A general formulation of quality factor for composite micro/nano beams in the air environment based on the nonlocal elasticity theory

The quality factor is known as a critical and important feature to achieve efficient resonant response of micro/nano beams. In fact, the quality factor plays a significant role in the sensitivity and resolution of resonant vibration behavior of small-size structures. The presented paper investigates the quality factor of composite micro/nano beams employing the nonlocal Euler–Bernoulli beam theory. Composite beams having arbitrary laminated layers and discontinuities are taken into consideration. Regarding to size effects, a general formulation is derived to calculate the quality factor of the nonlocal beams attributed to airflow damping and support losses. To reduce complexity of the problem, a nondimensional parameter is introduced to calculate the quality factor. To provide guidelines for determining the quality factor of the nonlocal composite beams, general results are presented for several resonant modes of vibration. The obtained results indicate that the quality factor is decreased by increasing the nonlocal size effects. However, the size effects play more prominent role at the higher resonant modes of vibration. Furthermore, it is shown that the quality factor is affected by the boundary conditions and dimensional characteristics of the micro/nano composite beams. Accordingly, the quality factor is increased by decreasing the slenderness ratio of the beam.