Parametric resonance of liquid sloshing in partially filled spacecraft tanks during the powered-flight phase of rocket

Liquid sloshing in partially filled spacecraft tanks during the powered-flight phase of rocket influences greatly the sensitive elements onboard by means of the sloshing frequencies and total sloshing forces. However, little research on the nonlinear parametric sloshing for this case can be found in the literature. In this paper, the equivalent pendulum model was incorporated into the spacecraft system to represent the liquid propellant sloshing motion. Besides, the dynamic model of liquid sloshing under both lateral and longitudinal excitations was developed by Lagrangian method. The nonlinear effect and the damping effect of liquid sloshing were accommodated in this model. Then, parametric resonance analysis of small amplitude sloshing was studied by the Floquet theory to plot the stability diagrams for different sloshing damping. The research emphasis of this paper was parametric resonance analyses on the nonlinear characteristics of relatively large amplitude sloshing under soft and hard excitations, which were carried out respectively by multiple scales method. The analytical and numerical results were presented in the forms of phase diagrams, frequency-response curves as well as time histories of sloshing motion and sloshing force to illustrate the effects of principal parametric resonance, sub-resonance and non-resonance conditions on the sloshing motion separately. The investigations in this paper provided an effective way to reveal the nonlinear parametric resonance of liquid sloshing in partially filled spacecraft.