Bending vibration of perforated beams in contact with a liquid

A theoretical study on the natural frequencies and the mode shapes of perforated beams in contact with an ideal liquid is presented. In the theory part, it is assumed that the beams are simply supported at both ends and the ideal liquid is in contact with the lower surface of the beams. Holes with an identical configuration are equally spaced in the beams and three specific patterns of square, rotated square and circular holes are considered. Along the contact surface between the beam and the liquid, the compatibility requirement is applied for the liquid–structure interaction and the Rayleigh–Ritz method is used to calculate the eigenvalues and eigenvectors of the system. The proposed theoretical method for the beams coupled with the liquid is verified by observing a good agreement with the three-dimensional finite element analysis results. In order to evaluate the dynamic characteristics of the liquid-coupled beam, the effects of the hole size in the beams and the pattern of holes on the natural frequencies and the mode shapes are investigated. Additionally the effects of the liquid depth on the natural frequency is investigated and compared with the solid beam case.