Subharmonic periodic solutions of order ( 1
2 , 1
4 ) to a weakly second order ordinary differential
equation which governed the motion of a micro-dynamical system are studied analytically.
Applying the method of multiple scales, we derive the modulation equation in the amplitude and
the phase of each type of periodic solutions. Determine the steady-state solutions (fixed-points
of the modulation equation). Obtained the frequency-response equation (The relation between
the amplitude and the detuning parameter and other parameter in the differential equation).
Stability analysis of the steady-state solutions is given. Numerical study of the frequency-response
equation are carried out. The results are presented in a group of Figures in which solid (dashed)
curves indicated stable (unstable) preiodic solutions. |
