Effect of internal liquids on the vibrations of aerospace structures

摘要

The case of structures partially filled with liquids (propellants, cooling liquids, etc.) is very common and many industrial domains are interested in this issue, especially the aerospace industry (for aircrafts, liquid propelled launchers, satellites, etc.). We propose here a linearized formulation to deal with the vibrations of such fluid-structure coupled systems. As our main interest is for weakly damped fluid-structure problems, the study of the conservative (undamped) associated system will be at the center of the method, and the liquid will be considered in a first step as inviscid. Taking into account this assumption, the linearized local equations describing the coupling between a sloshing liquid and a deformable tank will be reminded. Once the variational formulation is established, the integral operators will be discretized by a classical Rayleigh-Ritz Finite Element approach. An a posteriori damping model for the liquid will be introduced in this formulation by assigning to each sloshing mode a damping coefficient that can be evaluated experimentally or numerically. To simplify the construction and the implementation of this sloshing liquid model in a CSM code, a representation of the fluid dynamical loads on the structure wall by an impedance mass matrix will be proposed. In the case where the tank own deformations can be neglected with respect to the global deformations of the main structure, the size of the liquid impedance model will be drastically reduced to ensure low CPU-time and memory consumptions. The versatility of this approach will be illustrated by an application example.