Nonlinear Dynamics Study of Giant Magnetostrictive Actuators with Fractional Damping

Abstract

Since the structural mechanics of the super magnetostrictive actuator (GMA) system involves problems related to viscoelastic damping materials, the fractional order is more accurate than the integer order calculus to characterize the viscoelastic features in the structure. In order to further investigate the intrinsic mechanism and dynamical characteristics of the GMA dynamical system, the dynamical equations of the nonlinear GMA system containing fractional damping terms are established and the main resonance of the system is analyzed using the averaging method. The mechanism of the influence of some parameters on the GMA system is analyzed by MATLAB numerical simulation to study the bifurcation and chaotic motion phenomena of the system from the qualitative and quantitative perspectives. The results show that the fractional damping coefficient, external excitation amplitude and fractional order have significant effects on the amplitude-frequency characteristics of the system; the fractional order has a greater influence on the bifurcation and chaotic behavior of the system; the dynamic behavior of the system caused by the change of external excitation amplitude and fractional damping coefficient at different damping orders is similar but the chaotic region is different.

Keywords

• giant magnetostrictive actuator
• fractional calculus
• bifurcation and chaotic characteristics
• qualitative and quantitative analysis