Parameter design of a liquid-filled sloshing system

The nonlinear governing equations of the liquid sloshing modals in a cylindrical storage tank are established. Through analytical analysis, the analytical expressions of the solutions of this kind of system are obtained. With different parameters, the dynamical behaviors of the solutions are different from the trivial ones. To prevent system instability, two selection principles that the stiffness equations are positive-definite and the nonlinear terms of the system are not regenerative elements are given. Meanwhile, numerical simulations are also given, which confirm the analytical results. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)