Vibration analysis of magnetostrictive laminated cantilever actuator

Differential equation to analyze the vibration problem of a magnetostrictive laminated cantilever with thin-film actuator was derived by Hamilton's variational principle, using the nonlinear constitutive relation of magnetostrictive material. The free vibration and forced vibration of magnetostrictive laminated cantilever with thin-film were analyzed by means of the methods of separation variables and the analytic solution of ordinary differential equations. The numerical example shows that the calculation results of this paper are in good agreement with finite element results, which evidences validity of the theoretical model and solution method, and the effect of the geometric parameters and material parameters on natural frequency of the laminated beam was discussed. The deflection response of beam excited by a periodic input magnetic field was also analyzed, which present the dynamic characteristic of frequency multiplying effect. The deflection response of the cantilever beam excited by a periodic input magnetic field was also analyzed, which presented the double frequency effect of dynamic characteristics.