Subharmonic resonances of a mechanical oscillator with periodically time-varying, piecewise-nonlinear stiffness

The subharmonic (period-η, η>1) motions of a piecewise-nonlinear (PN) mechanical oscillator having parametric and external excitations are investigated. The system is formed by a viscously damped, single-degree-of-freedom oscillator subjected to a periodically time-varying, PN stiffness defined by a clearance surrounded by continuous forms of nonlinearity. A multiterm harmonic balance formulation in conjunction with discrete Fourier transforms is used to determine steady-state period-η motions of the system near the parametric instability regions. The accuracy of analytical solutions is verified through a comparison with direct numerical integration results. A parametric study is also presented to demonstrate the combined influence of a clearance and of cubic nonlinearities on period-η motions within typical ranges of system and excitation parameters.