Quasi-Hamiltonian principle of liquid-filled elastic body dynamics

Liquid-filled elastic body dynamics is an important branch of fluid-solid coupling mechanics. It deals with the study of motion of a body and the liquid contained in the body under the interaction between the two, for example, a liquid-filled satellite, a fuel tank of an airplane, etc. The research on liquid-filled elastic body dynamics is usually done by the variational method since the method has a feature of treating things as a whole. Considering the elastic motion of the liquid-filled body and the surface tension effect on the liquid-gas interface, liquid-solid interface and gas-solid interface, the present paper establishes a quasi-Hamiltonian variational principle for the above-mentioned system. After finding the stationary-value conditions of its functional obtained, a complete system of governing equations consisting of the stationary value conditions, preconditions and constraint conditions is established, and then the equations are reduced into some known ones in a special case.