Vibration analysis in micro beams

This study deals with variable cross-section micro beams. In order to observe the effects of micro size on the system, microstructure effects are also included in the system using the "Modified Couple Stress Theory" (MCST), which is different from classical continuum theory. Nonlinear motion equations have been obtained for variable cross-section micro beams using the Hamiltonian principle. Simply-supported and clamped-clamped support types are investigated for micro beams. Terms arising from elongations during vibration have given additional nonlinear characteristics. The resulting motion equations have been dimensionless to make the mathematical model independent of the material type and geometric structure. It is assumed that the beam section changes in proportion to the radius at the leftmost support. Approximate solutions of the system have been obtained using the "Multiple Scale Method", which is a perturbation method. The effects of microstructure, nonlinear terms arising from elongations, and radius ratio on natural frequency and solutions have been investigated. The MCST method used has been compared with classical beam theory and the existence of effects that need to be addressed differently in micro-sized beams compared to classical beams has been shown.