Differential evolution for free vibration optimization of functionally graded nano beams

A modified couple stress theory is used to study the influence of a scale parameter in the free vibration of a Timoshenko functionally graded beam. For energy harvesting of micro devices, it is require for the beam to resonate at low frequencies. In order to minimize the free vibration frequency of the beam, differential evolution optimization is used to solve the optimization problem. To describe the volume fraction variation along the beams thickness, a three parameter volume fraction law is chosen. Results show that for the selected volume fraction law, and considering linear analysis, the optimal material distribution across the beam thickness is independent of the scale parameter. Results are insensitive to tested boundary conditions.