Response Characteristics of Systems With Parametric Excitation Through Damping and Stiffness

Abstract Floquet theory is combined with harmonic balance to study parametrically excited systems with combination of both time varying damping and stiffness. An approximated solution having an exponential part with unknown exponents and a periodic term consisting of a truncated Fourier series is considered. When applied to a system with parametric damping and stiffness the analysis shows that combination of parametric damping and stiffness alters stability characteristics, particularly in the primary and superharmonic instabilities comparing to the system with only parametric damping or stiffness. 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 parametric damping case.