Internal resonances and dynamic responses in equivalent mechanical model of partially liquid-filled vessel

The paper treats dynamical responses in an equivalent mechanical model for oscillations of a liquid in partially filled vessel under horizontal harmonic ground excitation. Such excitation may lead to hydraulic impacts. The liquid sloshing mass is modeled by equivalent pendulum, which can impact the vessel walls. Parameters of the equivalent pendulum for well-explored case of cylindrical vessels are used. The hydraulic impacts are modeled by high-power potential function. Conditions for internal resonances are formulated. A non-resonant behavior and dynamic response related to 3:1 internal resonance are explored. When the excitation amplitude exceeds certain critical value, the system exhibits multiple steady state solutions. Quasi-periodic solutions appear in relatively narrow range of parameters. Numerical continuation links between resonant regimes found asymptotically for small excitation amplitude, and high-amplitude responses with intensive impacts.