Dynamic stability analysis of functionally graded sandwich micro-beams

In this thesis, the static, buckling analysis, free vibration and dynamic stability of size-dependent sandwich functionally graded micro-beam under the action of parametric excitation loads resting on elastic Winkler and Pasternak foundations with temperature change is investigated. Based on the nonlocal strain gradient theory (NLSGT) in conjunction with the various higher-order deformation beam theories (HOBTs), Timoshenko beam theory (TBT) and Euler beam theory (EBT) with Hamilton's principle, the governing equations of motion and corresponding various boundary conditions were obtained. The material properties of the FG part of sandwich micro-beam are varied gradually through the thickness of the micro-beam are calculated by using the Mori-Tanaka homogenization scheme and classical rule of mixture. The dynamic stability, transverse deflection, critical buckling and fundamental frequency can be determined with various boundary conditions (i.e. C-C, C-S, and S-S) by using the generalized differential quadrature method (GDQM). The sandwich FG micro-beam is considered with three different models and various cross section shapes. The Models are functionally graded material (FGM) homogeneous microbeam (Model I), a sandwich beam with FGM core and two homogeneous ceramic and metal skins (Model II) and a sandwich beam with homogeneous core with ceramic and FGM top and bottom skins (Model III). The influence of the dimensionless nonlocal parameter , the dimensionless length scale parameter , slenderness ratio , material property gradient index static load factor temperature change and various cross section shapes on the dynamic stability, static bending, buckling and free vibration of the sandwich micro-beam are discussed. To verify the present formulation and the present results (dynamic stability, static, buckling and free vibration), some of the current results are compared with the previously published results. Good agreement is observed.