Dynamics of size-dependent multilayered shear deformable microbeams with axially functionally graded core and non-uniform mass supported by an intermediate elastic support

The current study investigates the coupled dynamics of a size-dependent third-order shear deformable multilayered microbeam with an axially functionally graded core, a non-uniform mass distribution (mass imperfection) and an intermediate elastic support. A power-law function is used to model the material properties in the longitudinal direction of the core. The equations of motion are obtained by formulating the energies of the system while employing the modified couple stress theory to include miniature size effects within the multilayered microbeam structure. Hamilton's principle and the modal decomposition method are utilised to derive and solve the coupled motion equations. The equations of motion are first verified against a former work on a simplified microbeam system, while the numerical results are validated by comparison to those of a simplified functionally graded in axial direction obtained by finite element macrobeam simulation. It was concluded that increasing either the power term constant of the material grading or the value of the localized mass imperfection (when xm*=0.3) causes the first and second transverse and axial natural frequencies of the three-layered microbeam to decrease, whereas increasing the length-scale parameter causes the natural frequencies of transverse modes to increase, demonstrating the size-dependent effects of the three-layered microbeam.