PERIOD-1 MOTIONS IN A TWO-DEGREE-OF-FREEDOM NONLINEAR OSCILLATOR WITH PERIODIC EXCITATION

In this paper, analytical solutions for period-1 motions in a periodically forced, two-degrees-of-freedom system with a nonlinear spring are developed. The stability and bifurcation of the periodic motions are completed by the eigenvalue analysis. Both symmetric and asymmetric periodic motions are found in the system. Analytical solutions of both stable and unstable period-1 are presented. Finally, numerical simulations of stable and unstable motions in the two degrees of freedom systems are presented. The harmonic amplitude spectrums show the harmonic effects on periodic motions, and the corresponding accuracy of approximate analytical solutions can be observed.