定常回転する円筒容器内の液面揺動の固有振動数 : 楕円形振動モード

抄録

Free vibration analysis is presented for liquid surface motion in a rigid circular cylindrical tank which is rotating around its symmetrical axis at constant angular velocity. It is considered that the equilibrium surface forms a paraboloid of revolution. Basic equations of liquid motion are derived by using the acceleration potential under the assumptions that the gravity. effect is dominant in comparison with the centrifugal force and that the liquid is inviscid and incompressible. It is confirmed that both elliptic and parabolic vibration modes of free surface oscillation appear due to tank rotation. The characteristic equations for the elliptic modes are derived by applying Galerkin's method. It is noted that the natural frequencies of the elliptic mode are separated by the Coriolis force. An experiment was conducted using a model tank. A good agreement was found between the theoretical and experimental results.