Nonlinear Vibration Analysis of Micro Rotating Euler- Bernoulli Beams Subjected to Loading Based on the Strain Gradient Theory

In order to improve the performance or manufacture of new micro-components, research on the vibrations of the micro-technologies is one of the most pressing needs in the industry. In this paper, the nonlinear vibration analysis of rotating Euler-Bernoulli microbeames subjected to loading is investigated using the strain gradient theory. Firstly, the non-dimensional equations of motion are obtained by insertion of the strain energy, the kinetic energy, and the work of the external force in Hamilton's Principle. Then, by applying Galerkin method, the natural frequencies are extracted. Then the validity and accuracy of the presented analysis is confirmed through comparison of the the present analysis result with the result of another reference. Next, after extracting the mode shapes, the effects of some important mechanical and geometrical parameters such as Poisson's ratio, thickness to material length scale parameter ratio, material, rotation speed and size effect parameters on the vibration response of the microbeam are investigated. The results reveal that based on the strain gradient theory, increase of the Poisson's ratio reduces the natural frequencies, while the modified couple stress theory can't do this prediction. The results of the present research can be valuable for development of micro-technologies.