Study of the effects of fractional order and damping coefficient on the dynamics of giant magnetostrictive actuators.

The nonlinearity between input current and output displacement in giant magnetostrictive actuator (GMA) systems seriously destabilizes the system, and the inaccuracy of existing integer-order differential modeling makes it difficult to predict and control the output of the system. Therefore, the study of more accurate GMA nonlinear dynamical behavior is of theoretical guidance for system scheme design. Firstly, based on the working principle of GMA and Caputo's fractional-order differential theory, a GMA fractional nonlinear dynamics model is developed; secondly, the amplitude–frequency response equations and stability conditions at the main resonance of the system are solved by applying the averaging method; finally, the effects of fractional order and damping coefficients on the nonlinear dynamics behavior of the system are investigated by means of the power series method. The conclusions of the study serve for the scheme design of the system as well as the stability analysis of the system. [ABSTRACT FROM AUTHOR]