Nonlinear dynamic response of a base-excited SDOF oscillator with double-side unilateral constraints

Abstract

The aim of this paper was to study the dynamic response of a single-degree-of-freedom (SDOF) oscillator exited by a base acceleration and constrained by two unilateral constraints (bumpers). The coupled equations of motion are formulated in dimensional and dimensionless form for the case in which both SDOF oscillator and bumpers exhibit a nonlinear behavior. Two possible states characterize the system’s response: flight, when the mass of the oscillator is not in contact with the bumper, and contact, when the mass touches the bumper. When the system is in the flight state, the independent time evolution of the bumpers’ response is also considered in equations of motion. In the numerical investigations, a viscoelastic SDOF oscillator and viscoelastic perfectly plastic bumpers subjected to a harmonic base excitation are considered. First, the transient versus steady-state dynamic response is considered, and afterward the only steady-state dynamic response is studied by means of pseudo-resonance curves of maximum absolute acceleration and relative displacement excursion of the SDOF oscillator. Furthermore, the continuation technique is applied in some cases in order to highlight in the system’s dynamic response hysteresis ranges, jumps between multi-periodic orbits, and super-harmonics. The dynamic analysis with and without bumpers is compared to observe how unilateral constraints modify the dynamic response of the SDOF oscillator with respect to the absence of bumpers and when their presence may be beneficial with respect to response mitigation.