Effect of thermal environment on free vibration and buckling of partially cracked isotropic and FGM micro plates based on a non classical Kirchhoff's plate theory: An analytical approach

Abstract

A non classical analytical model is presented for free vibration of the cracked rectangular isotropic and functionally graded micro plates in the presence of thermal environment. The new approach is based on the combination of classical plate theory and the modified couple stress theory. The crack terms are based on the Line Spring Model whereas the thermal environment is accommodated in the form of thermal moment and in-plane forces. The solution for fundamental frequencies of the cracked plate is obtained by discounting geometric nonlinearity. A non classical relation for geometrically linear thermal buckling phenomenon of a cracked micro-plate is also proposed. The variation of critical buckling temperature and fundamental frequency with uniform rise in temperature of the cracked plate is studied for various crack length ratios, gradient index and internal material length scale parameter. Furthermore the variation of the buckling coefficient with plate aspect ratio and thickness of the cracked micro-plate is established. A comparison is presented between the classical results and present results as affected by thermal environment and microstructure of the plate. It is concluded that the presence of cracks affects the critical buckling temperature and fundamental frequencies of micro plates. The consideration of size effect increases the buckling temperature which shows the significance of the internal material length scale parameter in the presence of thermal environment.