of the dynamic model of elastically supported viscoelastic FG microsystem. Both base-excitation/frequency continuations are performed and the dynamics is investigated. •Large deformations soften the motion.•Three-to-one internal resonance occurs.•Number of saddle bifurcations is either two or four.•Internal resonance makes the motion complex.