Size-dependent vibration of single-crystalline rectangular nanoplates with cubic anisotropy considering surface stress and nonlocal elasticity effects

The presented paper investigates size-dependent vibration of single-crystalline rectangular nanoplates with cubic anisotropy based on combined surface stress and nonlocal elasticity effects. For this, the fundamental equations are derived with a discussion about the anisotropy formulations. The generalized differential quadrature method (GDQM) is used to solve the differential equation for applicable boundary conditions. The convergence and stability of the results are verified to obtain a suitable number of grid points. At first, the effective Young's modulus versus the thickness is verified by the existing experiments. Then, the problem is simulated for a complete set of single crystal orientation and a wide range of size scale parameters and material types. The results indicate that size scale parameters have different vibration effects at different material orientations and boundary conditions. The size-scale effects decrease the natural frequency of CCFF (two edges clamped) and CCCC (fully clamped) nanoplates rotates from [100] to [110] axis for FCC (Face Centered Cubic ) materials in contrast with cantilevered nanoplates (CFFF).

Automated summary

This paper investigates size-dependent vibration of single-crystalline nanoplates with cubic anisotropy using the generalized differential quadrature method. The results show that size scale parameters have different effects on vibration depending on material orientation and boundary conditions. In particular, the natural frequency of FCC materials decreases as the nanoplate rotates from [100] to [110] axis.