The effect of bi-axial in-plane loads on the natural frequency of nano-plates

In this paper, natural frequencies of nano-plates subjected to two-sided in-plane tension or compressive loads, based on Eringen nonlocal elasticity theory and displacement field of first-order shear deformation plate theory (FSDT), are investigated. By considering total rotational variables as the two rotations due to bending and shear, another formulation form of FSDT nano-plate is achieved, that can simultaneously consider classical plate theory (CLPT) and FSDT. In a comprehensive study, the effects of different parameters such as a nonlocal parameter, aspect ratio, thickness to length ratio, mode number, boundary conditions and also length of nano-plate are examined on the dimensionless natural frequency. The results show that simultaneously applying two-sided tension and compressive in-plane loads changes frequency in a manner which is different to one-directional loading.