Free Vibration Analysis of Nonuniform Microbeams Based on Modified Couple Stress Theory: an Analytical Solution

In this study, analytical solution is presented to calculate the free vibration frequencies of nonuniform microbeams. Scale effects are modelled using modified couple stress theory and the microbeam is assumed to be thin while Poisson's ratio effects are also taken into account. Nonuniformity is presented by exponentially varying width among the microbeam while the thickness remains constant. Results are presented for simply-supported, cantilever and clamped boundary conditions. First five natural frequency parameter are calculated for different scale and nonuniformity parameters and effects of each parameter on the results are discussed. Also, to understand the effects of Poisson's ratio, small scale and nonuniformity on the first frequency of the nonuniform microbeam and resonance domain, a comprehensive parametric study is done. This research is important in understanding the dynamic behavior of microbeams and effective designs using variable cross section in this type of microstructures.