Thermo-hygro-mechanical bending and vibration of functionally graded material microbeams with microporosity defect

In this study, the thermo-hygro-mechanical bending and vibration of functionally graded material (FGM) microbeams with microporosity defect are investigated. The mathematical model of the system is developed by using the sinusoidal beam theory and the modified couple stress theory. Based on Hamilton's principle, the governing equations and boundary conditions of imperfect FGM microbeams are derived. Then, Navier's method is utilized to calculate the deflections and natural frequencies of the system. Analytical results are presented to illustrate the effects of the microporosity volume fraction, the microporosity distribution type, the power-law index, the temperature and the moisture on the static bending and free vibration of imperfect FGM microbeams.