Coupled response of liquid in a rigid cylindrical container equipped with an elastic annular baffle

Abstract

The coupled dynamic response of liquid partially filled in a rigid cylindrical container equipped with an elastic baffle under lateral excitation has been studied. Firstly, the liquid domain is divided into four simple sub-domains so that the non-convex liquid domain changes to four convex sub-domains. Therefore, the liquid velocity potential in each liquid sub-domain has continuous boundary conditions of class C1. Based on the superposition principle, the analytical solution of the liquid velocity potential corresponding to each liquid sub-domain is obtained by means of the method of separation of variables. Then, the wet mode of the elastic annular baffle is expressed in terms of the dry-modal functions. The free surface wave equation, the interface equations and the coupled liquid-baffle vibration equations are all expressed in terms of the Fourier series along the liquid height and the Bessel series in the radial direction, respectively. The orthogonality among the coupled modes of the system is demonstrated. Finally, the total velocity potential function under lateral excitation is taken as the sum of the container potential function and the liquid perturbed potential function. The coupled dynamic response equation of the liquid-baffle system is established by combining the free surface wave equation and the governing vibration equation of the baffle. The surface wave height, the hydrodynamic pressure distribution, the resultant hydrodynamic force and moment for a container subjected to lateral excitations are discussed in detail.