Vibrations of cracked FGM microbeams based on Modified Coupled Stress Theory - Lien, Tran Van; Chu Thanh, Binh (Vietnam Journal of Science and Technology, 2025)
Free vibrations of cracked microbeams made of Functionally Graded Material (FGM) rested on the Winkler-Pasternak elastic foundation based on the Modified Coupled Stress Theory (MCST) are presented. Material properties of the beam vary throughout the thickness according to the power distribution and the Mori–Tanaka homogenization technique. The Timoshenko beam theory considering the size effect based on the MCST is applied. A size-dependent finite element model with new non-classical shape functions is proposed to obtain the stiffness and mass matrices of the intact FGM Timoshenko microbeam. The stiffness matrix of the cracked beam element obtained by adding an overall additional flexibility matrix to the flexibility matrix of the corresponding intact beam element can give more accurate natural frequencies. The influences of the size-effect, material, geometry, and crack parameters on natural frequencies and mode shapes are then analyzed. It is shown that the study can be applied to other FGMs as well as more complex microbeam structures