Theoretical analysis of soft impact oscillator periodic motions with small number of impacts in the motion period

摘要

Single degree of freedom (SDOF) system with piecewise constant characteristics in stiffness and viscous damping (Kelvin-Voigt model) is analysed. A mass vibrating across the boundary between media with different mechanical properties is excited by harmonic force. Analytically derived set of transcendental equations is solved by the quasi-Newton method. A stable crossing of a grazing boundary and existence of two stable periodic motion regimes is confirmed. Presented results for basic stable periodic motion with one impact in a motion period obtained by analytical solution and numerical simulations are in a good agreement.