关键词: weak supersolution, weak subsolution, monotone convergencetheorem, nonincreasing, nondecreasing, locally Hldercontinuous.locally Lipschitz continuous, strong maximumprinciple, solid-liquid interaction, vibration analysis, tank filled with liquid, liquid sloshing

Abstract: This paper studies the problem of free bending vibration of annular cylindricaltank partially filled with liquid in the consideration of surface wave.The exactformulae of the mode shape functions and frequencies are deduced.Results can beobtained by means of computer.The analysis shows that the effect of liquid on vibration of annular cylindrical tank is equivalent to different generalized distributivemasses attached to inner and outer cylinders respectively.

Key words: weak supersolution, weak subsolution, monotone convergencetheorem, nonincreasing, nondecreasing, locally Hldercontinuous.locally Lipschitz continuous, strong maximumprinciple, solid-liquid interaction, vibration analysis, tank filled with liquid, liquid sloshing