Nonlinear size-dependent metamaterial-based tunable sandwich microbeams with enhanced vibration characteristics

Compared to homogeneous beams, metamaterial-based sandwich beams are known to be lighter and provide better mechanical characteristics. However, their application has mainly been limited to large-scale structures, and their potential for granting small-scale structures enhanced characteristics has not been fully explored yet. The present manuscript aims to investigate nonlinear vibration in size-dependent metamaterial-based sandwich microbeams with hexagonal and triangular lattice cores. To do so, well-known homogenization techniques based on modeling the representative volume element (RVE) of the lattice have been utilized to find the equivalent properties of the nonlinear cores. Moreover, the modified strain gradient theory is used to obtain the governing equation of motion for a small-scale microbeam and the multiple scales method is adopted to investigate the free vibration and primary resonance of the discretized system. Further, size effects and the effect of geometry on the free and forced nonlinear vibration of lattice sandwich beams are examined. In addition to highlighting the size effects, the results indicate that properly implementing nonlinear metamaterials in microbeams can enhance and tune vibrational performance across various length scales. The results of the present paper can provide a more detailed perception of the concept of nonlinear metamaterial-based microbeams and their application in MEMS/NEMS devices.