To solve the problem of parameter sloshing instability, the work aims to investigate the free-surface parameter instability characteristics of liquid-filled containers under vertical excitation, so as to provide a basis for the anti-sloshing safety design of liquid-filled containers. With a rigid two-dimensional square liquid-filled container as the research object, the damped Mathieu governing equation was derived based on the potential flow assumption for small-amplitude sloshing, and the stability analysis was conducted via the multi-scale perturbation method and energy growth coefficient method. Specifically, the perturbation method was adopted to resolve the instability boundaries of subharmonic and harmonic responses and reveal the suppression law of damping on unstable regions. The energy growth coefficient quantified the evolution intensity of instability from the perspective of perturbation energy, making up for the limitation that the perturbation method could only judge whether instability occurred. An experimental platform integrated with vibration excitation, laser liquid surface vibration measurement and acceleration acquisition systems was established. Experiments were carried out on a square cavity with a liquid filling height of 10 cm. The natural frequencies and damping ratios of the first four sloshing modes were measured. Sweep-frequency and variable-amplitude tests were performed to obtain instability boundaries and mode coexistence intervals, and the steady-state wave heights of each mode under excitation of 0.2g, 0.3g and 0.4g were tested. The equilibrium wave height of a single mode after instability rose with the increase of excitation acceleration. Under identical excitation levels, the sloshing amplitude of low-order subharmonics is much larger than that of high-order modes. The wave height of the first-order mode reaches 82.2% of the liquid filling height under 0.4g excitation, which poses the most prominent hazard. This paper combines two theoretical methods to realize complementary evaluation of instability boundary identification and sloshing intensity quantification, and can provide theoretical and experimental support for the safety design of liquid-filled containers against parametric sloshing.
Key words
liquid-filled containers /
perturbation method /
energy growth /
parameter sloshing test /
vertical excitation /
parameter instability
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