Synchronous Hopf-Bifurcation and Damping Osmosis Phenomena of Liquid-Spacecraft Coupled System

Abstract

Nonlinear dynamics of a liquid ‐spacecraft coupled system are investigated. The spacecraft is modeled on a spring‐damper‐masssystem, and the liquid is insidea rigid cylindrical tank attached to the masswith and without an annular bafe e. A group of nonlinear dynamic differential equations is derived by Lagrange’ s method and symbolic operations using the software Mathematica . The symmetry of the equations verie es their correctness. Numerical simulations and amplitude-frequency response analyses show that the so-called synchronous Hopf bifurcation takes place in the nonplanar sloshing modes of the system without a bafe e. Also, the bafe e and the damper have different effects on the damping behavior of the vibration and the sloshing, so that the concept of damping osmosis in nonlinear coupled systems is describled.