Response of a nonlinear two-degree-of-freedom system subjected to an impact loading

Abstract

The solution of the equations of motion of an aircraft fuselage-landing gear configuration during landings is of interest to the designer who must predict the landing loads which an airplane encounters in service. In general such solutions are difficult because of the highly nonlinear characteristics of the oleo-pneumatic shock strut which couples the lower mass of the landing gear to the fuselage.

In the past, attempts to obtain solutions by linearization of these shock strut characteristics have resulted in unrealistic predictions of landing gear motions. Therefore, it has been necessary to carry out most of the theoretical analysis associated with landing gears by means of numerical integration procedures. These numerical methods are tedious, and as a result a large portion of design work has been carried out by means of trial and error drop testing of a system of masses representative of an airplane and landing gear. This in turn has proved to be time consuming and expensive.

This paper presents a method for obtaining an analytical solution of the equations of motion for a basically nonlinear system which closely resembles an actual airplane and landing gear configuration. The nonlinear system considered has two degrees of freedom and is composed of a large mass representative of the fuselage-wing combination connected by an oleo-pneumatic shock strut to a wheel. The shock strut is assumed to have velocity-squared hydraulic damping and coulomb friction forces on the strut bearings. The nonlinear spring characteristic of the tire is represented by a sectionally linear spring.

In the first part of this paper the equations of motion for this nonlinear system are derived making use of a few simplifications which previous papers have shown to be justified. Also, the degree to which these assumptions limit the results is discussed. Next these equations of motion are solved in analytical form by a method which may be called "equivalent non linearisation." It is shown that this solution is exact only for a specific combination of impact parameters, but that for a wide range of parameters the solution describes the motion of the system adequately for design purposes. Finally, a few analytical solutions are compared with solutions obtained by numerical integration methods; and the results are compared with experimental data for a typical impact.