Analyzing Free Vibration of a Cantilever Microbeam Submerged in Fluid with Free Boundary Approach

Abstract

This paper aims to present a detailed analysis of the free vibration of a cantilever microbeam submerged in an incompressible and frictionless fluid cavity with free boundary condition approach. In other words, in addition to the kinematic compatibility on the boundary between microbeam and its surrounding fluid, equations of the potential functions are modeled assuming the free boundaries. Galerkin’s method is used for simulations. The results of the proposed model are validated by comparing with the early analytical and numerical studies of pertinent literature. Finally, it is inferred that by involving the free boundary conditions, which is closer to the physical reality, the natural frequencies of the system have instability, especially in higher modes. In addition, the values obtained for natural frequencies are smaller than what were calculated by fixed bounary approach.

Keywords

• Vibration; Free boundary equation; Added mass; Microbeam.