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acceleration acoustic acoustic particle velocity acoustic resonances added mass amplitude analysis behavior bifurcation diagram boundary conditions branch calculated circulating flow co-axial cylinder coefficient components computed convection coordinate cycle damping damping ratio density displacement downstream tank duct earthquake effect equation experimental Figure finite element flow rate flow velocity Flow-Induced Vibration fluctuation Fluid-Structure Interaction fluidelastic free surface Froude number full-scale gate function horizontal excitation hydrodynamic hysteresis inlet velocity instability Interaction ASME 1993 Ishii linear Liquid level difference Lyapunov exponents manometer oscillation maximum mechanism method mode shapes motion natural frequencies Navier-Stokes equation nonlinear obtained overflow parameters phase speed plate pressure PVP-Vol ratio reactor resonance self-induced sloshing shear layer shell Shell model shown in Fig shows sloshing mode sloshing wave height small UCS Strouhal number structure Table tube bundles turbulence model two-phase flow UCS sections underflow upstream tank vertical excitations viscosity vortex vortices water level weir