Response Characteristics of Systems With Two-Harmonic Parametric Excitation

Floquet theory is combined with harmonic balance to study parametrically excited systems with two harmonics of excitation, where the second harmonic has twice the frequency of the first one. An approximated solution composed of an exponential part with unknown exponents and a periodic term consisting of a truncated Fourier series is considered. When applied to a two-harmonic Mathieu equation the analysis shows that the second harmonic alters stability characteristics, particularly in the primary and superharmonic instabilities. We also look at the initial conditions response and its frequency content. The second excitation harmonic in the system with parametric damping is seen to disrupt the coexistence phenomenon which is observed in the single-harmonic case.