Non-linear dynamics of functionally graded electromagneto-active elastomer-based actuators

In soft robotics, precisely controlling localised point loads is made possible by electro-magneto-active polymers, including a thickness gradient. Understanding their non-linear oscillation patterns is crucial for optimising actuator design during time-dependent motion. The present work investigates the non-linear dynamic characteristics of soft actuators that are composed of functionally graded electro-magneto-active elastomers. This dynamic behaviour is examined while considering the Gent model and characterising the thickness gradient by a power-law distribution. The governing equation of motion of the actuator is derived using the Euler-Lagrange framework, allowing us to analyse the non-linear behaviour of the system. The equilibrium states of the actuator over a range of defined functionally graded parameters are obtained along with the time-history responses, Poincare plots, and phase diagrams to examine the stability, periodic behaviour, beating phenomena, and resonance characteristics of the system.