Quantum mechanics

Galerkin method

Spring (device)

Materials science

Microsystem

Viscoelasticity

Classical mechanics

Infinitesimal

Thermodynamics

Physics

Nonlinear system

Nanotechnology

Mathematics

Elasticity (physics)

Mathematical analysis

Composite material

Kinematics

Mechanics

Continuum mechanics

European Journal of Mechanics - A/Solids

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.

Mechanics of viscoelastic functionally graded microcantilevers