Coupled vibration of a cantilever micro-beam submerged in a bounded incompressible fluid domain

This paper investigates the free vibrations of a cantilever micro-beam submerged in a bounded frictionless and incompressible fluid cavity. Based on the Fourier–Bessel series expansion and using linear potential theory, an analytical method is proposed to analyze the eigenvalue problem, where the fluid effect emerges as an added mass. Wet beam vibration mode shapes together with the sloshing modes of the oscillating liquid are depicted. Moreover, effects of geometrical configuration and fluid density on the natural frequencies of the coupled system are evaluated. Results show that in spite of the high added mass values related to lower modes, presence of the fluid changes the higher modes more effectively.