Dynamic stability of sandwich functionally graded micro-beam based on the nonlocal strain gradient theory with thermal effect

In this study, the dynamic stability of functionally graded (FG) size dependent sandwich micro-beam subjected to parametric axial excitation with different boundary conditions including thermal effects is investigated. Based on the nonlocal strain gradient theory (NLSGT) in conjunction with the first order shear deformation beam theory (FSDBT) and Hamilton's principle, governing equations of motion and corresponding boundary conditions were obtained. Differential quadrature (DQ) method is utilized to solve the derived differential equations. Material properties of the FG part of sandwich micro-beam are varied through the thickness of the beam by assuming the classical rule of mixture. Effects of the slenderness ratio (L/h), nonlocal parameter (ea), FG mixture index (k), length scale parameter (lm), static load factor (ηs), temperature change, various boundary (C-C), (S-S), (C-S) conditions and different cross-section shapes on the dynamic stability behavior of the sandwich micro-beam are investigated. Numerical solution for determining the parametric instability regions of a FG sandwich micro-beam under different boundary conditions and various effects are the original contributions of this study.