Coupled free vibrations of a cantilever plate with attached liquid drop

Coupled free vibration analysis has been performed on a cantilever thin elastic plate carrying a liquid drop attached on its arbitrary point in a zero-gravity environment. A liquid drop, having slipping edge boundary condition on the plate, has been treated as an inviscid ideal liquid with hemi-spherical shape. By using Rayleigh–Ritz method, coupled hydroelastic problem has been rendered into an eigenvalue problem, from which one can obtain coupled natural frequencies and modes of vibration. Since we have treated an attached drop as an ideal liquid drop not as added rigid mass or ‘mass–spring’ system, the problem consists of coupled system between a plate and a liquid drop, which have both multi-degrees of freedom. In the numerical calculations, present results have been compared with the results in which a liquid drop have treated as a ‘mass–spring’ system which has previously been presented by the authors.