Investigation of the heave dynamics of Air Cushion Vehicles (ACV): parametric and chaotic studies

Abstract

A highly non-linear model for the dynamics behavior of Air Cushion Vehicles (ACV) is presented. In this model the compressible Bernoulli's equation, the Newton's second law of motion, and the nonlinear isentropic relations are used to predict the dynamics behavior of only the vertical response of the ACV in both time and frequency domains. In this paper the mass flow rate inside the air cushion volume of the ACV is maintained constant. In order to assist in the design process of such vehicles, the self excited response and the cushion pressure of the ACV are calculated to understand the dynamic behavior of these vehicles. It is shown in this study that the mass flow rate and the length of the vehicle's skirt are the most significant parameters which control the steady state behavior of the self excited oscillations of the ACV. An equation to predict the transient time of the oscillatory response or the settling time in terms of the system parameters is developed. Based on the developed equations, the optimum parameters of the ACV that lead to minimum settling time are obtained. Also, the chaotic behavior of the heave dynamics is investigated with the aid of the Fourier analysis and the Poincaré map. It is shown that the heave dynamics does not manifest any chaotic behavior within the selected range of the control parameters. However, the cushion pressure manifested some chaotic behavior at some values of the skirt length and mass flow rate.

Chaotic Assessment of the Heave and Pitch Dynamics Motions of Air Cushion Vehicles

“…This study is a continuation of the study in references [16,22], where only heave motion was considered in modelling the ACV. Obviously, adding the pitch degree of freedom to the current study increases the complexity of the problem.…”

“…It should be noted that the cushion pressure is assumed homogenous throughout the base of the ACV. The change of the cushion pressure with time is derived in a previous work [22] of to be:…”

“…where d is the ACV vertical distance from the ground. The mass flow rate exiting in the cushion out m  is derived by applying the compressible Bernoulli's equation, and is given by [22] as:…”

Chaotic Assessment of the Heave and Pitch Dynamics Motions of Air Cushion Vehicles

“…It should be noted that cushion pressure is assumed homogenous throughout the base of the ACV as shown in Figure ( 1) (Bliault 2000). The change of cushion pressure with time is derived in a previous work (Sowayan et al (2013)) of the author to be:…”

“…The cushion volume V is defined as V A z d = × + ( ) , where z is the vertical distance of the vehicle, and d is the ACV vertical distance from the ground. The mass flow rate exiting the cushion m out is derived by applying the compressible Bernoulli's equation, and is given by Sowayan et al (2013) as:…”