Modeling of the Heave and the Cushion Pressure of Air Cushion Landing System (ACLS): Chaotic Dynamics Investigation

A theoretical model for the dynamics behavior of an incompressible Air Cushion Landing System (ACLS) is introduced. In this model the incompressible Bernoulli’s equation and the Newton’s second law of motion are used to predict the dynamic behavior of the heave (vertical response) of the ACLS in both time and frequency domains. The mass flow rate inside the air cushion of this model is assumed to be constant. The self excited response for the heave and the cushion pressure of the ACLS are calculated. In this study, the dimensionless mass flow rate and the dimensionless skirt of the ACLS’s skirt are the only parameters which are considered to be investigated to control the steady state behavior of the oscillatory motion of the ACLS. The equations of motion of the proposed nonlinear model are solved numerically using a code written on the Matlab software which is based on the Runge Kutta numerical integration method. The chaotic behavior of the heave motion and cushion pressure dynamics are investigated with the aid of the Fourier analysis and the Poincaré map. Periodic behavior is noticed in the vertical motion; on the other hand a chaotic behavior is manifest in the pressure inside the cushion volume of the ACLS. This model will help designers of the ACLS to understand the dynamics behavior of this system in order to redesign such system so that the violent oscillatory self excited motion can be reduced or eliminated.