Interactions between commensurate parametric and forcing excitations in a system with clearance

The steady state forced response of a system with clearance subject to commensurate parametric and external forcing excitation is investigated analytically by considering a mechanical oscillator with time-varying stiffness and a dead zone type clearance non-linearity. A generalized multiple term harmonic balance procedure is utilized to find period-eta (eta T) solutions with eta greater than or equal to 1. Interactions between periodically time-varying stiffness and forcing functions are characterized in the primary resonance regimes where solutions are mostly of 1T type. Closed form expressions for impact criteria are derived for 1T solutions where possible. The effects of system parameters on eta T subharmonic resonances are examined and experimental results are included which conclusively demonstrate the existence of subharmonic resonances in geared systems. (C) 1996 Academic Press Limited