Free vibration of micro rotating Euler-Bernoulli beams based on the strain gradient theory

In this paper, free vibration of rotating microbeams based on the strain gradient theory and Euler-Bernoulli beam assumptions is investigated. The Hamilton's Principle is applied on the attained strain and kinetic energy relations to obtain the equations of motion for the rotating microbeam. Then, by employment of the adimensional parameters, the nondimensional form of the equations of motion is derived. By applying the Galerkin approach on the dynamic equations of motion, the flapping and axial natural frequencies are calculated. Subsequently, the current results are validated by the existed papers results. After validation of the present results, the effects of the thickness to the material length scale parameter ratio, rotation speed and Poisson's coefficient on the flapping and axial frequencies are studied and the strain gradient theory results are compared with the modified couple stress and classical theories. The results show that the type of the theory which is appointed has essential effects on the predicted natural frequencies. The effect of rotation speed on the possibility of the occurrence of internal resonances is also examined. In addition, for the first time, the effect of different mentioned theories on the axial natural frequencies are inspected. The presented results illustrated, by considering the strain gradient theory, varying the Poisson's coefficient changes the axial frequencies, while, the modified couple stress and classical theories are incompetent to predict any variations on the axial frequencies and the mentioned theories predict the same results for axial frequencies.