Equivalent mechanical models of sloshing fluid in arbitrary‐section aqueducts

Abstract

SUMMARY This paper reports on a semi‐analytical/numerical method to model sloshing water in an arbitrarily shaped aqueduct. The water motion is assumed to be inviscid, compressible, and linear (small displacement). The transverse sloshing fluid in an aqueduct is equivalently simplified as a fixed rigid mass M0 and a mass–spring system (M1, K1). According to a rule that the actual fluid (computed with finite element model) and its equivalent mechanical model have the same first sloshing frequency and acting effects on the aqueduct, the analytical solutions of the fixed (impulsive) mass M0, sloshing (convective) massM1, spring stiffness K1, and their locations in the aqueduct body are acquired by the least squares (curve fitting) algorithm. Applying this equivalent principle, the equivalent mechanical models are respectively obtained for the sloshing water in rectangular, semicircular, U‐shaped, and trapezoid aqueducts. The equivalent principle and fluid models are validated through comparison investigations involving rectangular and U‐shaped aqueducts. The dynamic properties and seismic responses of the original and equivalent systems are simulated, compared, and discussed for a U‐shaped aqueduct bridge. The main purpose of this paper is to provide a simplified model of sloshing fluid for the seismic/wind‐resistant computation of the support structures of the aqueduct bridge. Copyright © 2011 John Wiley & Sons, Ltd.

An Approximate Analytical Solution of Sloshing Frequencies for a Liquid in Various Shape Aqueducts

“…The interface between liquid and the rigid aqueduct is treated as a slip boundary condition, such that the normal relative displacement of the fluid and rigid container on the interface is forced to be zero and the tangential relative displacement on the interface is not restrained. Many obtained results using ANSYS Code have been verified by the previous investigations [15,16]. For example, in [16] the fundamental frequencies in the rectangular tanks by ANSYS Code and the exact solution [3] were compared with each other, and the results showed the two solutions have a good agreement.…”

“…Many obtained results using ANSYS Code have been verified by the previous investigations [15,16]. For example, in [16] the fundamental frequencies in the rectangular tanks by ANSYS Code and the exact solution [3] were compared with each other, and the results showed the two solutions have a good agreement. When the liquid depth varies from 0.35 to 0.70 , the corresponding sloshing frequencies are both extracted by the finite element and present methods.…”

“…The compressible case can produce lower natural frequencies. According to [16], the sloshing frequencies in a rectangular tank by ANSYS Code are slightly lower than the exact solutions using (18).…”

“…On the basis of an analysis in Section 4.1, where the sloshing The rest of the roots of (15) are the unwanted solutions, which are neglected here. For an arbitrary-section aqueduct, the coefficients ( , , ) and ( , , ) can be obtained by using (16) through integrals in the static liquid domain Ω. Then, the coefficients and can be figured out by means of (17).…”

“…This displacement-based finite element formulation, which had been introduced into the commercial ANSYS Code [14], was usually used for simulating the sloshing problems [15,16] in certain engineering fields.…”