Lateral Free Vibration of Micro-Rods Using a Nonlocal Continuum Approach

The lateral free vibration of micro-rods initially subjected to axial loads based on a nonlocal continuum theory is considered. The effects of nonlocal long-range interaction fields on the natural frequencies and vibration modes are examined. A simply supported micro-rod is taken as an example; the linear vibration responses are observed by two different methods, including the separation of variables and multiple scales analysis. The relations between the vibration mode and dimensionless coordinate and the relations between natural frequencies and nonlocal parameters are analyzed and discussed in detail. The numerical comparison shows that the theoretical results by two different approaches have a good agreement, which validates the present micro-rod model that can be used as a component of the micro-electromechanical system.