Abstract
Because the defects in the existing modeling methods for the equivalent mechanical model of a sloshing fluid have led to incorrect or inaccurate results in the existing equivalent models, this paper discusses three different modeling methods for the equivalent models: the traditional method, Housner’s method, and the modified method. The equivalent models obtained by the three methods are, respectively, presented and compared with each other for a liquid in rectangular and upright cylindrical tanks. The results show that the traditional method cannot provide the correct location expressions of the equivalent masses because the two types of different excitations are simultaneously used in one equivalent model. An equivalent model is exclusively applicable to a certain excitation (a translational excitation in a certain direction or a rotational excitation about a certain axis). Housner’s method is based on physical intuition, instead of fluid dynamics theory, therefore the calculation precision of Housner’s solution is not satisfactory. Housner’s method is only suitable for vertical tanks with a flat bottom subjected to a horizontal excitation. Based on a conceptual mistake in the traditional method, the concept of the equivalent model is reclarified, and the modified equivalence method is therefore suggested. A supplementary solution for the equivalent model in a cylindrical tank is presented. The correct models can be acquired using the modified equivalence method, which is applicable to tanks of arbitrary shape.
Highlights
Equivalence Methods for the Equivalent ModelDr0′/dt can obtain the resultant force and moment that exert on the tank through the integrals of Equations (6) and (7)
Because the defects in the existing modeling methods for the equivalent mechanical model of a sloshing fluid have led to incorrect or inaccurate results in the existing equivalent models, this paper discusses three different modeling methods for the equivalent models: the traditional method, Housner’s method, and the modified method. e equivalent models obtained by the three methods are, respectively, presented and compared with each other for a liquid in rectangular and upright cylindrical tanks. e results show that the traditional method cannot provide the correct location expressions of the equivalent masses because the two types of different excitations are simultaneously used in one equivalent model
An equivalent model is exclusively applicable to a certain excitation
Summary
Dr0′/dt can obtain the resultant force and moment that exert on the tank through the integrals of Equations (6) and (7). . .) of the sloshing uid must equal to the corresponding frequency of the spring-mass oscillator, that is, ωn. (4) Under a certain excitation (translational or rotational excitation), the uid system and the equivalent model must have the identical resultant force and moment that exert on the tank, that is, Foriginal Fequivalent (under translational excitation),. (i) Use force Equation (11a) (under the translational excitation) to obtain the sloshing masses Mn (iii) Apply force Equation (12a) (under the rotational excitation) to acquire the location expressions of the sloshing masses hn (i) Under a certain excitation, the equivalent model must have the same (or approximately same) modal frequencies, force, and moment (which exert on the tank) as the actual fluid system. E above discussion is on the spring-mass equivalent model. e modeling problem of the pendulum equivalent model of sloshing fluid is similar to the one above
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