An Investigation on Resonant Characteristics of Micro/Nano-Beams Based on Nonlocal Elasticity Theory

In present paper, resonant characteristics of vibrating micro/nano-beams are investigated based on the nonlocal elasticity theory. The natural frequency and quality factor of the micro/nano-beams are known as important resonant characteristics which play crucial roles in resonant vibration of the beams in air environments. To determine the resonant characterizes of the micro/nano-beams, the governing vibration equation of the nonlocal beam with fixed end supports is derived considering the air damping force. As the beam is modeled the beam as a string of vibrating adjacent spheres in interaction with the ambient air environment, the air damping force is obtained as a function of the resonant frequency. Furthermore, to calculate the quality factor of the size-dependent micro/nano-beams, the time-dependent vibration equation is presented in modal space based on the orthogonality conditions. Therefore, the quality factor obtained as a function of the natural frequencies and size-dependent nonlocal parameter at various resonant modes of vibration. Then, a parametric study investigates the nonlocal effects on the quality factor of the resonant micro/nano-beam. The obtained results indicate that the nonlocal size effects decreases the quality factor. In addition, the size effects play more prominent role at the higher resonant modes of vibration.