The effect of bi-axial in-plane loads on nonlinear dynamics of micro-plates under harmonic excitation

Based on the theories of the first-order shear deformation (FSDT) plate and the modified couple stress, a nonlinear micro-plate model is developed for steady state dynamics of harmonically excited micro-plates subjected to two-sided in-plane tension or compressive loads. The governing equations of motion and corresponding boundary conditions are derived using Hamilton's principle. The semi-analytical method of Galerkin's is utilized to discretize the governing equations of motion into ordinary differential equations. By performing complexification-averaging method and arc-length continuation techniques, semi-analytical approximations for nonlinear steady-state response is developed. For micro-plate with post-buckling deformation coexisting attractors are observed. These attractors have different nonlinear behaviors such as multi frequency, period doubling, intermittency, quasi-periodic and chaotic behaviors. The effects of different parameters such as in-plane load, load ratio, the material length scale parameter and aspect ratio on the nonlinear forced vibration are examined.