Frequency Response of a Nonlinear Pneumatic System

This paper studies the dynamic behavior of a pneumatic chamber connected to a reservoir through an orifice and to a linear mechanical system. In this paper, we focus our attention mainly on the nonlinearity associated with mass flow rate through the orifice and its effect on the overall system behavior. Nonlinearities induced by the friction and gas compressibility are also considered. Using the method of harmonic balance, we reduce a difficult mathematical formulation of this nonlinear pneumatic system to a simple nonlinear governing equation and a set of algebraic equations which yield frequency response easily at the first, second, and third harmonics. An excellent agreement between the method of harmonic balance and numerical integration has been found. Results obtained using a quasi-linear model are also given.