Size-Dependent Vibration Analysis of FG Microbeams in Thermal Environment Based on Modified Couple Stress Theory

In this paper, free vibration of functionally graded (FG) microbeams under thermal environment based on modified couple stress theory is investigated. The internal length-scale parameter is considered to account for material size effect. The Rayleigh-Ritz method is employed, and the eigenvalue problem for obtaining the natural frequencies of FG microbeam is solved for different boundary conditions. Trial functions are expressed in simple algebraic polynomial forms, and application of different boundary conditions in Rayleigh-Ritz method is explained in detail. The convergence of the method is investigated, and the results are compared with the available results in the literature. The material properties of the microbeam are assumed to vary in the thickness direction with a power-law function. It is shown that by increasing the temperature change in the microbeam, the natural frequencies decrease. In addition, it is observed that natural frequencies of microbeam based on modified couple stress theory differ significantly from natural frequencies of classical beam. It is also concluded that increase in FG index results in increase in natural frequencies, but for very high FG indexes, natural frequencies do not change considerably.