Abstract
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.
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