Abstract
The large-amplitude vibrations of axially functionally graded (AFG) microcantilevers is investigated for the first time. Due to a harmonic base-displacement, the AFG microcantilever undergoes large time-varying deformations; the small-size influences are incorporated using the modified couple stress theory (MCST) and the large-amplitude vibrations is moderated. Exponential distributions along the length are considered for material properties. Hamilton’s work/energy principle is used to balance the energies of the oscillating AFG microcantilever. The harmonic base-displacement is included via a relative motion rule. A truncation is conducted and a large-dimensional multi DOF system is obtained for an AFG microcantilever under inextensibility. A continuation method is utilised and frequency and base-displacement diagrams are obtained for different material gradient indices and the spatial variation of the material properties.
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