Analytic solution for size-dependent behaviors of micro-beam under forced vibration

This paper focuses on the size-dependently mechanical behaviors of a micro-beam under forced vibration. Governing equations of a micro-beam under forced vibration are established by using the modified couple stress theory, Bernoulli-Euler beam theory and D’Alembert’s principle together. A simply supported micro-beam under forced vibration is solved according to the established governing equations and the method of separation of variables. The dimensionless deflection, amplitude mode and period mode are defined to investigate the size-dependently mechanical behaviors of a micro-beam under forced vibration. Results show that the performance of a micro-beams under forced vibration is distinctly size-dependent when the ratio of micro-beam height to material length-scale parameter is small enough. Both frequency ratio and loading location are the important factors that determine the size-dependent performance of a micro-beams under forced vibration.