This paper investigates bifurcation and combination re sonance of the hysteretic nonlinear system with three-frequency excitation by Multi-scale Method.

As an example, an approximate analytic solution of nonlinear vibration for a plate strip in lateral magnetic field is obtained by the multi-scale method.

Then, the analytic solution of the geometrical nonlinear vibration system and the frequency-response properties of the actuator were analyzed by using multi-scale method.