Hydrodynamic impact of a system with a single elastic mode I : theory and generalized solution with an application to an elastic airframe

Solutions of impact of a rigid prismatic float connected by a massless spring to a rigid upper mass are presented. The solutions are based on hydrodynamic theory which has been experimentally confirmed for a rigid structure. Equations are given for defining the spring constant and the ratio of the sprung mass to the lower mass so that the two-mass system provides representation of the fundamental mode of an airplane wing. The forces calculated are more accurate than the forces which would be predicted for a rigid airframe since the effect of the fundamental mode on the hydrodynamic force is taken into account. In a comparison of the theoretical data with data for a severe flight-test landing impact, the effect of the fundamental mode on the hydrodynamic force is considered and response data are compared with experimental data.