Nonlinear dynamics of a parametrically excited pneumatic artificial muscle (PAM) actuator with simultaneous resonance condition

Abstract

In this present work, the pneumatic artificial muscle is modelled as a single degree of freedom system and the governing nonlinear equation of motion has been derived to study the responses of the system under simultaneous simple and principal parametric resonance conditions. The equation has been developed considering the pneumatic muscle force as a function of the static and the time varying pressure, dimensions and material properties of the artificial muscle. The second order method of multiple scales has been used to find the approximate solutions and to study the dynamic stability and bifurcations of the system. The influences of the various system parameters in the amplitude for the muscle have also been studied with the help time responses, regions of parametric instability and frequency responses. The applications of the present study are illustrated through numerical examples. This work will help the designer or researchers working in this field to determine the safe operating range of the system parameters for different applications of pneumatic artificial muscle.