Liquid Sloshing in a Rigid Cylindrical Tank Equipped with a Rigid Annular Baffle and on Soil Foundation

Abstract

Fluid sloshing in a rigid circular cylindrical tank is investigated; the tank is resting on soil foundation and is excited by horizontal seismic accelerations. A rigid annular baffle is connected to the inner wall of the storage tank to reduce liquid sloshing. By using the fluid subdomain method, the convective velocity potential is derived. An equivalent model with mass-spring oscillators is proposed to describe the sloshing motions of the contained liquid. Then, by means of the least square method, a complex polynomial fraction is employed to fit the dynamic impedance of the soil. A nested lumped parameter model is established to model the effect of the soil foundation. The substructure method allows to obtain the soil–tank–liquid coupled model. The equation of motion of the coupled system is solved by the Newmark-[Formula: see text] method. A comparison between the present sloshing results and those published in the literature shows an excellent agreement. The effects of the soil parameters, the baffle position and its size on the dynamic behavior of the soil–tank–liquid system are discussed in detail. The results demonstrate that the soil properties and the baffle parameters can have a remarkable influence on liquid sloshing. The novelty of this research is that an analytical model for the soil–tank–liquid–baffle coupled system is derived for the first time and it allows to study the dynamics and sloshing response of the system with accuracy and low computational cost.

Lid induced sloshing suppression and evaluation of wall stresses in a liquid storage tank including seismic soil‐structure interaction

“…Table 4 also indicates that the first three experimentally determined frequencies of the tank‐water system are similar for the FSL case in both support conditions, which coincides with the results of previous studies, for example Refs. 8, 48 In the sand‐supported case, the rest of the frequencies are, as anticipated, lower than those of the rigid‐supported case.…”

“…Several studies, for example Refs. 8, 48, 58 point out that the influence of SSI on the convective components of response is negligible, that is the sloshing behaviour is independent (within engineering accuracy) of the supporting medium stiffness. In contrast, SSI has a remarkable influence on the impulsive components of response, that is the hydrodynamic force distribution and the overturning moment 11,19,59 .…”

“…The effects of rigid and flexible baffles on the tank response had been investigated theoretically and experimentally, for example Refs. 46–48. A floating roof reduces the sloshing height through additional damping, but increases the stress in the tank wall 49 .…”

Stable parameters identification for rational approximation of Single degree of freedom frequency response function of semi‐infinite medium

“…In CRA‐related research, Wolf et al 26,27 and Wang et al 28 used CRA to fit the basic frequency response function, established different first‐ and second‐order spring‐damping models, and provided a posterior method for ensuring the stability of the identification result. Wu et al, 29 Zhou et al, 30 and Sun et al 31 used the polynomial elimination method to expand the rational function into continued fractions and established different nested lumped‐parameter models; Okada et al 32 used the least‐squares method to fit the foundation frequency response function and established a time‐domain differential equation to solve the foundation response; Birk et al 33 fitted the frequency response function of the dynamic stiffness of the hydrodynamic pressure on a dam; Zhao et al 34,35 used the penalty function method 36 to fit the frequency response functions of soil and water to ensure the stability of the identification result; and Han et al 37 and Zhang et al 38 studied the rational approximation of the dynamic stiffness matrix of a rigid foundation and an underground pipeline and conducted a time‐domain dynamic analysis of the research object using the mixed variable method. In DRA‐related research, Wolf et al 39 and Safak et al 40 used rational functions to fit the foundation frequency response function and gave the stability conditions for the DRA based on the posterior method; Paronesso et al 41 used the method of equilibrium approximation to derive the difference equation for the interaction force and displacement and expressed it as a DRA; Laudon et al 42 used the method of Safak 40 .…”

Seismic performance evaluation of a base-isolated steel liquid storage tank with limiting-devices considering soil-structure interaction

“…Ormeño et al [28] conducted a shaking table test on the effect of flexible foundation on tank stress and found that compared with rigid foundation, the axial compressive stress was reduced after considering the foundation. Sun et al [29] established a lumped parameter model to simulate the foundation and discussed the influence of soil parameters on the dynamic characteristics of the soil-tank-liquid system. Lv et al [30] derived a simplified mechanical model considering the soil-tank-liquid interaction based on the potential flow theory and the soil model theory, obtained that the main seismic responses such as the base shear force and overturning moment of the storage tank were increased by 25%-58% after considering the soil-tank-liquid interaction.…”